About

This site is currently hosting

updates on my mathematical research;
expository articles (such as my articles for the Princeton Companion to Mathematics, or for the tricks wiki);
discussion of open problems;
talks that I have given or attended (such as the Distinguished Lectures Series at UCLA);
my advice on mathematical careers and mathematical writing;
information about my books and applets;
my lecture notes on ergodic theory, on the Poincaré conjecture, on random matrices, on graduate real analysis (245A, 245B and 245C) and introductory graduate probability (275A), on Hilbert’s fifth problem, on expansion in finite simple groups of Lie type, on higher order Fourier analysis, and on analytic number theory;
and various other topics, usually related to mathematics.

While most of the posts are aimed at those with a graduate maths background, I will also occasionally have a number of non-technical posts aimed at a lay mathematical audience. My selection of topics is guided by my own personal taste; I do not take requests for specific topics to post about on this blog.

I welcome comments from people with all kinds of mathematical backgrounds and levels of expertise; my only requests are that the discussions are kept constructive, polite, and at least tangentially relevant to the topic at hand. Comments which are spam, self-promoting, off-topic, or otherwise not fulfilling the above requests will be summarily deleted; repeated offenders in this regard may be subject to blocking. In particular, comments devoted primarily to promoting one’s own research are subject to deletion. Also, comments which essentially duplicate previous comments may also be deleted, or used to replace the previous comment, as appropriate. Finally, comments whose sole purpose is to solicit an answer to a homework problem are discouraged, and will be deleted if they are unlikely to lead to any discussion of wider interest. (However, questions inspired by a homework problem, for instance inquiring as to further connections between two mathematical topics connected by such a problem, or questions centred on a very specific technical point in the solution of that problem, are welcome.) Of course, I will not be able to personally respond to all the comments made on this blog.

I have enabled the ability to rate comments on this blog. However, this rating system is unregulated and should not be taken as any sort of official evaluation of one’s comments. In the interest of constructive criticism, negative ratings should be used sparingly. To discuss the ratings system, please visit this thread.

Any discussion, feedback, questions or suggestions not related to one of these topics can be placed as a comment to this “About” page, or at my open thread. Comments about formatting and presentation can be made at this page.

See also the Google+/Google Buzz feed that complements this blog; details of this feed are available here.

Terence Tao

[Update, Mar 31 2007: Opened this page to comments.]

— Some technical remarks —

WordPress has the ability to insert LaTeX math code (e.g. $\int_{-\infty}^\infty e^{-\pi x^2}\ dx = 1$ ) into both posts and comments. The format for this is “$latex [Your LaTeX code]$” (without typing the square brackets). See this announcement for details. Note that LaTeX macros and environments are not supported, similarly, double dollar signs $$ do not create LaTeX displays (one can use \displaystyle to get an approximation of these displays, though.) Also, line breaks are not allowed within a LaTeX code.

There used to be a number of quirks with the WordPress LaTeX plugin, but they have now largely been fixed. If you find any problems, please report them at this page.

WordPress also supports a certain amount of HTML. As a consequence, be careful with using the < and > signs in a comment, they may be misinterpreted as HTML tags! You can use < and > instead. (Inside of a LaTeX environment, you can use \lt and \gt.)

In case a comment really gets mangled up by formatting errors, you can contact me and I can try to manually correct it.

I have heard that it is possible to configure wordpress so that comments can be previewed; if anyone has any specific knowledge on how to implement that feature, I would appreciate knowing about it. [Removed, Apr 8 2007, in response to comments.]

If a comment does not immediately appear after you submit it, it may have been accidentally flagged as spam (this in particular can happen for a post with an excessive number of links). In that case, please contact me and I will de-flag it.

I do not have PDF copies of my posts. However, the “print preview” feature in your browser should convert the post to a format which is suitable for conversion to PDF, with the sidebar and header removed. Also, at the end of every year, I convert many of my blog posts into a book format; see this page.

I have occasionally been asked for the formatting I use for my own posts. I use the Tarski theme with a modified CSS, in order to do things such as boxed theorems. (To use the CSS, one needs to purchase a CSS upgrade.) I also use Luca Trevisan’s LaTeX to WordPress converter to write the more mathematically intensive posts.

— Copyright etc. —

Readers are welcome to copy, link to, quote from, or translate reasonable portions of the content of this blog (e.g. a single article) into other media, though for items longer than one or two paragraphs, I would appreciate it if a reference or citation to the URL that the content originates from is provided. If you wish to copy a significantly larger fraction of the content (e.g. an entire series of articles), please contact me about it first.

175 comments

Comments feed for this article

8 April, 2007 at 8:21 am

thomas1111

About prewiewing comments (which I was interested in too): this feature is not available at wordpress.com for security reasons, according to this answer of a wordpress.com person.

On the other hand wordpress.org releases software for people to run a blog either on their own server or on recommended hosts. In both cases this requires some unix/linux administrator skills, especially on security issues in the first case.

In that setting, previewing comments is then possible using plugins: there are many possibilities, for example this one has live preview. Besides, $\LaTeX$ display in the main posts is also available via this pluging (requires apparently a small manual change in the code to enable LaTeX in comments too). But I’m not sure how the LaTeX then interacts with comment preview, probably some further hacking is required (which almost means back to square one as far as I’m concerned, so I gave up on that).

22 August, 2007 at 6:34 pm

Gary

Dear Prof Tao,

There is a 9 years old, Hong Kong talented kid, got A in GSE A level. Very talented in Math, but probably no HK university accept him.

Do you have any suggestion to him? Since you are a genius as well.

http://hkstandard.com.hk/news_detail.asp?we_cat=4&art_id=51052&sid=14893640&con_type=1&d_str=20070811

7 February, 2014 at 2:30 pm

Ronnie Brown

I read in “Men of Mathematics” that Cauchy’s parents asked for advice and it was suggested that he should learn his own language well, and that there was plenty of time for mathematics. I would also argue that he should learn some sport in a competitive way, and why not music, drawing, painting, acting, reading, …, whatever is convenient and congenial, and also encourages social contact. Some or all of these activities are likely to enrich a life, and also to see mathematics in context.

22 August, 2007 at 8:49 pm

Terence Tao

It depends on many, many factors, including the development of the child in both academic and non-academic areas, and the situation of the parents and the university, and so forth. The one thing I would say though that going to university at such a young age purely for the chance to hold some sort of record is a very bad idea; these records ultimately don’t mean very much in the long run, and if the child is not ready it can actually be harmful to pursue these things. But if the child has already gotten everything he can from the high school level (and this includes social development as well as academic), and is eager for more, and the parents and university are both sufficiently flexible, then it might be something to seriously consider. See my page

https://terrytao.wordpress.com/career-advice/advice-on-gifted-education/

for more thoughts in these directions.

6 October, 2007 at 7:26 am

Jonathan Yedidia

Dear Prof. Tao,
You have a great blog, but could you please turn off the terrible Snap preview feature? Besides being incredibly annoying, it sometimes slows down the loading of your pages to unbearable lengths (I can tell because my browser stalls while trying to load pages from ixnp.com, which is Snap preview.) You can remove the Snap preview feature by going to the wordpress dashboard, and then looking under Presentation, and “Extras”.

6 October, 2007 at 9:00 am

Terence Tao

Hmm. I never noticed the loading times myself, but I could see that it would be a concern. I’ve disabled it for now.

6 October, 2007 at 6:31 pm

Jonathan Yedidia

Thank you! I think that most of the time, if you have a broadband connection, the delay is not noticeable, although I understand it is a problem for those with dial-up connections. Occasionally though (like last night for me) if there is a problem with the Snap Preview servers, your blog can become completely unreachable, even for those of us with good connections, while other wordpress.com blogs that have turned Snap Preview off are reachable. Given that the feature probably annoys more people than it helps even when it works, I can’t understand why wordpress.com turned it on by default.

6 October, 2007 at 8:48 pm

James Cook

I have always liked the Snap Preview feature, and have never experienced any problems with it, so I hope the disabling is temporary. It is especially useful for mathematics blogs such as this, since it allows one to quickly review the definition of a term, for example, without having to leave the site or open a new window.

6 December, 2007 at 2:49 am

Caroline

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11 January, 2008 at 12:09 pm

Anton

Dear Prof. Tao,
Could you, please, recommend me some French blogs about mathematics? I find it really useful to train my language skills.
Thank you in advance,
Anton.

25 February, 2008 at 8:09 am

Nishu

I’ve disabled it for now.

it still hows snap previews to me …
And more so a mathematics site referring to other mathematical resource dont need to show preview of site visitors are going to…Even in preview what a visitor can see will be mostly text.. so doesnt make much difference

25 February, 2008 at 9:42 am

Terence Tao

Dear Nishu,

After some discussion (see https://terrytao.wordpress.com/2007/10/16/snap-preview/ ), I decided to re-enable snap preview for Wikipedia articles but disable them for others (though I am not able to prevent all such previews from showing up, for various technical reasons).

4 September, 2011 at 6:33 am

Luqing Ye

Dear Pro.Tao
I see that you like to add a box to your theorem so that the theorem can be separated from other material.I search for so long a time on the internet but I can’t find how to do that.Could you please give me a hint?Do you make use of css to manage that? I don’t know how to do that because I know little about css.

28 February, 2008 at 5:49 am

Anonymous

Hi Prof Tao,

I was doing some work on Prime numbers(specifically Twin Primes) and found a strange (seems like not so obvious) property amongst the Twin Primes. I have checked it just to a small number of Twin Prime Pairs (all the Twin Primes occouring upto 2.7 x 10^7) and that holds well within that limit with no exception.

It is a method for generating of the N+1th Twin Prime Pair using the previous N Twin Prime Pairs. I am able to generate a set of Pairs one of which in the N+1th Twin Prime Pair.

Have checked this for all the Twin Primes up to 2.7 x 10^7 and it holds with no exception.

If Proven that it is always Possible to generate the N+1th Twin Prime Pair ALWAYS using the previous N Twin Primes Pairs then it will also Prove the Twin Prime Conjecture.

But as this is currently a conjecture so am not sure what to do to bring it to the Attention of the Maths community. Can you please guide me on this.

Thanks in Advance

An Amateur (Can’t call Myself a Mathematician)

16 March, 2008 at 9:39 am

Vishal

Dear Prof Tao,

This is a rather silly question, but how do you put a box around some text in your posts?

21 March, 2008 at 9:27 am

anonymous

Dear Professor Tao,

Another silly question: I personally find it very annoying to have to type “$ latex … $” to use latex in wordpress, rather than just “$ … $”. But it seems like you have become quite adept at this. Did you just get used to typing the extra “latex”, or perhaps do you use another program to replace all “$ … $”s with “$ latex … $”s?

Response to above comment: probably < blockquote> < /blockquote>

Thank you

21 March, 2008 at 11:13 am

Vishal

Dear anonymous,

I type “$ latex $” first, then copy it and paste it wherever/whenever I need it while writing posts. You can insert your Latex code inside “$latex $” every time you paste it. I would certainly be interested in knowing if there is a more efficient way of doing the same!

The blockquote tag ideally should work but it only places the text in a block without the border. I want the border to be visible.

Cheers!

21 March, 2008 at 1:11 pm

Terence Tao

Dear Vishal,

I use blockquote but I have modified the CSS of the Tarski theme to make blockquotes in boxes instead of indented and italicised. The precise CSS I used (which I adapted from someone else’s CSS file) is

blockquote {
border-top:1px solid #000;
border-bottom:1px solid #000;
border-left:1px solid #000;
border-right:1px solid #000;
background:#FFFFFF;
color:#000;
margin:25px 25px 15px;
padding:5px 10px 0;
}

As for the $latex $ thing, I just type it in by hand, and it has become fairly automatic to me at this point; it turns out not to be the dominant contributing cost for me to the time it takes to write one of these posts.

24 April, 2008 at 8:24 pm

utgalois4234

Hi Professor Tau,

I was curious how you produced Theorem/Proof/Equation type environments in your lecture posts. I initially just tried rather naively typing something like

$\begin{equation}\int_\mathbb{R}fd\mu<\infty\end{equation}$ ,

but of course this doesn’t work. Any suggestions would be greatly appreciated. Thanks very much.

24 April, 2008 at 8:42 pm

Terence Tao

Dear utgalois,

I don’t believe that wordpress supports LaTeX environments; I use HTML markup (boldface, blockquote, etc.) instead to simulate them instead. (It means that I have to number theorems etc. by hand, but that’s only a minor inconvenience.)

25 April, 2008 at 2:33 pm

louisyangliu

Dear Prof. Tao,

In LaTex environment, as we know, we can use $$…$$ to make equations to the center of a line, and you can also make them in wordpress very prettily and nicely. I am curious how to make them. Thanks.

25 April, 2008 at 4:22 pm

Terence Tao

Dear Louis,

One can simulate a display environment by centering a latex string (in HTML), and using \displaystyle to make the formatting of large symbols (e.g. \sum, \prod, \int, etc.) come out nicely. It’s a hack, but it works.

One thing I haven’t figured out how to do nicely, though, is to how to align multiple equations other than manually inserting spacing. Also, I don’t know how to right-justify equation numbers, which is a little annoying.

26 April, 2008 at 2:23 am

Américo Tavares

Dear Professor Tao,

Would you please give me a hint how do you manage to insert here diagrams like the one in your post https://terrytao.wordpress.com/2007/09/14/pythagoras-theorem/ ?

As a matter of fact I have in mind an even more basic question, that is, where can I find information on constructing geometric figures by means of LaTeX?

26 April, 2008 at 3:46 am

Anonymous

Hai ,Mr Tao, I am currently pursuing an undergraduate course in India, i would
like to know how to solve intricate(complex) math problems, i want to know how could solve complex problems so well,do you follow any specific problem solving strategies,how to become an excellent problem solver like you are there any specific character traits in order to become one??? please answer these queries Mr Tao i would be extremely grateful to you, thanking you
Your admirer….

26 April, 2008 at 10:59 am

Indian

Mr TAO ,if u read the above Anonymous query and yet didn’t answer it, you might be thinking i am some sort of an impostor ,please don’t think like that, i am not an impostor or some sort of a prankster,please answer the above query,maybe it isn’t related to mathematics in some way but it is very much related to problem solving as a whole and this includes multitudinous disciplines like Mathematics,Physics etc.

Can you give me some tips on how to solve tough problems,if you read this query and yet didn’t like to answer you can tell me (by commenting here) i would not ask this sort of query again, i want an answer from an excellent problem solver like you ,please do answer my query if you like to….

Please don’t think i am some kind of a fraud or prankster ,i am genuine and the reason for not me including my complete details is that i am ab it insecure and i am concerned about my privacy.. Thanking you,

Your humble and sincere admirer

26 April, 2008 at 2:16 pm

Terence Tao

Dear Indian,

Please see

https://terrytao.wordpress.com/career-advice/solving-mathematical-problems/

for my thoughts on these sorts of issues.

27 April, 2008 at 12:41 am

tumur

Dear Américo Tavares,

There are packages called texdraw, and pstricks. If you use these packages you have to draw line by line so to speak, so it takes much time. So normally you would use some external software to produce a picture file and include into a tex document. Adobe Illustrator is excellent, and a cheaper but simpler alternative would be xfig. Also there are gimp and Photoshop of course.

27 April, 2008 at 12:47 am

tumur

There are also specialized applications like geomac that comes handy when you do plane geometry constructions.

27 April, 2008 at 2:37 am

Américo Tavares

Dear tumur,

Many thanks for your information.

I will look for the packages/applications you have mentioned.

Currently I’m using Scientific Work Place (Scientific Word, Scientific Viewer, Note Book) that does not allow me to produce the LaTeX code of geometry constructions, only plain LaTeX or TeX documents, with plots inserted if needed, then generates a dvi file that can be converted to the pdf format.

27 April, 2008 at 6:01 pm

damidami

Dear prof. Tao,
I don’t know where to ask this but, how do you make the latex formulas look “grayer” (brighter) and not black.
If you don’t understand what I mean you could look at my blog http://analisis2.wordpress.com, my formulas can’t be easily separated from the text, visually speaking.
I’m just starting this blog for my students, so I have a lot to learn on to how to present the information.

Thanks a lot,
Damián.

27 April, 2008 at 6:21 pm

Terence Tao

Dear damidami,

I didn’t make the latex grayer; I made the text darker (a trick I learned from Carl Brannen). This was accomplished by modifying the CSS (you need to purchase an upgrade for this). The precise CSS I used was

body {
background:#fff;
color:#000;
}

It is possible to change the colour of LaTeX displays too, see

http://faq.wordpress.com/2007/02/18/can-i-put-math-or-equations-in-my-posts/

but it is somewhat cumbersome (there appears to be no way to permanently change the default colour).

29 April, 2008 at 11:07 am

Indian

Dear Mr Tao,i would like to know how do you get such good solutions to intricate problems,do you rely on your intuition or is it just through brute mental power????

4 May, 2008 at 10:16 pm

Rolando

I am extremely interested in these posts and I would like to copy them into a LaTex file, but when I paste the $ signs are removed. Is there a better way than manually adding in the $ signs?

5 May, 2008 at 1:09 am

John Armstrong

Rolando, it should be short work with a regular expression parser like perl. Take the page source — for instance

WordPress has the ability to insert LaTeX math displays (e.g. <img src='http://l.wordpress.com/latex.php?latex=%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty+e%5E%7B-%5Cpi+x%5E2%7D%5C+dx+%3D+1&bg=ffffff&fg=545454&s=0' alt='\int_{-\infty}^\infty e^{-\pi x^2}\ dx = 1' title='\int_{-\infty}^\infty e^{-\pi x^2}\ dx = 1' class='latex' />) into both posts and comments.

Notice that the LaTeX code itself is in the source field of the img tag. You just have to replace what goes before and after with $, and replace all the URL escape codes with the actual symbols (%5C = \).

9 July, 2008 at 8:44 am

JOE

Dear Dr Tao,

Hello Dr Tao. =) I will be pursuing a math undergraduate degree at Imperial College soon and would like to hear some advice from you.

Currently, some prospective UK university math students have a special qualification called STEP (Sixth Term Examination Paper) aside from the usual A levels Math and Further Math. Apparently, having this propels one to have utmost advantage at university as one will need to prepare rigorously for it. (I did not know of its existence until recently) I fear that without this, I may lose out to my future course mates and this worries me a lot. The thought of seeing your course mates always having the upper hand while you struggle ‘to make meets end’ is absolutely mortifying! What if I can’t keep up? Nevertheless, I am currently doing the STEP papers myself but my gut feeling tells me I can’t compete with some of the students who had prepared it for 6 months! I LOVE math VERY MUCH and have always worked hard but upon learning this, my confidence gradually slips.(I do have some aptitude for math but I am turtle, I grasp things slowly. Sounds contradictory..:S) What should I do Dr Tao? I do realise this problem is more of a psychological one but hearing some advice from a revered mathematician would definitely put my mind at ease.

Lastly, thank you for responding to a small fish in the huge and vast mathematical sea!

With regards,
Joe

12 July, 2008 at 10:43 pm

linh

Dear Tao,
you have many many friends!!??
my E is very bad, I wish I could better
I admire you
can I make friend with you?
I’m from Vietnam.
I’m waiting for you.

28 August, 2008 at 4:35 pm

Indian

Hello Mr Tao, I would like to know if imagination plays a comprehensive role in solving intricate problems, if so do you possess vivid powers of imagination? How do you approach a convoluted problem? Do you apply “Imagination” , other “tricks” ,etc, in arriving at a solution, please answer this query, I thank you in advance.

10 October, 2008 at 2:05 pm

Geraldo Almendra

Dear Mr. Tao

I live in Brazil and I am competing to be accepted to do a graduate math course in March 2009 in a most important institution of math education in Latin America.

I need to prepare myself (study alone) untill december.

In January and February I will do a course in Real Analysis that is the necessary test. The answer about my enrols will be in February.

Because of my age (56) I must have an excellent result to be accepted.

I have until December to study and I am using your book and your material that I found in your page.

With your experience would you advise me how can I have the best possible performance and about other books that I have to study?

Thanks for your help.

Geraldo Almendra

22 October, 2008 at 12:04 pm

Srikant Vadali

Terry,

Reg right-alignment of equation numbers, the following is cumbersome but seems to work:

$$y \sim f(x,\theta)$$(1)

Alternatively, it may be possible to use CSS without tables but I do not know much about CSS to be able to come up with a solution. Hope the above is useful.

Srikant

22 October, 2008 at 1:10 pm

Anonymous

hmm, looks like wordpress eats up the html. The basic idea is to create a table with two cells. In the left cell we have the equation and in the right cell we have the equation no. If you want, I can email you the code. The output will look like so:

$$y \sim f(x,\theta)$$
(1)

Srikant

23 October, 2008 at 9:13 pm

cjohnson

Your quick fix to use {} in front of […] in WordPress LaTeX is very nice. I’ve been doing \left[ … \right] for months!

20 November, 2008 at 10:09 am

Thai

Greets m Prof. Tao
What’s the meaning of human life ? I want to know your answer
mail to stvantu@gmail.com
Thanks

23 November, 2008 at 9:11 pm

Hi Prof Tao,

Do you have any post that explains why you like maths? If don’t, could you tell me why because I am quite interested to know why some people have a liking for such a difficult subject.

Many Thanks!

11 January, 2009 at 6:42 pm

Anonymous

Dear Prof. Tao,

You often link to Wikipedia articles. I am interested to know if you edit Wikipedia, and if you do, to what extent?

Thanks!

20 January, 2009 at 1:35 pm

Anonymous

Is that Hail to the Chief in the header image :) [Yes – but the image has now reverted. -T.]

20 January, 2009 at 4:32 pm

Påfågel

Dear Professor Tao,

Thanks for a great blog. I have a suggestion which is to make your blog posts printer friendly. As it seems you have purchased a CSS upgrade you would be able to insert CSS hacks required (http://en.forums.wordpress.com/topic/nice-blog-printing-using-css-and-sandbox?replies=2). I would loved to have your posts printed out and read them that way (I know you have a book but it isn’t updated as fast as this blog).

20 January, 2009 at 10:28 pm

Terence Tao

Dear Påfågel,

Actually I already have the CSS modifications you mentioned in place (if you “print preview” a blog page you will see the changes from the display version of the blog).

12 February, 2009 at 6:03 pm

Anonymous

I recently noticed that when I access a blog article via a google search, the page is displayed with an advertisement at the top. But when I reload the advertisement disappears. You should be able to replicate this. Is google altering the page?

22 February, 2009 at 5:06 pm

LaTeX in my blog « Ivanky’s Weblog

[…] to Terence Tao’s […]

15 March, 2009 at 4:55 pm

Career advice from the Fields medalists and some other mathematicians « Academic Career Links

[…] advice and writing tips from the blog of Terence Tao Possibly related posts: (automatically generated)Career advice from […]

11 April, 2009 at 10:21 pm

waterloo2005

Font size of your blog is too small . If I enlarge your blog , your latex picture is poor .
Can you change your font size bigger in your blog css?

Thanks a lot!

5 May, 2009 at 8:30 pm

Anonymous

Are there slides from your Fefferman conference talk, today? If so, could you post them?

27 May, 2009 at 9:53 am

Ali İlik

Dear Tao,

Do you have any advice on how to manage time?

Thanks.

Ali İlik

27 May, 2009 at 10:10 am

Ali İlik

I saw this: https://terrytao.wordpress.com/career-advice/work-hard/ and hope you publish a paper on time management in your blog if you did not.

27 May, 2009 at 10:27 am

Successful Researcher: How to Become One

To Ali: Prof. Tao has already published this post on the time management. For more academic time management tips and links see e.g. here.

27 June, 2009 at 7:08 pm

lutfu

Dear Prof. Tao,

Could you please put a specific ”space” in your blog with the title ”ASK DR. TAO”? Because sometimes we have some questions and there is no appropriate post to ask our question?

it would be really perfect

thanks

28 June, 2009 at 8:39 am

robert

Dear Prof Tao,

You must surely qualify to be the Euler of the 20th/21st century. You write more high quality math on your blog each day than most mathematicians (I guess) would write in a year! And you write so simply and clearly for what must be deeply complex ideas. I am not a mathematician but I enjoy visiting your blog daily just to see what’s new from you. I am nicely surprised almost everyday.

Thanks so much.

5 October, 2009 at 6:39 pm

Successful Researcher

Just learned that Israel Gelfand is no longer with us.

30 October, 2009 at 1:16 am

Raj

Complex Decisions are taken by the rules engines which are rudimentry in the logistics space to optimize the route and reduce the cost.

Need help in making the Rule Engine intelligent ….

Are there any specifc Mathematical Models which can be used to simulate the scenarious before a decision is taken ? ( Which can be baked into a IT tools)

How can we build a AI model on top of existing model ?

13 January, 2010 at 7:43 am

ateixeira

Dear prof Tao:

Do you think you can make some of the material of your lectures available in pdf format?

25 January, 2010 at 1:08 am

ekta1007

What a resourceful blog Terry. I am going to check it out !
Keep sharing

4 March, 2010 at 8:09 am

J Nunnelly

Dr. Tao,
Thought you and your readers might want to know that SAMSI, SIAM and ASA are holding an electronic town hall meeting on April 6, 2010 from 2-4pm to discuss uncertainty quantification. SIAM may form an activity group after the discussion is complete. ASA is just looking into what interest there may be with the statisticians to form an interest group. Everyone is free to join in via video stream and watch the discussion and email any questions while the event is taking place. For more info, go to http://bit.ly/cslk10.

4 March, 2010 at 7:25 pm

Anonymous

Today I noticed that the “Papers and preprints” link (on your UCLA page) brings me directly to your work on Arithmetic combinatorics and number theory and I can’t find your work on other topics. Is this intentional?

13 April, 2010 at 9:28 am

TeZ

A request: I am currently reading your post “A computational perspective on set theory” and one thing sprung to my mind. I would love to see a post on the issue of proving that something can not be proved!

13 April, 2010 at 9:39 am

Terence Tao

https://terrytao.wordpress.com/2009/11/05/the-no-self-defeating-object-argument/

14 April, 2010 at 1:46 am

TeZ

Thank you prof. Tao. Keep up the good work. :)

3 May, 2010 at 8:09 pm

For those using LaTeX | The Cryptography Reading Group

[…] Posted on May 4, 2010 by J.Hoak WordPress has a good introduction to LaTeX. Terry Tao also has some good things to say. Lastly, I use a very efficient LaTeX to WordPress’s LaTeX […]

11 June, 2010 at 3:25 am

porton

I received the following post by email:
https://terrytao.wordpress.com/2010/06/10/the-structure-of-polynomials/
Indeed opening this URL says “page not found”.

11 June, 2010 at 7:49 am

Terence Tao

That article was posted to this blog by mistake; it has now been removed.

25 July, 2010 at 7:18 am

Latex for text formatting « Live

[…] Technical remarks from Terrence Tao To know how to include LaTex code in ur post, use this […]

20 September, 2010 at 8:23 am

Quick Updates | Sun Ju's Blog

[…] tool written by “in theory” (well, not his true name) LaTeX2WP, which has received the honorable mention in Terry Tao’s blog and seems to have help Terry a lot. I’m planning to use this a lot […]

22 September, 2010 at 3:48 pm

George Lowther

Dear Prof. Tao.

Many thanks for this amazing blog. I’ve been following your posts for a while now, and always learn something new.

I just read your comment above about wordpress not aligning equations or right-justifying equation numbers (https://terrytao.wordpress.com/about/#comment-29330. A couple of years old, but maybe still relevant). I set up my own blog and came across the same issues, which I managed to find hacks to work around. Maybe, these could also be of help here (although it is a bit messy)?

To align equations you can use the array environment in math mode. Put the latex code inside

$latex \setlength\arraycolsep{2pt}\begin{array}{rl}… \end{array}$

using the standard latex ‘&’ alignment tab. I just added a macro to my editor for this, although you still have to remember to terminate rows using ‘\smallskip\\’ and put an extra ‘\displaystyle’ after each alignment tab.
To right-justify equation numbers, you can use a table, such as the following (I hacked my latex2wp.py file to do this automatically).

<table border=0 cellspacing=0 cellpadding=0 width=100%><tbody><tr><td align=center width=93%><a name="eqref"></a><p>$latex \displaystyle … &fg=000000$</p></td><td align=left width=7%><p>(*eqno*)</p></td></tr></tbody></table>

For example, putting these together (in Faulhaber’s formula, 10),
$\setlength\arraycolsep{2pt}\begin{array}{rl}\displaystyle\sum_{n=1}^Nn^s&\displaystyle=\frac{1}{s+1}\sum_{j=0}^s\binom{s+1}{j}B_jN^{s+1-j}\smallskip\\ &\displaystyle=\frac{1}{s+1}N^{s+1}+\frac12N^s+\cdots+B_sN.\end{array}$ (10)
Hopefully that displays correctly!

22 September, 2010 at 3:56 pm

George Lowther

ok, the centering and right-justification went a bit wrong :( Maybe I did something dumb, or it’s something to do with the way comments are displayed, but it works fine for me on my wordpress blog.

24 September, 2010 at 8:59 am

Hadi

Dear Prof. Tao

is there any way to get the latex resource of your excellent notes?
I printed your notes but the quality of printed formulas is not good!
Do you suggest another method?
thanks anyway!

30 September, 2010 at 1:38 pm

Anonymous

Dear Prof. Tao,

I am a little bit confused with the following issue. Could you please clarify it?

$\frac{d\sin(\theta)}{d \theta}=\frac{\pi}{180}\cos{\theta}$

if $\theta$ is measured in degree.

Thanks

11 October, 2010 at 4:14 am

linfengliu.china@gmail.com

Hi, I want to follow your site.

19 October, 2010 at 4:36 pm

LaTeX – extra examples and some bugs | Математик

[…] with a discussion of peculiar issues. Some other also interesting remarks can be found in the About page of Terence Tao’s blog What’s […]

20 October, 2010 at 6:32 pm

a certain real analysis student

Hi Prof Tao,

I am wondering if you have any advice for (someone like me) who has problems dealing with the concepts of measure and integration, it seems like the ideas taught in class does not come straight to mind when the problems are posed; i.e.

“prove that a monotone function defined on an interval is measurable”

does the question require us to show that monotone function is continuous and then use the fact that continuous functions on a measurable set (interval) is measurable
-or-
it requires us to use the fact that WLOG an monotone increasing function can be written as {f>k} for some k in R?

i know this question is really trivial but hope you can help! thanks~

29 October, 2010 at 3:35 pm

aumana

Hi Prof Tao, I am writing with an uneducated observation, with the naive thought that you will find it interesting. I find infinity to be a compelling philosophical subject. I have noticed that some partially limited sets are considered infinite, such as the set of integers, or odd numbers, and that this has been used to justify a ‘sizes of infinity’ notion. My observation is that making any limitation means you are not talking about infinity, and these ‘little infinities’ are not at all the same. If there is an infinity, there is no line of division between it and anything else, there is nothing else, except perhaps some form of self replicating behavior. Ok, enough said :)

5 November, 2010 at 11:53 am

Tengyu Ma

Dr. Terence Tao,
I am a student from Tsinghua University, China. I read your blog these days and learned really much! I think more students in China should have the opportunity of reading your advices on career choice and writing. Do you mind if I re-post some of your articles about advices to students, and probably with my translation in Chinese, on my blog or bbs of Tsinghua University, where the article is more likely to be read by Chinese students?
I tried to put my question earlier to save your time. One of the reasons why I intended to re-post your article is that the greatest firewall in China blocks WordPress. As discussed in your previous blog, bypassing the GFW is not an easy thing, thus maybe many undergraduate students will not intentionally do that.
I found your advices are really helpful , especially for students in theoretical fields (I am only an undergraduate student ). I didn’t really care about time management and always followed my passion before. Though passion can make me more creative, sometimes when I was really tired and was not in a good state, trying to do some hard problem passionately not only wasted the time, and wasted the passion as well. If I could read your advice before, I would save a lot of time. Fortunately, I am preparing to write a paper, and your advice on writing is really helpful. (I have not been able to grasp the advantage of using English for now, but I am trying).
That’s why I think it will be a really good thing if more Chinese students can read your blog. By the way, I am visiting Rice University as an exchange student, so I can access your blog without difficulties. :)
Thanks
Tengyu Ma

17 November, 2010 at 3:40 pm

TECHStyle | Blog | Five Things Everyone Should Know About Copyright and Open Access: An Open Forum on Authorship and Your Intellectual Property – Redux

[…] that a number of Fields Medalists already maintain high-profile blogs (A quick search found What’s New, maintained by 2006 Fields Medalist and UCLA mathematician, Terence Tao), and the panelists seemed […]

22 January, 2011 at 3:14 pm

Ahmed

Can the theory behind the success of human evolution, ‘The Prisoner’s Dilemma’, be improved upon through mathematical modelling?

There will come a time when global economic advancement stalls, likely to be within 100 to 200 hundred years, when everyone has everything they need and competition between individuals ceases to yield any further advancements worthwhile to society; so society has no motivation to pay for anything other than basics (really, how many iPhone irritations can there be over the next 100 years?).

Is there a way to speed up economic utility as a basis to human advancement by math modelling, to allow people to start thinking about productive change now?

14 March, 2011 at 5:09 am

math dictionary

Nice.
Dear sir Terry You are very brilliant and popular too,
math rocks and so do you.

16 March, 2011 at 6:58 pm

Anonymous

Dear Prof. Tao
You provided most of the links from wikipedia. Do you think it always reliable(or accurate enough for, say, some mathematical concepts)? Or how should people(or students?) treat those links?

14 April, 2011 at 5:17 am

J.P. McCarthy

As someone who probably uses Wikipedia fairly regularly I would use Wikipedia to look up definitions. I would be wary of proofs up there and to believe them I have to go through them myself.

Quoting theorems from there is another matter altogether; you need a proper refereed reference to quote a theorem unseen.

Definitions: yes.
Proofs: maybe
Theorems: No.

20 March, 2011 at 9:24 am

K.C.

Dr. Tao,

What’s your option on multiverse theory? If so, do you think it’s possible to travel to the other universes from our universe? Also, do you think time is one linear? If so, do you agree with Newton’s realist view or Leibniz’s belief that time and space are relational? I also have a question regarding theory of relativity. If the universe is expanding at faster than speed of light, then is there something even faster than the speed of light? If I know these questions are vague, but I really want to know your opinions on them. Thank you very much.

2 November, 2011 at 11:07 pm

M.K.

Could you please consider turning off the “Follow” button? (you hardly need it.) It appears on the bottom right of the screen for everyone not logged in. There is no way known to me for turning it off.
The problem is that in printing your posts, on every single page, a tiny field on the same bottom right of every page is lost, covering words, formulae etc.
The site detailing how to turn it off is
http://en.blog.wordpress.com/2011/09/21/more-traffic-for-your-blog-with-the-follow-button/
Thanks.

7 November, 2011 at 11:34 am

Anonymous

Dear Prof. Tao,

Could you please write an expository article on convex functions? Even proving that a convex function is continuous is very hard and I could not find a source to look it up.

Thanks

17 November, 2011 at 12:59 am

Sean

I have enjoyed watching you lectures on youtube. Thank you for explaining things clearly. I studied pure mathematics in graduate school before pursuing medicine. As a neurosurgeon I find the nervous system fascinating and helping people extremely rewarding. However, I feel that there is nothing more beautiful than pure mathematics. There is something very special about working on a difficult subject in mathematics with nothing more than a pencil and paper. Congratulations on your accomplishments and for inspiring so many people!

1 December, 2011 at 9:02 pm

Hi Terence,

You’ve got a great site here! Would it be possible to get my math page linked from yours? My site is Math Concepts Explained, at http://sk19math.blogspot.com. I’ll put up a link to your site as well from mine. Thanks!
SK

12 January, 2012 at 12:54 am

mohammed901

Dear professor,

Could you give me a clue of what this infinite plane is? and what branches of math can help me understand it more?

Thanks,

12 January, 2012 at 1:03 am

J.P. McCarthy

Mohammed,

That’s a big “times tables” for integers.

12 January, 2012 at 1:36 am

mohammed901

but every single point has a value so it can’t be a table, it’s a some kind of an infinite group of number lines

for example: the space between 0 and 4 on the top, there are infinite numbers that are bigger than zero and smaller than 4 (0<n<4) including fractions like 0.25

and the value of a point increases as it goes further away from the center or the 2 axes

I understand that the plane can be expressed as a function/mathematical statement and it can be expanded into an infinite cube

I just don't understand what exactly it is and what branch of math it
belongs to

14 March, 2012 at 11:01 pm

Gordon Sung

Dear Professor Terry Tao,

Hello, my name is Gordon Sung and I am an undergraduate at Stony Brook University (yep, all the way in New York). I am majoring in Pure Mathematics and pre-medicine. The reason why I chose to do Pure math is I like the ideas (theorems) and proofs that are presented and these proofs sort of remind me of having conversations or argument with people. Can you back up your argument? Sure, I have a “proof” for that. I am also doing Pre-medicine because I love understanding how the human body works (both molecular and anatomy wise); it’s so amazing. My goal is to become either a doctor of mathematics or a doctor of medicine/surgery. However, the reason why I am emailing you is I wanted to ask probably the most vague and perhaps most un-answerable question of all: “what drives you everyday to learn math? How do you keep on motivating yourself when you’re tired or don’t feel like doing mathematics? What’s that “push”? Thank you so much for your time Professor Terry Tao. I am so grateful for even being able to find your webpage and reading about your ideas. Thank you.

28 March, 2012 at 5:49 pm

Parham

Dear Terence,

1 Would it be possible for you to make it possible to download your blog posts in PDF format? (So it can be easily saved on the computer)

2 There a great number of strongly motivated math students in Iran and I’m sure that they would all love to read your blog, but unfortunately the WordPress domain is filtered in Iran. So I was wondering if anything could be done so your weblog would be accessible in Iran.

Thanks for the great blog.

28 March, 2012 at 6:25 pm

Terence Tao

1. Every year I collect most of my blog posts into a book, online versions of which can be downloaded from https://terrytao.wordpress.com/books/

2. There is some discussion on ways to get around such filters at

https://terrytao.wordpress.com/2009/04/27/wordpress-blocked-again-by-great-firewall-of-china/

24 April, 2012 at 3:04 am

Anonymous

We learned about you in class today, and we have to write a paper about you. I wrote that it’s disgusting to me how I asked 45 people on campus if they knew who you were, no one did. I then asked those 45 people if they knew who Britney Spears was. Everyone did. I’m 22 years old and double majoring in Neurology and Microbiology at the University of Hawaii. Sorry I didn’t know about you sooner.

10 July, 2012 at 6:24 am

Notes Software

Dear Prof.Tao,

What software do you use to write down your mathematical notes?It is obvious that you make a lot of mathematical notes on your PC,what software do you use?I am very curious,as for me,I use Wikidpad.

11 September, 2012 at 6:04 am

Anoymous

Dear Doctor Tao,

I suggest you move to Blogger,it shows equations well,for example,
http://irrep.blogspot.com/2011/07/mathjax-in-blogger-ii.html?showComment=1347370874039#c8712231710379098950

13 November, 2012 at 2:01 pm

Anonymous

This is just an example of MathJax (http://www.mathjax.org/). It renders actual text as opposed to generating tons of images. I use it on my WordPress blog through the MathJax-LaTeX plugin (http://wordpress.org/extend/plugins/mathjax-latex/).

27 September, 2012 at 8:50 pm

Rhetorical analysis | yoeripegelenglish1001

[…] https://terrytao.wordpress.com/about/ […]

8 October, 2012 at 2:09 am

Henry

I noticed when mouse hovering over a numbered equation will appear a red block border,when mouse hovering over an unnumbered one it will not.How you managed that…What is the hidden mechanism..

12 November, 2012 at 11:05 am

Anonymous

Hi Prof. Tao. I’ve JUST heard about you today. I just wanted to say hi and I wanted to ask you if you can write Chinese. (lol). It said in a biography that you couldn’t. Me either. (I’m Cantonese. 11 yrs. old, and i can’t write it either.) I absolutely LOVE math! ~Ashley

19 November, 2012 at 7:52 pm

Nishant

Hello Terence,
In case the question is still open (perhaps unlikely after all these years), here is a solution to aligning equations within wordpress. Rather than using the array environment, which requires you to specify up front how many columns there will be, you can you can use the “aligned” environment; aligned appears to behave much like the familiar “align” environment. For instance,
\begin{aligned}
x \cdot y
&= y \cdot x && \text{(from commutativity of } \cdot \text{)} \\
&= e \cdot x \cdot y && \text{(since } e \text{ is the identity element)}
\end{aligned}
yields
$\begin{aligned} x \cdot y &= y \cdot x && \text{(from commutativity of } \cdot \text{)} \\ &= e \cdot x \cdot y && \text{(since } e \text{ is the identity element)}\end{aligned}$

20 April, 2013 at 2:54 am

Daniel

Hello, I heard that you previously read some (wrong) proofs of the Riemann Hypothesis, but have you seen this one: http://arxiv.org/abs/0809.5120?

25 April, 2013 at 4:15 am

Daniel

Sorry to double-post, but I did genuinely want to know if the Riemann Hypothesis proof from that link (http://arxiv.org/abs/0809.5120) was correct – because it has already been quite some time already, and there is no confirmation.

To the down-voter: if you know what is wrong with the proof, please explain.

11 May, 2013 at 1:32 am

Mats Granvik

There is an error in Arne Bergstroms paper in section 3. Poles and zeros. The solution he gives to the equation Reduce[Exp[Exp[u]] + 1 == 0,u] is not categorically wrong as they do appear to satisfy the equation, but the paper would be easier to read if he used the correct solution.

15 June, 2013 at 11:07 pm

David

Sorry I don’t understand why you say that there is an error in section 3. The solutions he gave for e^(e^z)=-1 are correct, and I have verified everything else in section 3 myself. What specifically did you think was wrong?

25 June, 2013 at 11:58 pm

Mats Granvik

Try entering the following line in Wolfram Alpha:

Reduce[Exp[Exp[u]] + 1 == 0,u]

and compare it with the solution in the paper.

Also, I did not downvote Daniel’s comment and I am not competent to evaluate the rest of Bergstroms paper.

26 June, 2013 at 1:43 am

David

You obviously don’t realize that Wolfram Alpha didn’t simplify the solution! The solution in the paper is perfectly correct! I think you need to learn about complex numbers before you pretend to find fault with a paper that uses complex numbers. In any case, as I said earlier I have already verified the entire section 3. You are simply wrong when you say that there is an error there.

14 May, 2013 at 7:54 am

Mats Granvik

Dear Terence,
I have watched your youtube videos about Structure and Randomness in the Prime Numbers, over and over again. I learned from them about the von Mangoldt function and the connection to the zeta zeros via the Fourier transform.

16 May, 2013 at 10:03 pm

Daniel

Dear Prof Terence Tao and others,
How can one delete their own comments here ?

[Unfortunately this is not possible, but if you send me a request to delete a comment, either by email or on this blog, then I should be able to take care of it. – T.]

1 July, 2013 at 3:41 pm

H. J. Bae

How am I following?

9 July, 2013 at 5:06 am

Luqing Ye

It is a bit pity that when I copy material,for example,an exercise, from your post to my editor,the dollar sign ＄ do not appear.For example,if I copy $x^2+y^2=z^2$ ,what appears in my editor is {x^2+y^2=z^2} instead of ＄｛ｘ＾２＋ｙ＾２＝ｚ＾２｝＄.

In fact,This is a flaw of wordpress.It is important that the ＄sign appear,in this way,it will be more convenient to transform post into latex file.

10 July, 2013 at 2:22 am

Luqing Ye

Well,there is a reluctant solution to this problem.If you copy $x^2$ ,what appears in your editor is x^2.

However,if your post is transformed from your latex file by latex2wordpress program,then what appears in your editor is {x^2}.

So you can modify the latex2wordpress program a bit so that when I copy $x^2$ ,what appears in my editor will be {{{{x^2}}}},then I can use the search and replace function of my editor to replace {{{{ and }}}}as ＄.

This is a lot more convenience.

And,further more,if you use latex2wordpress program,when I copy the displayed equation $\displaystyle x^2+y^2=1$ ,what appears in my editor is \displaystyle x^2+y^2=1 ,so if you would like to modify the latex2wordpress software,you had better change this also,so that let me copy ＄＄\displaystyle x^2+y^2=1 ＄＄.

That’s all,thanks.

10 July, 2013 at 2:28 am

Luqing Ye

Let me try it,I think the {{{{ symbol and }}}} symbol will also work well in wordpress.

${{{{x^2+y^2=1}}}}$

If the above equation render well,than {{{{ and }}}} is OK.

10 July, 2013 at 5:55 am

Luqing Ye

Here is the modified latex2wp.py file,

https://docs.google.com/file/d/0B_8b3nT3YboHV204MWliQkJ1TFE/edit?usp=sharing

Let this file replace your corresponding file,you can get the above result,i.e,it will transform the code $x^2+y^2=1$ in your latex file into ＄ｌａｔｅｘ　｛｛｛｛ｘ＾２＋ｙ＾２＝１｝｝｝｝＄,and will transform $$x^2+y^2=1$$ into ＄＄ｌａｔｅｘ　｛｛｛｛＼ｄｉｓｐｌａｙｓｔｙｌｅ　ｘ＾２＋ｙ＾２＝１｝｝｝｝＄＄
It also works fine with \begin{} \end{}.

So when I copy your word,I will get {{{{x^2+y^2=1}}}},etc.

10 July, 2013 at 6:37 am

Luqing Ye

There is a small bug in my file,I have to distinguish between the displayed environments and the inline environments,so I need to transform $$x^2+y^2=1$$ into ＄＄ｌａｔｅｘ　｛｛｛｛｛＼ｄｉｓｐｌａｙｓｔｙｌｅ　ｘ＾２＋ｙ＾２＝１｝｝｝｝｝＄＄　，in which there is one more { and } than ＄＄ｌａｔｅｘ　｛｛｛｛＼ｄｉｓｐｌａｙｓｔｙｌｅ　ｘ＾２＋ｙ＾２＝１｝｝｝｝＄＄.So I can replace {{{{ and }}} by $ ,and replace {{{{{ and }}}}} by $$.

Here is the new modified latex2wp.py file:https://docs.google.com/file/d/0B_8b3nT3YboHcEJZcExZaHgxa2s/edit?usp=sharing

19 July, 2013 at 12:15 pm

Anonymous

Is there a way to add a “more…” link to additional recent comments?

19 August, 2013 at 7:19 pm

Mohammed Ahmed

Mr Tao? I have a question.
You are one of the smartest people in the world. So why don’t you get involved in the Mathematics that is involved in Physics? The subject needs another Einstein, there are so many things that we do not know about the Universe, and as a Mathematician I am sure that you could go a long way toward solving such problems.

12 October, 2013 at 1:35 pm

Anonymous

Hi Prof. Tao,

I have a question: Assume that we have a box with n red and m blue balls, but we do not know the numbers n ,m . You can draw balls with replacement from the box as many time as you can. And you are only allowed to do so. The question is that can you determine exactly the numbers n,m? if you need to put the extra conditions on n,m to solve the problem, what would be the minimum condition?

Thanks

16 October, 2013 at 12:35 pm

5 Things Everyone Should Know About Copyright and Open Access - TECHStyle

8 November, 2013 at 9:04 am

Patrick Poirier

Hello Prof. Tao,

I am currently running a crowd funding campaign for my upcoming educational game Sweet Math. I was wondering what is the process to get a story out on your blog.

Here’s more information about the game itself: http://www.kickstarter.com/projects/89952638/sweet-math

—

For those of you who think education is a key to make the world a better place check out our educational game Sweet Math. We are currently at 69% of our funding goal and the campaign will end on November 14th. We accept donation for as low as $1. http://www.kickstarter.com/projects/89952638/sweet-math

The game let player practice arithmetics with their entire family.

18 November, 2013 at 6:04 pm

Math Blog Snippet | the Cyclic Grizzly

[…] theme with a modified CSS (to do things such as boxed theorems). As stated on his About page, he uses Luca Trevisan’s LaTeX to WordPress converter to write his more mathematically […]

28 November, 2013 at 7:40 pm

Shang

Dear Professor Tao,
I’m a college freshman from China. I’m interested in math, but I’m never good at math, math is really hard for me. Do you think it requires talent to learn math well? because I see some people do math really good without working hard to learn it. I think I don’t have much talent, but do you recommend any method to study math, or any book? (I read your math book about how to solve math problem and it is still hard for me). I really like math and I want to learn it well.
Thank you!

27 December, 2013 at 10:42 am

Sana

Dear Tao,

Thank you for creating such a wonderful website. I have just come across this site, and I want to take this time out to appreciate your efforts and share my own with you..

I have created a Mathematics website that is aimed to help kids from grade 1 to grade 12 practice and learn Mathematics. It is called http://www.ipracticemath.com .. This website maintains a progress report for each and every kid who registers themselves on the website. Both kids and their parents can see this progress report whenever they want.

I would like you to view my website and provide me with your worthy feedback and suggestions, thank you.

Best,
Tayyab

14 January, 2014 at 4:53 am

About | Statistics Hacks

[…] remarks are borrowed from Terence Tao’s blog) WordPress users can insert LaTeX math code (e.g. ) into both posts and comments. The format for […]

26 January, 2014 at 6:14 am

Hind

Hello Prof Tao,

I’m an undergraduate physics student, and I’ve recently gotten interested in random matrix theory, but haven’t had much hope in learning the actual mathematics of it as the books I tried reading (including yours) seemed inaccessible to all but graduate level math students. I was wondering if you knew of any resources I might benefit from?

Thanks

29 January, 2014 at 6:29 am

preethi shreeya

Hello Professor,

I have been working on a project relating to compressed sensing. My Guide and I have a few doubts that needs to be addressed to. It will be really helpful for me if you can give me an idea about how to proceed with the problem statement.

Given: I have a beam fixed at one end and lose at the other. It obviously results in vibrations due to the disturbances in the environment or when induced.And this system can be represented using a differential equation. The vibrations are sensed using sensors, analysed and reduced. Now, the sensing is done through compressed sensing technique.

My question is how is it possible to find the optimal sensor placement (minimal number of sensors along with the details of it’s spatial position) just with the help of the Measurement matrix (that we design in compressed sensing for reconstruction purpose)?

5 February, 2014 at 5:37 pm

Anonymous

hello mr. Tao,
I am in 10th grade and am currectly working on a project about your for my functions, stats, and trig class. you seem like a very amazing and cool person. i was wondering if you had any hobbies?

5 February, 2014 at 5:42 pm

Anonymous

Hello Professor Tao,
I am in 10th grade. my partner and I are currently working on a project about your for our functions, stats, and trig class. you seem like a very amazing and intelligent person. The project requires us to teach about your personal life as well as your academic contributions.Your academic contributions are easy to research, but not so much your other interests. so I was wondering if you had any hobbies currently? Also, what did you like to do for fun as a kid?

Thanks for any help,
Zachary Mahalak and Cooper Homic

9 February, 2014 at 6:52 am

largeur

hi Tao ,
I like this blog . we know , you’re the best mathematician n the wrld . wht do u think about beal cnjecture ?

9 February, 2014 at 11:47 am

Sima

Dear Terrance,

I wonder if you ever think about other problems in the world. The problem of people who can not get along with each other over their difference in opinion. I also wonder if there are mathematical solutions to our political/social/economical problems and if there are such solutions whether or not you communicate them with the leaders of the world?

I know it takes long but currently, those who advise our leaders have not been very effective in ridding the world of many harmful human behaviors so far. for example, Islam and its radical anti-human ideology which I believe is going to destroy humanity and all it’s achievements if not stopped.

If I had a son as genius as you, I would encourage him to spend some of his time on these issues because I, know that there IS a solution and some smart person just needs care enough to take the time and find it.

I am not a very smart person but I am tired of seeing the people of this world suffering over our ignorance. I wish to see the world in harmony and peace in my life time.

Love,
Sima

10 February, 2014 at 5:06 pm

Magnus

Other mathematicians have worked at a solution to the Middle East conflict, see:
http://www.ams.org/journals/notices/201310/fea-saaty-with-link.pdf
However, political decision makers may not always follow logical solutions. Other factors may dominate their decisions. These other factors are the main issues, which no mathematician can help with.

10 February, 2014 at 8:17 pm

Sima

Dear Magnum,

Thanks for sending your reply and the article. It is a fascinating proposal. Not that I understand any of those formulas. :)

It must be extremely frustrating for the two professors to see that their mathematically perfect solution to the middle east problem is not being implemented due to human arrogance and ignorance.

However, since Terrance Tao has a unique gift of seeing things much more clearer and has the ability to find solutions to much more complected equations with infinite unknown elements and factors then perhaps, he is the only one that can solve this conflict. (With the cooperation of the political decision makers of the world, of course.)

I truly believe that he can use his genius to bring peace to the world.

Sincerely,
Sima

25 June, 2014 at 11:03 am

Petar Maymounkov

Math is a system of knowledge that is unambiguously stored within an
“accounting” grammar, underlying all ever written on the subject that is held
in common agreement.

That language is—by choice of taste and agreement—acyclic: It begins with
axioms (of Set Theory) and grows with operations of logic.

Acyclic graphs are not the only one we know. Systems of truth can be
circular—as if suspended in air without axioms— and their sophistication can
be accomplished by refinement as opposed to growth.

That very argument would seem to give hope in resolving two painful paradoxes
in math: the correlation-cause-effect confusion and the question of existence
of one-way functions. And the resolution would simply be to rethink the
language of mathematical expression so that those two characters are one and
the same, thereby going from two conundrums to none.

I find it odd that experimental sciences (when they are correct) report: “The observations
report a correlation of … and we are going to use some side theory to disambiguate
between cause-and-effect.” What side theory?

The very side theory they are appealing to is Math and Math resolves their
meaningless and inane (due to cognitive bias and short historic memory)
question (of “Is correlation cause or effect?”) into another
meaningless one, which is the collection of paradoxes intrinsic in Math—the
provider of the answer.

But if Math wasn’t serving to the asking experimentalist and rather aiming
to build a lanuage that explains everything as seen and observed and testified to
by its users (people), in a consistent and non-arguable manner, it would have
to offer a new tool to record and reason about correlation without breaking it
into cause and effect. No?

Thank you
Petar

28 June, 2014 at 3:55 pm

KHOA TRAN

Dear Prof. Tao,

Would it be a good idea to record your university lectures in Youtube so your talks can spread wider?

Best regards!
Khoa

26 July, 2014 at 3:08 pm

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1 October, 2014 at 7:57 am

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10 November, 2014 at 10:40 pm

Anonymous

hi Dr. Terence !
i admire your exposition and your prodigy. I would like to have your suggestion about my present research on number theory specifically about prime numbers. i revisited Wilson’s theorem and generalized it. Among the results that I deduced is the fact that every prime numbers of the form 2n+1 where n is even is a divisor of some number x^2-1. Further proved that x=n! mod 2n+1. What do you think of the result?? thanks

13 November, 2014 at 2:25 am

uldissprogis

Dear Tao, you are a talented busy man but in your free time consider going to uldissprogis.com to expand your analytical powers to other areas of life. SCIENTIFIC THESAURUS is my book which I recommend for you because it has the logical definition of about 7000 words with subsets, frequency, probability and other mathematical and scientific concepts included to make them logical definitions. Someone with your youth and genius may be able to benefit by my lifelong efforts. Best wishes. Uldis
P.S. If you email me at uldissprogis@gmail.com I can send you a copy of SCIENTIFIC THESAURUS for free. It is my attempt at trying to make language more logical and therefore smarter and less emotionally biased as is the case today with all languages.

19 December, 2014 at 10:05 pm

bobsdfa

Hi Terence, I believe the reason you are intelligent is because you have a large brain. People with large brains tend to have higher IQs, etc and have better working memory and more processing power.

From visual inspection of your head size and unique shape it is clear you have a huge cranial capacity. You mostly likely wear an extremely large helmet size.

If you would take a head MRI brain scan you will see that your brain has huge volume i.e massive cranial capacity. Just something you should know one day before you pass away.

21 December, 2014 at 11:23 pm

H. Schoenich

On the Twin Prime Conjecture.

Prof. Tao and this participating in the polymath project:

Please permit me to make a few conjectures related to this conjecture, which is the holy grail of the bounded prime polymath project.

After recent work, it is my view that a group of the polymath project should be able to solve the Twin Prime Conjecture within a year if properly organized. The problem is not that difficult, despite the lore. (More on that to come.)

1. Prof. Tao has provided one important element for the polymath project to succeed. That is, a forum for the collection and ready dissemination of information and ideas.

2. The success of the project on bounded gaps depends, as with all polymath projects, on the correct incentive structure. While Prof. Tao has taken the first step, there is no general structure of incentives — simple good will — to give individual contributors with very good ideas an incentive to share them rather than to make them their own. (I will add more about this in a subsequent post if Prof. Tao reposts my post as a main entry for the day, say, tomorrow, December 22.)

3. The best incentive structure for organizing group activity involve incentives where the group and the individual can benefit at the same time. In economics, these result in what are known as Pareto optimal exchanges. That is lacking in the polymath project — it is like saying, “go forth and do good.” It is a nice idea but all kinds of conflicting incentives undermine the collective goal.

4. It is my view, given what I know about the Twin Prime Conjecture, that the collected group of participants in the polymath project on bounded prime gaps could solve the problem within a year.

5. Hint: Bombieri-Vinogradov and Zhang approach are unlikely to yield a solution, if they yield approximations for relatively large bounded gap. That is bounds much greater than 2, 4, or 2^n, for n < 6.

6. If the project does not organize itself with better incentives, I am willing to help. The most powerful incentives are going to encourage (a) monetary self-interest, and (b) sharing of ideas amongst the group — seemingly conflicting goals, but there are well-known ways for creating such incentives in market arenas.

7. I believe I can likely solve the Twin Prime Conjecture within six months but it will require me to put aside other work, and health permitting. I will not provide a better hint than the one in item 5. I am at a stage in life, of an age, and with sufficient professional accomplishments, that my main interest is in seeing the problem resolved. I also have the personal incentive that I would like to see others solve it, and I am quite happy to see others obtain the credit. I would strongly prefer that a polymath group solve it (think Manhattan project — though there the government organized and basically sequestered the group — so they couldn't freelance or avoid sharing insights).

8. If the group of polymath mathematicians forms itself, but does not solve the problem within a year, I am willing to then step in and attempt to solve it. I will not share credit, because it will involve too much personal sacrifice, even if my healthy holds out. I believe I can solve it in six months but certainly no more, at this point, than two years of diligent work — modulo the time needed to convey the ideas in LaTeX format, which always considerably slows down my output. As Montgomery says, "I believe LaTeX is a conspiracy to reduce my productivity." He is definitely correct.

(cont'd)

21 December, 2014 at 11:23 pm

H. Schoenich

There is the challenge. The gauntlet thrown down. Not to be embarrassed, as a group, by a single mathematician, who in fact cares not a wit if he gets credit.

You say you want more than a hint, you want a full path laid out? Well, that is like a child asking for you to do his homework when you are the parent.

I will, however, try to help with the incentive structure if a specific, credible request is made by a group (of some defined nature, but not a group closed to new admitted). Some form of joint prize is likely to be necessary; how to ensure that the prize cannot be appropriate by a few is the trick.

As background motivational material, I do not want to see this happen, as recited by Prof. Godfeld at some length — and about which I have seen numerous similar, frankly silly, childish and egotistical attempts to gain individual credit for a process that yields results over time:

http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf

That two of the finest mathematicians between 1940 and 1980 should have had such a dispute is evidence of the extreme power of individual incentives, against the collective, unless a structure is put in place to harness those incentives.

One year; I conjecture I can do it in two if folk don’t start posting ideas to form a collective effort to do so, without free-rider incentives, and incentives for people to “cherry-pick” for self-aggrandizement, in blunt terms.

If the challenge is not accepted, I will, reluctantly given my other time commitments, step in and attempt to solve the Twin Prime Conjecture, which, without hints to you, I believe I can do given what I now know within no more than two years.

I look forward to notification that Prof Tao takes this seriously enough to post it as other than a mere comment.

H. Schoenich.
December 22, 2014

25 December, 2014 at 5:46 pm

H. Schoenich

How does one attach a Latex document?

I think the moderator should be able to review and cut and paste as much into a post as he/she likes. I have a hint for others, on a problem, but I don’t want to include the entirety of my hint, without a moderator making their own judgment — knowing of course that I have taken the time to write up the hint, in weighing how much of it will be passed along.

26 December, 2014 at 6:34 am

Bullsh!t Wiki

Dear professor Tao
I just wanted to say that this is an awesome blog about math. Learned a lot through it. Thank you.
I also wanted to ask you if you could add a link to my website on your link list. It is a free wiki about mathematical proof: http://proofs.wiki/.
Best regards, Brunner Nathan

27 December, 2014 at 8:14 am

brianphilp

On twin primes: Many years ago, looking for heuristic evidence that there were infinitely many twin primes, I noticed that around 1 million there were 5 twin pairs with no primes in between. This surprised me as Sierpinski believed that anything that happened, happened early on in the natural numbers. A while ago I continued the search and come across an interval with 8 twin primes with no primes in between. The endpoints are: 1107819733063 to 1107819732823. Gaps with 5, 6 occur many times while 7 is rarer. I wonder if there are arbitrarily large such gaps.

30 December, 2014 at 5:20 am

Samuel Chu

Dear Prof Tao,
I observed one interesting prime factorization of the three consecutive numbers 2013, 2014 and 2015, 2013=3x11x61, 2014=2x19x53 and 2015=5x13x31, they are all factorized into three distinct primes. I guess there should be no other three consecutive numbers with this property but I can’t find a proof. What do you think?

5 January, 2015 at 7:46 pm

Capablanca

Dear Prof. Tao

I’ve read that professor Durán (a mathematician from Venezuela) claims to have the proof of the following conjectures; “There is an infinite number of Mersenne primes” and “there is an infinite number of Fermat primes”, this is the link that i found: http://www.el-nacional.com/sociedad/Venezolano-demostro-teorema-planteado-anos_0_550145051.html, and, As a consequence of it he said that is completly proved the infinity of perfect numbers, these are the papers:

1. Mersenne Primes Cardinality (2013): http://www.open-science-repository.com/mathematics-70081967.html

2. Fermat Primes Cardinality (2014); http://www.open-science-repository.com/mathematics-45011817.html.

I hope you can read this comment and take this seriously enough to post about it.

Capablanca. H

9 March, 2015 at 11:56 am

Robert Clark

Hello. Professor Tao. I am very impressed about your ability to make important contributions to very different fields of mathematics.
A question I’m interested in is the validity of climate models that show a large human contribution to global warming. These global climate models are quite complex mathematically. Perhaps you could offer some new insight into the validity of such models.

Bob Clark

23 March, 2015 at 3:39 am

Luke

Hi Professor Tao.

I am a high school mathematics teacher in Australia, but have been recently working with an 8 year-old boy who is having mathematical discussions with me that go well beyond the Australian National Senior Curriculum.
I am in the process of trying to provide him with opportunities to be challenged in his mathematics (Senior Level) while still provide social and emotional connection with his peers. Do you have any advice or programs or resources that would be useful in ascertaining what the capabilities of this young boy are? His interests are so far beyond his age that I am sure there gaps in his understanding of mathematics if it were to be taught in a linear, scaffolded manner. I want to provide a focus and purpose to his mathematical studies, including filling in the gaps, without tempering his natural curiosity and interest to push the boundaries of what he is capable of understanding.

Any advice would be much appreciated.

Regards, Luke

23 March, 2015 at 2:17 pm

Ronnie Brown

The book “Men of Mathematics” by Bell records that the parents of the young Cauchy took advice on what mathematics he should be taught. That advice was that there was lots of time for maths, but he should be taught to write his own language! Look this up to see if I have got it right, and to what extent you agree!

You can also look at articles on popularisation on my web site. At Bangor we have run Masterclasses for selected 13 year olds and covered a variety of topics: spherical geometry, higher dimensions, knots. See also my presentation “Out of Line”.

Hope that helps.

23 March, 2015 at 6:16 pm

Terence Tao

The Australian Mathematics Trust http://www.amt.edu.au/ may have some suitable programs or suggestions for this.

2 April, 2015 at 6:17 pm

Ashley C. Fernandes

Dear Prof. Tao,
I have written a book on problem solving using puzzles and games. Would you know or recommend anyone to proof the book?

Someone with basic math skills and an eye for detail would be desirable.

Please view the samples, and you are welcome to comment of forward the link.
http://ashley.mypressonline.com/puzzles-games.html

Have a nice day.

25 May, 2015 at 12:26 am

Category Theory Anyone? | Category Theory

[…] he doesn’t offer any classes in the Spring or Summer and we haven’t managed to talk Terence Tao into offering something interesting à la Leonard Susskind, we’re all at a loss for what to […]

28 May, 2015 at 4:11 pm

Anonymous

Do you have any thoughts on the Erdős–Straus conjecture?

12 December, 2015 at 10:52 pm

Bill

It’s been solved. Just type William Bouris into YouTube, and you’ll find it among the list of my videos. Thanks! Bill

26 July, 2015 at 9:03 am

Ed Gerck, Ph.D.

Dear Prof. Tao,

Mathematics education in US middle and high-school, albeit generally acceptable, is literally in the 1900’s level in several key areas (even for AP courses). For example, Gibbs vector analysis (not even useful for Physics in three-dimensions), complex numbers, and linear algebra.

I wonder what your thoughts or plans might be on this topic. I can volunteer to help, and would love to also have your participation in some of our “experiments” in La Jolla / San Diego.

As a physicist, I see that not only the exponential increase in scientific knowledge but also the increasing jargon (err, language specialization) in physics and mathematics has driven this situation — i.e, keeping modern knowledge insulated — to an extreme lag of more than two centuries. Only the humanities might be further behind in US middle and high-schools (e.g., look at the essay level we see there).

Thank you for your blog and space for mathematical science as well as gifted-child education.

16 September, 2015 at 5:53 am

Bill Tao

Dear professional Tao
I’m a Chinese sophister majoring in finance.There being extensive applications of analysis in equlibrium theory and others, I started to learn it and choose the translation of your masterpiece. But there exists an problem:Lack of correspondent answers,I’m not sure whether my proof was acceptable or not after I finished some of the exercises in the book.So would you please tell me how to get complete answers of this book?Thanks a lot for your help.
Bill

2 October, 2015 at 10:38 am

Right To Learn, Part 2 | Minds on Fire

[…] development across domains. They are out-of-sync not just with their peers but within themselves. Terry Tao, currently one of the world’s leading mathematicians, scored a 760 (out of 800) on the math […]

2 November, 2015 at 6:41 pm

Andrew Palfreyman

Dear Professor Tao –
I’ve run across what seems like a peculiar property of a particular subset of primes; namely, those generated by Euler’s polynomial n^2 – n + 41. For each 41-cycle (barring the 1st which is 100% primes), a simple quadratic sieve identifies all composite numbers with 100% accuracy, thereby leaving only primes. Sieve quadratics in adjacent 41-cycles are related by expressions which are easily derived. I am surprised that it only takes a set of simple quadratics to produce a perfect prime number generator which works forever. Do you have any insight here? Should I publish?

12 December, 2015 at 10:49 pm

Bill

Do you realize that NO ONE should be coming to you for advice, and that YOU should not be giving any of it? LOL

22 January, 2016 at 12:03 am

Lost_In_Space

This page tells me nothing “About” Terrence Tao, and is so overloaded with comments that it takes forever to load, thus amounting to its own Denial Of Service attack. I think I’ll join a Christian monastery. Waiting for the second coming is certainly a much more appealing thought than queuing behind the plethora of worshippers here just to find out “About” Terry.

29 January, 2016 at 1:45 pm

Anonymous

This page is about “Tao’s blog”, not about Tao himself.

18 March, 2016 at 5:04 am

Ramy

Professor Tao,
I have been working for four years on modeling systems by transforming system logic dependency using stereographic projection. My goal was to simulate the creation/annihilation process.

I found consistently some patterns similar to Lie groups. From system’s perspective, these groups controls and balances the system evolution process. For example representing Fibonacci sequence as a system uses primes to create the sequence; the groups balancing the process are: Cyclic, Solvable and another group X.
I am not sure of its type, but this action resembles Euler Totient function.

My background is engineering and I am looking for help to further investigate these patterns. I would appreciate any guidance.

30 May, 2016 at 11:13 am

Tao Chi

hi…

my name is Tao Chi… and because I know… that primes can be stable and in balance… only in interaction with non-primes… because without them… there are holes between primes… and vice versa too… I am sending to you this presentation in which I explain why is so… and why is impossible with only one individual algorithm to determine prime number… all the rest… you can find in this presentation… I will be grateful for your feedback…

from my practical knowledge… the Riemann hypothesis is false or better said it is an illusion…

with love and gratefulness…

TaoChi

10 June, 2016 at 10:16 pm

Tao Chi

6 June, 2016 at 8:11 am

Daniel

Dr. Tao, what is the relationship between the golden ratio (approx 1:1.618) and prime numbers? Both, are naturally observable, but our mathematical knowledge is limited. How do Cicada’s come into this?

3301

7 June, 2016 at 12:49 am

Tao Chi

hi Daniel…
thank you for your question…

everything in the nature is created by cycles and patterns… and in math is also everything created by cycles and patterns…
like… 1 2 3 4 5 6 7 8 9… 1…
like… 1 3 6 1 6 3 1 9 9… 1…
like… 1 2 4 8 7 5… 1…
like… 1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9… 1…
like… 1 4 9 7 7 9 4 1 9… 1…
etc…
so… if you don’t have cycles… you also don’t have patterns… and therefore we need by the primes… also non-primes… if we wish to have the cycles and patterns…
like… 1 5 7 2 4 8… 1…
if we do not join also the non-primes… like… 25… 35… 49… 55… etc… we interrupt the cycles and patterns…

and therefore Cicada’s have their own cycles and patterns… like everything else… in the nature…

TaoChi

6 June, 2016 at 10:00 am

André Luís

Dear Professor Tao,
Do you have some information about a mathematician called Giovanni Gallavotti? Is he an important researcher in Mathematical Physics?

23 June, 2016 at 1:53 pm

Anpama C

Dear Professor Tao , This might be a silly question but I was wondering about below scenario for twin prime conjecture

Similar to infinite number of primes proof, take the set of first N primes 2, 3, 5,..,Pn
(2*3*5*..*Pn) +1 will be a prime number since it is not divisible by any of the prime numbers
Wouldn’t that be the same case for (2*3*5*..*Pn) -1 as well?

Doesn’t that prove there is infinite number of twin primes?

Thank you,
Anu

27 June, 2016 at 12:11 am

Tao Chi

hi Anu…
thank you for your question…

if you look only for twin-primes… you have a lot to do… because they don’t have any constant sequence… therefore if you wish to have an easy way… with what you can also build the geometric shapes… you must also use the non-primes…

thank you…
TaoChi

1 July, 2016 at 7:16 am

roedmario

Dear professor,

Recently a new state of water was apparantly discovered:

https://www.ornl.gov/news/ornl-researchers-discover-new-state-water-molecule

I am writing to inquire, if you will be involved in the follow up work, to explore ie. the potential for a water based quantum computer. ( I am currently looking at a video with some of your thoughts on fluid computing at https://youtu.be/DgmuGqeRTto)

Personally I would hope that a large multidisciplinary group of people would gather soon to discuss water, and the many potentials it has, as energy source (H+O), energy storage (electrolysis) ect., as computational fluid to name a few.

Any thoughts you may have will be most welcome.

23 August, 2016 at 10:36 am

Abel Wolfe

Dear professor,

I think i have lost the taste for life. Everything, and mostly everyone, seems really bland for me. I started to obsess with the concept of general intelligence and how almost every skill and trait i used to value are correlated with it. Like for example creativity, personality and empathy, that recent theories shows that are way more linked to general intelligence than we used to thought.
Now its really hard for me to see people differences as something unique or special, it looks like flaws that are rooted in their incapability of developing certain skills due to their low intelligence. Life doesn’t feel beautiful anymore, with multiple layers of complexity and various ways for people to be different and valuable.
As a consequence, my self esteem is no existent and for example the relationship with my gf, which i was really proud of, looks shallow and extremely liked to our intelligence, because everything that is good looks to be linked to general intelligence. Income, happiness, stable marriage, empathy and so on.
Working as a engineer really made things worsts. It’s almost like anything matters but the ability to solve the problem at hand that is practically 100% of the time solved by the most intelligent person on our group.
I know this is a very reductionist mindset, but i am not finding myself able to change it and its pretty much destroying my life. I also think this is a more modern problem, that was born with the concept of I.Q. and G Factor and the findings that support these theories, but nevertheless i find myself in such a depressive state that i wan’t to ask if you can give me any advice that can help me see this issue at another perspective.

23 August, 2016 at 11:30 am

Ramy ElBehery

I truly believe individual’s value is what they stand for rather than their achievements. Everyone of us has a set of principal values, their kernel, which are independent. Our authenticity is reflected in how our actions consistently satisfy our Kernel. From system’s perspective, our actions are like System Action/Law, and their time rates are the Lagrangians. Through our actions we commute between two unique Undecidable states. The more interstates we have between these two Undecidable states the more complex our actions are.
-The more abstract our principal values are the more effective we can utilize our I.Q.
-The more complex they are the more efficient we can utilize our I.Q. (providing the problem at hands does not provoke any conflict among such variables)
I view I.Q. as Utility, what matters are what we stand for and how authentic and true we are principal values.

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