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), on Hilbert’s fifth problem, on expansion in finite simple groups of Lie type, and on higher order Fourier analysis;
- 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. 
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.
108 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,
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
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
http://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
Congrats! Your blog has made it into the TOP 30 of The
Math Bloggers blog community, powered by SocialRank!!!
As you might know, every day the SocialRank algorithm is tracking
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Plus, when you add the badge, your blog gets a link back
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You can check out your ranking here: http://www.MathBloggers.com/community
Let me know what you think about the new features… and keep writing
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Kind regards,
Caroline
SocialRank Community Manager
http://www.MathBloggers.com
PS: We’ve launched a couple of other SocialRank powered sites,
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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
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 http://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
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 http://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
http://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
wg
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: http://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
http://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:
http://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 (http://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),
(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?
if
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
SK
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?
http://i43.tinypic.com/fld309.jpg
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 http://terrytao.wordpress.com/books/
2. There is some discussion on ways to get around such filters at
http://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
[...] http://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
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.
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.]