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;
- my lecture notes on ergodic theory, on the Poincaré conjecture, and on graduate real analysis (245B and 245C);
- a campaign to support mathematics, statistics, and computing at the University of Southern Queensland;
- 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. 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.)
Comment ratings have been provisionally enabled, however they are 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.
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. 
![<em>[Your LaTeX code]</em>](http://l.wordpress.com/latex.php?latex=%3Cem%3E%5BYour+LaTeX+code%5D%3C%2Fem%3E&bg=ffffff&fg=545454&s=0 "<em>[Your LaTeX code]</em>")
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 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.
57 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
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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).
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 “
” 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
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
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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 ?