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, sock-puppetry, 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.
Comments that involve AI-generated content may be approved, provided that this AI-generated nature of the output is explicitly disclosed, and the text provided has a genuine chance of contributing positively to the discussion.
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.
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. ) 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. [EDIT, Apr 5 2024: WordPress comments now default to a non-HTML format; however now backslashes are removed unless one uses double backslashes \\ instead of single backslashes \.]
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 some years, 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.

250 comments
Comments feed for this article
25 November, 2023 at 3:17 pm
Anonymous
Can someone use chat GPT 4 to convert many of the posts on this blog into PDF format?
20 August, 2024 at 5:40 pm
Anonymous
Maybe you can use “Ctrl+P” to read for convenience.
6 June, 2024 at 3:34 am
Anonymous
Hello, thx a lot for ur quotes ollection Sir. May I report that the quote ” “There once was a time when all people believed in God and the church ruled. This time was called the Dark Ages.”-–
is from Richard Lederer, Anguished English: An Anthology of Accidental Assaults Upon Our Language “
Pls refer to e.g.:
https://www.thevintagenews.com/2017/01/14/the-remains-of-the-winchester-palace-once-one-of-the-largest-and-most-important-buildings-in-all-of-medieval-london/
Jan CT. Beckmann Dipl.-Eng.
former PhD student in Munich on plasma physics, germany
2024
[Attribution added, thanks – T.]
8 August, 2024 at 6:25 am
Jack
<i>WordPress has the ability to insert LaTeX math code (e.g.
) into both posts and comments. The format for this is “$latex [Your LaTeX code]$”</i>
Has the Comment box been changed in wordpress?
After copy-and-past some content one wants to quote from the article, like above, it seems that one can no longer use the instructed way to insert a math formula. Just another try:
15 August, 2024 at 1:01 pm
Anonymous
I see on google you are the smartest person on earth . I however have just taken you over as I just cracked the market , which makes me the smartest person on earth. Have a great day- regards the sienna
10 October, 2024 at 7:25 am
quicklydreamb858b23121
Recently, I am working on a topic about embedding into Lp spaces. I feel quite hard to solve it. So I am asking for helps and comments here. Thank you pretty much!!!
Let (X,d) be a discrete metric space. Suppose that X has exponentially controlled growth, i.e. there exists a point x_0 in X and r>0 such that the volume of the ball B(x_0, n) is at most
for all integers n.
Fix an integer p>10.
Does there exist a map h: X →
such that
(1) for all x, y in X, || h(x)-h(y) ||≤d(x,y)/
;
and
(2) there exists N>0 such that for all d(x,y)≥ N, || h(x)-h(y) || ≥ 1/√p .
22 February, 2025 at 2:07 pm
Anonymous
Dear Prof. Tao,
Do you have backup plans for your blogs here? Trump has been doing more and more shocking things, and one day it may be possible that he targets academic scholars as they mostly don’t fall for his bullshit.
Many commercial online platforms have already implemented censorship for his sake. Because your blogs rely on commercial WordPress, it is not impossible that WordPress may do something to your blogs under the pressure of Trump, especially since you have criticized him before (for very good reasons).
I have really enjoyed your high quality blogs here, and it would be such a loss if they are somehow censored. That’s why I want to ask if you have any backup plans in mind, or moving your site to somewhere independent of commercial influence.
All the best.
3 March, 2025 at 1:53 pm
inspiring mathematicians, for me – Yang
[…] Tao’s blog […]
12 January, 2026 at 10:03 am
J
It looks like the “Tarski theme” link on this page now points to an unrelated (and likely defunct) website rather than the original resource.
For reference, the author’s original repository is still available on GitHub here:
https://github.com/beastaugh/tarski?tab=readme-ov-file
You may want to consider updating the link.
[Updated, thanks – T.]