Terence Tao
terrytao.wordpress.com · Personal blog · on HN since 2007
Fields medalist Terence Tao writes about mathematics, research practice, formal proofs in Lean, and how to think about the subject.
What HN saysCommenters call him one of the greatest living mathematicians and cite his prolific blogging as proof that top experts still write publicly.
462HN people shared it
299linked it in comments
280stories submitted
8.5Kstory points
2 months agolast shared
2007people per year2026
Most-shared posts
- 1Nines of safety: a proposed unit of measurement of risk (by Terence Tao)41 people · 4 points · first shared 2007 · discussion on HN
- 2Does one have to be a genius to do maths?40 people · 275 points · first shared 2007 · 56 comments on HN
- 3There's more to mathematics than rigour and proofs (2007)35 people · 352 points · first shared 2018 · 98 comments on HN
- 4There’s more to mathematics than rigour and proofs24 people · 262 points · first shared 2012 · 36 comments on HN
- 5Work Hard (2007)11 people · 450 points · first shared 2012 · 188 comments on HN
- 6Benford’s law, Zipf’s law, and the Pareto distribution10 people · 61 points · first shared 2009 · 4 comments on HN
- 7Formalizing the proof of PFR in Lean4 using Blueprint: a short tour10 people · 6 points · first shared 2023 · discussion on HN
- 8How to assign partial credit on an exam of true-false questions?9 people · 178 points · first shared 2016 · 83 comments on HN
- 9Career advice from Terence Tao9 people · 25 points · first shared 2008 · 1 comments on HN
- 10Compressed sensing and single-pixel cameras9 people · 7 points · first shared 2009 · 1 comments on HN
- 11Terry Tao on how to compute non-converging infinite sums (2010)8 people · 113 points · first shared 2014 · 24 comments on HN
- 12Eigenvectors from eigenvalues7 people · 533 points · first shared 2019 · 86 comments on HN
- 13The 3n+1 conjecture: Terry Tao has some thoughts ...7 people · 46 points · first shared 2011 · 8 comments on HN
- 14Terence Tao on Biases between consecutive primes7 people · 11 points · first shared 2016 · discussion on HN
- 15Terry Tao (Fields medalist) on time management6 people · 78 points · first shared 2008 · 19 comments on HN
What HN people wrote when they linked it
C-x_C-f · 2023-04-26
Elusiveness is subjective, but there's certainly plenty of patterns to be found (though, to be fair, what constitutes a pattern might also be subjective). You should check out Terence Tao's blog [0], he's not only one of the most prominent mathematicians in the field but he's also excellent at explaining things. These slides [1] for example don't require any background in math.
[0] https://terrytao.wordpress.com
[1] https://www.math.ucla.edu/~tao/preprints/Slides/primes.pdf
JadeNB · 2023-04-14
> If you are an actual expert in such things, you don't have the time to be doing podcasts.
I'm not sure about podcasting, but this is false for blogging. As a mathematician, the first example that springs to mind is Terry Tao's extraordinary blog https://terrytao.wordpress.com , and it's one of the best, but there are tons of others.
feoren · 2023-02-23
One of the greatest living mathematicians blogs all the time:
https://terrytao.wordpress.com/
Simp4Zuck · 2022-05-16
Find a good resource with lots of difficult problems to solve. The resource is basically useless if it doesn't come with a well written answer key.
Leetcode is good for learning leetcode. The Art of Problem Solving books are good for pure math. Stuff like that.
That'll get you through the "basics" if you really like math and also go to undergrad/grad school for it. If you want to be "the best" then you'll have to compete with people who actually are geniuses. Idk how to compete with them, maybe read their blogs and try to replicate their practice methods?
Here's a really smart guy's blog:
https://terrytao.wordpress.com/
gus_massa · 2021-12-22
There is a lot of variation, for example https://terrytao.wordpress.com/ and I remember some guy that claimed that got a fantastic method for factorization that broke RSA and posted it in the arxiv, and the first 5 page of the preprint was an explanation of the rule of nines. (If the sum of the digits of a number is divisible by 9 then the number is divisible by 9.)
selfishgene · 2021-02-13
Best place to learn about a lot of topics in math including the necessary background for understanding the Feynman trick and related maneuvers is Terrence Tao's website:
https://terrytao.wordpress.com/
Measure theory in particular:
https://terrytao.files.wordpress.com/2011/01/measure-book1.pdf
opportune · 2020-04-30
Yes, my favorite thing about Tao is how well he explains concepts on his blog [0] and on mathoverflow[1]. He does not put on airs of being an unapproachable genius. I guess he knows he has nothing to prove
[0] https://terrytao.wordpress.com/
[1] https://mathoverflow.net/users/766/terry-tao
S4M · 2019-02-15
I found this one by Terence Tao, though I haven't checked it yet: http://www.math.ucla.edu/~tao/resource/general/115a.3.02f/
Tao is a top mathematician who is well known for his ability to make complex topics seem simple (see his blog https://terrytao.wordpress.com) so his class is probably worth checking if you are interested in linear algebra.
kutkloon7 · 2015-03-07
Terrence Tao has a blog where he writes about his work. It definitely doesn't cover the depth of his work, but it shows the type of work he is doing. Many entries are very readable (of course, there is a lot of mathematics in it, but Terrence Tao does an excellent job explaining in a relatively simple way).
https://terrytao.wordpress.com/
tokenadult · 2012-05-12
Mathematician Terence Tao, a Fields medalist and the youngest ever International Mathematical Olympiad gold medalist to date, did the work described in the article kindly submitted here. His blog
http://terrytao.wordpress.com/
is not to be missed. The "Career Advice" section of the blog
http://terrytao.wordpress.com/career-advice/
includes several classic articles, of which I especially like and recommend "Does one have to be a genius to do maths?"
http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-geni…
(Tao's answer is no.)
karamazov · 2011-07-24
It all depends on what you view with the Internet, just like the quality of a life spent with books depends on exactly what books you're reading. If all you read is romance novels, you won't be stimulating yourself adequately; the same is true online. If you choose to access only brief news articles and simulator entries, for example, you may learn a lot; but you won't stretch your mind.
Every now and again read something difficult; something that makes you think and leaves you confused. You'll learn more in the long run. A great place start, if you happen to be interested in math, is Terence Tao's blog, and a number of the blogs he links to. (At the least, I find it challenging; the blog is over at http://terrytao.wordpress.com/ .)
shadowmatter · 2011-07-16
I did a math minor at UCLA, and he taught the upper-division linear algebra class I took. He didn't like the book, so he decided to write his own lecture notes, which formed a book unto themselves. They're still available online at http://www.math.ucla.edu/~tao/resource/general/115a.3.02f/. If you ever have the itch to learn linear algebra, read them, they're quite excellent.
It was pretty obvious at class and obvious hours he was crazy smart -- but I had no way of knowing he was Fields Medal smart. But unlike other crazy smart professors I've had, he's a very gifted teacher as well. I mostly learned by reading the books and considered the lectures as an ancillary learning aid, but his lectures were very illuminating. I'm glad he now has a blog to teach a wider audience at http://terrytao.wordpress.com/, but unfortunately most of it is beyond what I can understand. If you're a math die-hard, be sure to read that.
btilly · 2025-12-13
Let's see.
I could believe you, an internet stranger. And believe that this problem was effectively solved 20 years ago.
Or I could read Terry Tao's https://terrytao.wordpress.com/wp-content/uploads/2024/03/machine-assi… and believe his experience that creating a machine checkable version of an informal proof currently takes something like 20x the work. And the machine checkable version can't just reference the existing literature, because most of that isn't in machine checkable form either.
I'm going with the guy who is considered one of the greatest living mathematicians. There is an awful lot that goes into creating a machine checkable proof ecosystem, and the file format isn't the hard bit.
madars · 2025-11-23
Good background reading/watching - Terence Tao's "The Notorious Collatz conjecture" talk. https://www.youtube.com/watch?v=X2p5eMWyaFs Slides: https://terrytao.wordpress.com/wp-content/uploads/2020/02/collatz.pdf
I especially like how he highlights that Collatz conjecture shows that a simple dynamical system can have amazingly complex behavior; also 3n-1 variant has two known cycles - so "any proof of the Collatz conjecture must at some point use a property of the 3n+1 map that is not shared by the 3n-1 map." And this property can't be too general either - questions about FRACTRAN programs (of which Collatz conjecture is a special case) can encode the halting problem.
If you haven't seen it, FRACTRAN itself is amazing - https://www.cs.unc.edu/~stotts/COMP210-s23/madMath/Conway87.pdf and the paper is pure joy to read.
tea-coffee · 2025-09-12
Imagine if Richard Feynman used his IQ as a metric for deciding whether he should become a physicist. Physics would not be the same.
I am certain that there are mathematicians below, near, and above an IQ of 145 that all have great research productivity. IQ tests do not approximate the creativity, effort, and collaboration required in a mathematician. Not to mention the dubious nature of the 145 claim.
Of course, there are some people that will have a greater aptitude for mathematics than others. But you do not need to be a genius, and this is echoed by Terence Tao [0].
[0] https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-gen…
lanstin · 2025-02-12
Well I am studying mathematics, and I use the LLM to help me learn.
They aren't terrible, and they have all of arXiv to train on. Terrence Tao is doing some cool stuff with it - the idea will be an LLM to generate Lean proofs.
https://mathstodon.xyz/@tao/113132502735585408
https://terrytao.wordpress.com/2024/12/05/ai-for-math-fund/
(Professor Tao is probably the best or at least most productive in the most fields current mathematician).
syadegari · 2024-10-08
While not a community itself, Terence Tao's blog (https://terrytao.wordpress.com/) is a good source of high quality, clearly explained maths. As you may know, he has a very broad range of interests, and there might be something for you to pick up and get involved in. He has also been involved in several collaborative math communities, which he writes about at length in his blog. I recall Polymath project and recently some project involving Lean Theorem Prover that even showed up on the first page of the HN.
wenc · 2024-08-24
Absolutely. No matter how gifted a person is, there is going to be some point in their lives or some domain where pure talent will be insufficient.
Even super geniuses like Terence Tao struggled (he nearly did not pass his generals).
https://terrytao.wordpress.com/2019/06/27/living-proof-stories-of-resi…
https://web.math.princeton.edu/generals/tao_terence
The American Mathematical Society has a PDF of essays of brilliant mathematicians (including Terence Tao) who despite their abilities, faced obstacles and difficulties that their sheer talents were inadequate to overcome, and they had to persevere.
https://blogs.ams.org/inclusionexclusion/2019/06/26/living-proof-a-mus…
OscarCunningham · 2024-07-07
That's assuming that wind tunnels are not Turning-complete. Terry Tao has this fantastic idea of proving the Navier-Stokes equations blow up by proving the existence of a 'fluid computer'. https://terrytao.wordpress.com/2019/05/31/searching-for-singularities-…
dan-robertson · 2024-06-04
He has a blog which has some more elementary posts and some less. But I’m not sure if that would be sufficiently ‘beginner friendly’ for your needs. https://terrytao.wordpress.com/
Strilanc · 2024-04-24
Another danger is some sort of bug in Lean itself. This isn't unprecedented in theorem provers [1][2]. These might be hard to hit by accident... but there are larger and larger collaborations where arbitrarily people fill in steps (like [3]). Someone trolling one of these efforts by filling a step in using a bug they found might become worth worrying about.
[1]: https://inutile.club/estatis/falso/
[2]: https://www.youtube.com/watch?v=sv97pXplxf0
[3]: https://terrytao.wordpress.com/2023/11/18/formalizing-the-proof-of-pfr…
svat · 2023-09-21
That AMS article ("A Close Call: How a Near Failure Propelled Me to Succeed") is great and sobering. I am sure it has helped some people, by showing that even Terence Tao cannot succeed without working hard.
> this was the first time I had performed poorly on an exam that I was genuinely interested in performing well in. But it served as an important wake-up call and a turning point in my career. I began to take my classes and studying more seriously. I listened more to my fellow students and other faculty, and I cut back on my gaming. I worked particularly hard on all of the problems that my advisor gave me […] In retrospect, nearly failing the generals was probably the best thing that could have happened to me at the time.
See also https://terrytao.wordpress.com/career-advice/ which among other things links to "Work hard": https://terrytao.wordpress.com/career-advice/work-hard/
airgapstopgap · 2023-07-27
You are frustrated and this makes you act in a deliberately obtuse manner.
There is a world of difference between "anyone who has worked with the guy" and "has worked with the guy + has hundreds of comments on HN identifying career track over the last few years". The former grants each suspect plausible deniability, while the latter pinpoints the true author.
> Anonymity is not a realistic goal.
It obviously is for a throwaway account. Time to reread the classic
https://terrytao.wordpress.com/about/anonymity-and-the-internet/
O__________O · 2022-10-17
Found the examples of power laws starting on page-5 interesting; all the following follow power law: Word frequency, Citations of scientific papers, Web hits, Copies of books sold, Telephone calls, Magnitude of earthquakes, Diameter of moon craters, Intensity of solar flares, Intensity of wars, Wealth of the richest people, Frequencies of family names, Populations of cities, etc.
Terence Tao also has a post on it here from 2009:
- Benford’s law, Zipf’s law, and the Pareto distribution
https://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-t…
Vsause has video on it too:
- https://youtube.com/watch?v=fCn8zs912OE
peterhalburt33 · 2022-04-19
I love Terry Tao’s writing on math. One thing that strikes me about him is that, despite being an absolute technical powerhouse, he writes in a very down to earth style that connects disparate areas of math - e.g. his article on “what is a gauge” https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/amp/ where he explains how dimensional analysis might be viewed as a change of coordinates. Too often exposition in math is myopic and fails to impart a unique perspective on the subject, but Tao imbues his writing with a wisdom that I consider the sign of a true genius.
jl2718 · 2022-03-02
The meme commands me to obey:
Terry Tao once famously published a result with non-mathematicians Denton et al., and was bombarded by responses (including my own first math paper) showing the result previously published in many different ways in several fields of math. Of all that Tao has accomplished as a Fields medalist and espoused “greatest living mathematician”, this became the most famous single moment of his career.
https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalue…
nopinsight · 2022-01-28
I think the gratuitous cynicism toward the mathematician is uncalled for. Terence Tao has devoted a lot of time writing educational articles on his blog. [1] If he mainly cares for passive income, he could divert a bit of time to hire a production company and film a few courses. He would own 100% of the contents and make millions simply out of his global name recognition.
Going with Masterclass is probably the path of least resistance for him to create high-quality video content while continuing to spend most time on research and other educational activities.
Another possible factor: Many good mathematicians are quite perfectionistic and would not want to create homemade-quality videos if they can avoid it.
[1] https://terrytao.wordpress.com/
jjgreen · 2021-11-30
Terrence Tao https://terrytao.wordpress.com/
Nick Higham https://nhigham.com/
andrepd · 2021-11-18
>Just look at HN
Well no offense but what are you doing here if you think that the comments are so bad? I quite disagree, hn comment threads are generally quite good quality and civil, and you will find knowledgeable people chiming in.
>almost every discussion revolves around people trying to find things to complain about
Quite meta x))
Also: here is a blog which definitely wouldn't be the same without comments https://terrytao.wordpress.com/
vavooom · 2021-10-27
https://terrytao.wordpress.com/
Terence's blog is a wonderful view into his research and background, as well as a catalog on the immense amount of work he has accomplished in such a short time. Will be interesting to see what future accomplishments he can achieve.