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Comment by Jun8 | Hacker News Reader

The idea of a world class mathematician as as weird genius is common and may be said is not totally without base (Perelman comes to mind). Tao's interactions on his blog is always unassuming, trying to help, "super normal" as this article puts it.

But to me the even more amazing thing is how good an educator he is. Most mathematicians I have encountered were of the "proof is left as an exercise" type, where if you didn't see how things done would't or couldn't help you in learning how to proceed. Tao is a big outlier in this regard. His How to Solve Mathematical Problems (http://www.amazon.com/Solving-Mathematical-Problems-Personal...) is more focused than Polya's famous book but is a much better help in learning how mathematicians think. You can get the first chapter for free (http://www.math.ucla.edu/~tao/preprints/problem.ps), an excellent way to finish off a Friday.

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I used Tao's books on Real Analysis during college and my feelings are mixed on his capabilities as an educator. On the one hand his books were really great as he gave a lot of proofs (although most proofs were still left to the reader, but I guess that you can't really learn Analysis without proving Rolle's Theorem or the First Theorem of Calculus on your own) and what I also really liked was that he made no assumptions about your knowledge and started from scratch (first set theory, then properties of natural, whole and rational numbers before constructing the real numbers using Cauchy sequences). On the other hand there were a lot of errors in his books and sometimes he is hard to follow, I guess the books contents are too easy for him and he wrote the book without ever reading back. Even though his books weren't perfect I learned so much about pure mathematics as a non-math major and I don't think I could have learned so much through Rudin's books.

Sounds like he just needed a few math grad student editors. A real reason for a new edition!

> (first set theory, then properties of natural, whole and rational numbers before constructing the real numbers using Cauchy sequences)

This is the standard presentation in every textbook I have read.

It's probably worth pointing out that Good Educator != Good Author. I have heard from people who would know that your guess is not so far off, but having taken classes from him I can attest he is an excellent teacher in addition to being a world class mathematician.

I also want to add that although he is extremely friendly and helpful, it'd be dishonest to say he isn't a bit weird. However, that is probably just an ingredient/consequence of greatness; I reckon most of the big name tech founders discussed on these forums are a bit weird.

How is he weird? Just curious.

Not in any specific way, but he has a nerdy demeanor. There are many interviews of him online your can watch.

For anyone looking for a Real Analysis textbook, I’ve heard several recommendations for Pugh as an alternative to Rudin.

I used Abbott in college. The best math textbook I've ever read.

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