Tao's Solving Mathematical Problems: A Personal Perspective (https://www.amazon.com/Solving-Mathematical-Problems-Persona...) mentioned here is an excellent book that provides keys to mathematical approach to problems and is now a classic ranking there with Polya's How to Solve It.

One thing the article doesn't touch on is Tao's prominence in massively collaborative math research through his blog (latest such work from there was discussed on HN a day ago https://news.ycombinator.com/item?id=21542054). This new approach, first proposed by Tom Gowers (https://gowers.wordpress.com/2009/01/27/is-massively-collabo...) in 2009 has successfully solved a number of open problems in the past ten years (https://polymathprojects.org/2019/02/03/ten-years-of-polymat...).

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.