Terence Tao

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.

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/

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.

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/

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/ .)

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-assisted-proof-notices.pdf 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.