I saw a note today about Akshay Venkatesh winning the Infosys Prize:

Akshay Venkatesh wins the Infosys Prize

Here’s the first paragraph of Venkatesh’s bio:

“Akshay Venkatesh was born in New Delhi in 1981. His family moved to Perth, Australia where he grew up. By the time he was 12 he had become a child prodigy winning medals in International Olympiads in both Mathematics and Physics. He entered the University of Western Australia at the age of 13 and graduated with honours at 16. He also won the J. A. Woods Memorial Prize for the best graduating student. At 17 he started his doctoral work with Peter Sarnak at Princeton University and received his Ph.D. at the age of 21.”

Yikes!

It reminded me a bit of the story of Maraym Mirzakhani winning two gold medals at the IMO after getting a problem solving course started at her high school (as described in the Quanta Magazine article about the Fields Medal):

A Tenacious Explorer of Abstract Surfaces

“Eager to discover what they were capable of in similar competitions, Mirzakhani and Beheshti went to the principal of their school and demanded that she arrange for math problem-solving classes like the ones being taught at the comparable high school for boys. “The principal of the school was a very strong character,” Mirzakhani recalled. “If we really wanted something, she would make it happen.” The principal was undeterred by the fact that Iran’s International Mathematical Olympiad team had never fielded a girl, Mirzakhani said. “Her mindset was very positive and upbeat — that ‘you can do it, even though you’ll be the first one,’ ” Mirzakhani said. “I think that has influenced my life quite a lot.”

In 1994, when Mirzakhani was 17, she and Beheshti made the Iranian math Olympiad team. Mirzakhani’s score on the Olympiad test earned her a gold medal. The following year, she returned and achieved a perfect score. Having entered the competitions to discover what she could do, Mirzakhani emerged with a deep love of mathematics. “You have to spend some energy and effort to see the beauty of math,” she said.”

and there are, of course, many more stories of incredible work done by mathematicians who seem to have found tremendous success in mathematics from a very young age – from Terry Tao to Jordan Ellenberg to Jacob Lurie to Melanie Wood and even to David Yang who just won the 2017 Morgan Prize for undergraduate research after winning two gold medals at the IMO in high school.

I remember my analysis professor telling me in college that I wasn’t cut out to be a research mathematician. It was hard to hear at the time, but even though I went on to get a PhD I think he was actually right – competing with any of the people above for jobs or grants or anything, really, in academic math wouldn’t be much of a competition or much fun in general, I think.

But I’m not sad to have left academic math. I’ve been lucky to find a job where I have interesting problems to work on and think through. Not academic math problems – not even close – but interesting problems nonetheless.

I’ve also been lucky to have been drawn back into slightly more academic math by finding interesting math ideas to share with my kids. Looking for things to share with them has been a joy and has led me to explore some work (or at least some public lectures) of some extremely talented research mathematicians. I’m glad that I have the luxury of looking at their work and figuring out how to share it with kids rather than trying to complete with them for work, though!

Even most of we academic mathematicians can’t really compete with the Venkatesh’s, Tao’s, and Shor’s of the world. My PhD advisor also told me I wasn’t cut out to do research as a professor; I ignored him (and ignored my observations of Shor, with whom I shared an office in grad school) and have turned out to be reasonably successful, despite being several steps below these guys in raw mathematical talent. Enthusiasm, persistence, and hard work can take one a long way. That being said, there are certainly good reasons not to work at a university — and it sounds as if you made a good choice for yourself.

(I’m only commenting to prevent students who see others around them doing math more easily from giving up on doing math professionally. While a realistic view of one’s own abilities is important, one does not need to be the absolute best to be successful.)

What’s with these mathematics advisers telling either of you that you weren’t cut out to do research??? Maybe they didn’t want you to compete with them!

Nevertheless I enjoyed reading this post, and it has filled me with wonder as well as given me a lot to think about.

Wow! So, I know this isn’t what you want to hear but your advisor was full of hogwash! You were great as an academic and by far one of the best (if not best) teacher that I have ever met. If you had stayed, you would have found your passion and it would have taken you very far. Your gift is your passion for math, for teaching math at a very high level and your amazing ability to communicate mathematics. You may not have been the Tao of math but you would have been the Neil Degrasse Tyson of math. Think of the number of students you would have turned on to math. That being said, you are living a very fulfilled life that allows you to do ALL the things that you love so much. It doesn’t get better than that.