I want to celebrate the achievements, but I’m glad I left academic math

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!

Using 3d printing to explore some basic ideas from calculus.

A few days ago we did a short project with some shapes that the boys and I had made using the F3 program:

Using 3d printing to talk math with kids

My older son made a “twisted octahedron” based on one of the examples that comes with the program. When we talked about the shape he wondered how you would calculate the volume of the shape. Today I made some slicing models that you might see in a calculus class to help him see the answer to that question.

I’m still 3 steps below a novice at using F3 but am learning a bit more every day. The program I wrote to make the slicing models is pretty easy (and pretty short) and didn’t take that long to figure out. The code is below – I show it not because it will make sense to everyone, but rather to show how easy it is to make really cool shapes with the F3 program. The code is a very slight modification of F3’s twisted tetrahedron example that caught my son’s eye the other day, and running this code allowed me to make the three sliced examples in the second video below.

slicing-program

So, for our project tonight we first revisited the twisted octahedron and talked about the volume:

Next we looked at the sliced models I made. Unfortunately I made the models way too small. By luck they showed up ok on camera (though sorry for going off screen a few times) and the boys were able to see how the smaller slices converged to the shape we had originally:

I’m not teaching the boys calculus – don’t worry! It still is really neat to be able to show them some of the ideas from calculus using 3d printed models. Can’t wait to play with more shapes this week!