The Math Doctor Is In
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Today I completed a HYROX relay in New York City with one of my former students, his brother, and their dad.
A day before the event, they texted me asking if I could step in because one of their teammates was unable to participate. I had not been training for this event, but I knew I wanted to be on their HYROX team. I immediately said yes.
I was moved by the way they treated me. They picked me up so we could drive into the city together, and from the beginning of the day I felt like part of the team.
My stations were the SkiErg and the burpee broad jumps. The burpee broad jumps were brutal.
After I finished them, I raced to tag in my teammates. As I ran, I noticed the New York City skyline in the background. In that moment, I felt drained but also content.
Before the race, I shared some tips with my former student about the sandbag lunges.
I smiled a bit when I noticed he was really listening to another one of my lessons—this time on sandbag lunges.
Later, he told me that he really dug deep to complete the sandbag lunges.
It took a lot of heart, and I felt proud of him.
One of the things I value most about education is the relationships that develop over time.
What began as mathematics lessons eventually led to us tackling a HYROX relay as teammates.
Of course, I wore a π T-shirt.
My former student didn't even blink when he saw it. At this point, I think he expects it.
A clip from a live stand-up set at the People's Improv Theater where I proved that every prime congruent to 1 mod 4 can be written as a sum of two perfect squares.
When I was 17, I spent 8 weeks learning this proof as a student at the Ross Mathematics Program.
Now I perform it on stage in New York City in under 45 seconds.
One of the things that surprised me when I first learned the proof was that it used ideas about Gaussian integers (complex numbers whose real and imaginary parts are integers) in an essential way to prove a theorem about ordinary integers.
This proof inspired me because it did not merely show that the theorem was true.
To me, it explained why the theorem had to be true by revealing a much deeper mathematical structure underneath the result. I still find this proof beautiful.
Years later, I taught an intensive number theory class to high school students at the COSMOS program (California State Summer School for Mathematics and Science), affiliated with UC Santa Cruz.
In the final week of the course, the students carefully learned this proof.
Many of them could follow it even when I explained it in 45 seconds.
I am sometimes a little nervous performing mathematics live on stage, but I think mathematics becomes more alive when people are willing to share their enthusiasm for it publicly.
What is your favorite theorem in mathematics?
One of the most memorable experiences I had as an undergraduate math student at Brown happened during a number theory course with Professor Steven Lichtenbaum.
I went to his office hours with a question about a homework problem on Gauss sums.
He looked at me and simply said:
“Write out what you’ve done on the board.”
So I started writing.
I explained my ideas, my computations, and where I was stuck.
He stayed quiet and just let me speak.
For about ten minutes, I kept talking and writing.
And then suddenly, in the middle of explaining the problem, I saw the solution myself.
I still think about that interaction sometimes.
As a student, I knew that Professor Steven Lichtenbaum was a Putnam Fellow and an internationally respected mathematician with important conjectures about L-functions named after him.
And yet in that moment, he did not overwhelm me with his expertise.
He simply stayed quiet and let me think.
As a student, it felt almost magical. But later I started to understand what made it such powerful teaching.
He didn’t immediately jump in.
He didn’t interrupt my thinking process.
He gave me enough space to reason my way through the problem.
I didn’t fully realize it at the time, but by staying quiet for nearly ten minutes and simply listening to me, Professor Lichtenbaum was quietly building my confidence as a mathematician.
Sometimes students do not need someone to instantly provide an answer. Sometimes they need time, attention, and the opportunity to hear themselves think.
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