I study mathematics. More specifically, I study number theory and algebraic geometry. As an undergrad, I really enjoyed elementary and additive number theory. As a grad student studying under Dr. Jeff Hoffstein at Brown, I focused on analytic number theory, arithmetic dynamics, and $L$-functions. As a postdoc working with John Cremona at the University of Warwick, I began to work on the LMFDB and incorporate computational number theory techniques into my repertoire. At ICERM I continue my work in number theory, arithmetic statistics, computational number theory, math software, and related topics.
What is number theory?
I get this question a lot, but I’ve never been really good at answering it. When I took my first number theory class with Dr. Matt Baker, an excellent inspirateur likely responsible for my career path, it was apparent to me: number theory is the study of numbers. We like divisibility tests, primes, or density of special numbers in progression. This encompasses much of what I now call elementary number theory, from the prime number theorem to modern cryptography. But this does not even begin to actually answer the question (this is sort of a Dunning-Kruger classification error).
I think a better question is ‘What is Mathematics?’ Once you see that mathematics is exploratory rather than a series of trite, uninspired exercises, I think number theory arises as the study of the properties of the basic building blocks of whatever system you’re working in. (Did you know that there is a topological proof that there are infinitely many primes? Is this a statement about topology or number theory?) For more, I encourage you to read A Mathematicians Lament by Lockhart.
Why do you blog?
Because it helps me reduce how often I need to repeat myself, and because I was inspired by Terry Tao’s blog when I was younger. Much of the material here is for my students, and writing it down here means I’ll have to do less later. I also find that I sometimes repeat the same series or sort of calculation or computation, or get stuck in the same process in papers – so I write it here so that I can easily document it and reuse it later. Further, all articles I write here with math in the post is originally written in $\LaTeX$, and then converted with my script latex2jax. This gives me that little extra push to TeX up my notes for talks I give, some of which I’ve already reused, or to TeX up parts of my research along the way.
I also use this site as a way to distribute and communicate my math research, including the rationale behind certain approaches and some of the less successful attempts along the way.
I also spend a good part of my time programming, and trying to conjure a way to work this into my career. You see, I’m a mathematician. But I like to program too, and there are many ways to use programming to advance mathematics.
Finally, I am a big believer of the Do Things, Tell People or Do Things, Write About It philosophy. In short, do cool things. Along the way, google is your friend. If it hasn’t been done before, or hasn’t been done well, then document your own path. Write about it. Do cool things, write about it.
Should anyone want to contact me, don’t hesitate. Shoot me an email at email@example.com, firstname.lastname@example.org, or comment here.
There’s also the original and free wordpress version of my blog at mixedmath.wordpress.com. I’m still building this site, and I’m not certain about sticking with wordpress. It’s a work in progress, certain to be changed or updated.
For those close enough for this to make sense, you can often find me in my office at ICERM (or at Brown University) or at other times in Boston, Massachusetts.
Disclaimer: I have been off and on the gracious support of the NSF and other grant giving bodies in the past. So I note: “Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or any other institution.”