The Thesis That Everyone In My Family Is Talking About, When I Bring It Up

If you are a human person, please read my Ph.D. Thesis!!! (This version is the last one I’m doing and is ever so slightly more correct than the bound copy; the result is joint work with Manjul Bhargava.)

It was written with you, the people, in mind.  It is math (Number Theory; keywords: equidistribution, lattice shapes of number fields), but it is also me (Non-visual Art; keywords: social justice, layspeak, mild hilarity, home birth).

Read my guest post at mathbabe (!!) to find out the story (sorta) behind my thesis.
Check out this recommendation from madartlab! and this post from Scientific American’s blog!!
Here’s an interview with me at The Hindu’s thREAD blog!


A fascinating tale of mayhem, mystery, and mathematics. Attached to each degree n number field is a rank n − 1 lattice called its shape. This thesis shows that the shapes of Sn-number fields (of degree n = 3, 4, or 5) become equidistributed as the absolute discriminant of the number field goes to infinity. The result for n = 3 is due to David Terr. Here, we provide a unified proof for n = 3, 4, and 5 based on the parametrizations of low rank rings due to Bhargava and Delone–Faddeev. We do not assume any of those words make any kind of sense, though we do make certain assumptions about how much time the reader has on her hands and what kind of sense of humor she has.


Respected research math is dominated by men of a certain attitude. Even allowing for individual variation, there is still a tendency towards an oppressive atmosphere, which is carefully maintained and even championed by those who find it conducive to success. As any good grad student would do, I tried to fit in, mathematically. I absorbed the atmosphere and took attitudes to heart. I was miserable, and on the verge of failure. The problem was not individuals, but a system of self-preservation that, from the outside, feels like a long string of betrayals, some big, some small, perpetrated by your only support system. When I physically removed myself from the situation, I did not know where I was or what to do. First thought: FREEDOM!!!! Second thought: but what about the others like me, who don’t do math the “right way” but could still greatly contribute to the community? I combined those two thoughts and started from zero on my thesis. What resulted was a thesis written for those who do not feel that they are encouraged to be themselves. People who, for instance, try to read a math paper and think, “Oh my goodness what on earth does any of this mean why can’t they just say what they mean????” rather than, “Ah, what lovely results!” (I can’t even pretend to know how “normal” mathematicians feel when they read math, but I know it’s not how I feel.) My thesis is, in many ways, not very serious, sometimes sarcastic, brutally honest, and very me. It is my art. It is myself. It is also as mathematically complete as I could honestly make it.

I’m unwilling to pretend that all manner of ways of thinking are equally encouraged, or that there aren’t very real issues of lack of diversity. It is not my place to make the system comfortable with itself. This may be challenging for happy mathematicians to read through; my only hope is that the challenge is accepted.