Tools for Discovery is a monthly profile series that inspects the tools, computer programs, gadgets and methods behind WID’s ideas and discoveries.
Jordan Ellenberg is a professor of mathematics and Discovery Fellow at WID. He collaborates with WID’s Optimization research group and has authored numerous popular articles and a book on the role of math in society.
Question: What is your WID research focus?
A lot of my research life is devoted to pure mathematics, especially number theory and algebraic geometry. These subjects date back to the dawn of mathematics and typically address very abstract questions such as “What are the different ways a high-dimensional shape — the sort that some physicists think describes the small-scale geometry of the universe — can curve and intersect itself?” and “Which equations can be solved in whole numbers?”
Here at WID, my research is directed differently and focuses on bringing ideas from these subjects to bear on problems in data science and optimization, which is kind of a whole new world for applied math, bringing in a lot of parts of math that traditional applied math problems haven’t really used. One thing I’m trying to understand at the moment is making sense of data that aren’t easy to visualize, whether they’re data from a computer server or a psychology study. The kinds of questions we like to think about are not just how you would draw the data on a flat screen, but why should the screen be flat? Maybe the data is better understood as living on some sort of curved space.
Tools for analysis?
One big tool that I’ve learned about here is programming in Python. And based off of Python, there’s a package called Sage, which is being developed by pure mathematicians as a kind of massive, collaborative open-source development platform for mathematical computations. In math, people have very different relationships with computers. Some people code a lot, some people don’t. I think for somebody like me who has been working in very traditional, classical areas of math and hasn’t done a lot of computation, learning about Python is really revelatory. Computer languages have changed a lot in the past 15 to 20 years, and it’s much more possible to communicate with machines and instruct them. It’s not so much that using computers is more powerful, but more that there’s now less friction between brain and machine, so to speak. I’m not going to say it’s like talking to a person, but it works more the way the mathematician wants it to work; that’s completely new.
“We’re very good at racing ahead of the things that computers can do… If there are things we now think of as brain functions that computers take over, we’ll stop thinking of those things as interesting and continue to race ahead and value the next things that the machines can’t do.”
— Jordan Ellenberg
Tools for writing?
It totally depends on the thing that I’m writing. I think for anything technical, every single mathematician on Earth uses LaTex. And I do too. It takes a certain amount of time to learn, but it’s one of those things where you can sort of never go back. For writing a book, I’m using Scrivener, which is very popular. For MS Word, the track changes feature is very useful for interaction between a writer and an editor. And the truth is that if there were a LaTex editor with a really robust track changes feature like in Word, I probably would use it to send things back and forth for my students. But I don’t think that exists as far as I know.
Tools for collaboration?
I like Google Hangouts a lot. I was a Skype user for collaboration with distant collaborators, but Google Hangout is much better when you have three people. Skype is fine for two. I think it’s not a substitute for being in the same place, but it’s some kind of trick you play on your mind — it shouldn’t matter that you set aside an hour together to think about a project, but it does matter. In principle, it’s not clear why you can’t do it sequentially by email. But for whatever reason, that doesn’t seem to be the way our brains work. You have to trick yourself into thinking that the other people are there with you, and Google Hangout is pretty good at that.
Ultimate tool for discovery?
I don’t know. My brain, still? So far, it hasn’t been replaced. Some of its functionalities are being replaced.
There are some set of tasks that people don’t do now, like learning people’s phone numbers since you can use a phone to do that. In addition, I access Google’s resources hundreds of times a day. Still, my brain knows things that I don’t think Google does. I tend to think that in the history of math there are things that used to be called “theorems” and now would be called “computations.” These would be facts that, in the old days, a math professor would have to work out by hand and would write a paper and get professional acclaim for. And now you can type a query into a machine and just get the answer, and no longer does the mathematician get credit for it. We’ve sort of outsourced that problem from our brain. But the truth is we’re very good at racing ahead of the things that computers can do. There are people that think that won’t be true forever. If there are things we now think of as brain functions that computers take over, we’ll stop thinking of those things as interesting and continue to race ahead and value the next things that the machines can’t do.