What Would I Buy With $3 Million for Math[s]?

Leading off the topic of my previous post, I think it’s a good time to ask what we can do with resources that are already allocated. How can we fine-tune the application of resources already set aside for a certain purpose, and so achieve the best outcome in the current Situation?

This post will be a gentle fantasy, because sometimes, in the Situation, we need that, or because that’s all I can do today.

Last month, Evelyn Lamb asked, how should we revamp the Breakthrough Prize for mathematics? This is an award with $3 million attached, supported by tech billionaires. A common sentiment about such awards, a feeling that I happen to share, is that they go to people who have indeed accomplished good things, but on the whole it isn’t a good way to spend money. Picking one person out of a pool of roughly comparable candidates and elevating them above their peers doesn’t really advance the cause of mathematics, particularly when the winner already has a stable position. Lamb comments,

$\$3$ million a year could generously fund 30 postdoc years (or provide 10 3-year postdocs). I still think that wouldn’t be a terrible idea, especially as jobs in math are hard to come by for fresh PhD graduates. But […] more postdoc funding could just postpone the inevitable. Tenure track jobs are hard to come by in mathematics, and without more of them, the job crunch will still exist. Helping to create permanent tenured or tenure-track positions in math would ease up on the job crisis in math and, ideally, make more space for the many deserving people who want to do math in academia. […] from going to the websites of a few major public universities, it looks like it’s around $2.5 million to permanently endow a chair at that kind of institution.

I like the sound of this, but let’s not forget: If we have $3 million per year, then we don’t have to do the same thing every year! My own first thought was that if you can fund 10 postdocs for three years apiece, you can easily pay for 10 new open-source math textbooks. In rough figures, let us say that it takes about a year to write a textbook on material you know well. Then, the book has to be field-tested for at least a semester. To find errors in technical prose, you need to find people who don’t already know what it’s supposed to say, and have them work through the whole thing.

If we look at, say, what MIT expects of undergrad math majors, we can work up a list of courses:

  • Calculus (2 semesters)
  • Differential equations
  • Linear algebra
  • Algorithms and computation
  • Discrete mathematics
  • Abstract algebra
  • Complex analysis
  • Probability and statistics

That’s roughly nine semesters of material, all of which is stable enough that a good book could be useful for decades.

Really, we should have solved the textbook problem long ago, roughly at the time when the Web became a thing. Recently, the American Mathematical Society started hosting Open Math Notes, “course notes, textbooks, and research expositions in progress.” This is a good thing, but it’s only a step in the right direction. What we ought to have is a repository, officially stamped with AMS approval (or that of some suchlike organization), so that anybody who has to teach a class on a core math subject can go to one place and find everything they need. Not many students might have the gumption (or the leisure time) to sit down and work through the whole curriculum on their own, but we really ought to support the teachers—and by doing that, we benefit the autodidacts too.

This would be something like OpenStax, but depth-first: We focus on one major that we know really darn well, and we do it right. And then, God willing, we build a website that isn’t so bloated with JavaScript that my laptop gives up before the site can load. (Seriously, you bastards: Text. Pictures. Click to download file. We had this sorted twenty goddamn years ago. In the rapidly approaching post-Net-Neutrality age, we really ought to be cutting our bandwidth requirements wherever we can.) And we provide the content in as flexible a manner as possible. Want an ebook to plop onto your reader? Click to download the whole thing! Want a page on a specific topic, something like a Wikipedia article that’s actually edited and curated? Here’s a URL right to it!

We could have done this long ago, but it was never in anybody’s short-term interest to get enough folks organized to do it. And when people do get organized, they run off to “innovative” schemes that create niche products, benefiting those who needed the least help in the first place. But with $3 million, I bet we could make it happen.

Another thing that $\$3$ million could probably pay for? An indie film. Aronofsky and friends made $\pi$ for under $70,000 and brought in over $3 million at the box office, for crying out loud. Wouldn’t it be neat to make, say, a dramedy about the intersecting lives of young mathematicians—less schmaltzy than A Beautiful Mind, perhaps tapping into the two-body problem for conflict.

Anyone can be unlucky in love, even if they stay in the same city their entire lives. But academic shuffling is particularly hostile to romance. The short-term contracts mean that when you arrive in a new country, if you’re interested in finding a long-term partner, you have something like two years to identify and convince a person you’ve just met to agree to follow you wherever you might end up in the world, and you won’t be able to tell them where that will be. If you happen to have different citizenships (which is likely), you have to take into account immigration issues as well—your partner may not be able to follow you without a spousal visa, which can mean a rather hasty life-long commitment, or, depending on the marriage laws of the country in question, a total impossibility.

Don’t tell me there’s not a screenplay in that!