## The investigative mathematical journalist

I’ve been out of academic math a few years now, but I still really enjoy talking to mathematicians. They are generally nice and nerdy and utterly earnest about their field and the questions in their field and why they’re interesting.

In fact, I enjoy these conversations *more* now than when I was an academic mathematician myself. Partly this is because, as a professional, I was embarrassed to ask people stupid questions, because I thought I should already know the answers. I wouldn’t have asked someone to explain motives and the Hodge Conjecture in simple language because honestly, I’m pretty sure I’d gone to about 4 lectures as a graduate student explaining all of this and if I could just remember the answer I would feel smarter.

But nowadays, having left and nearly forgotten that kind of exquisite anxiety that comes out of trying to appear superhuman, I have no problem at all asking someone to clarify something. And if they give me an answer that refers to yet more words I don’t know, I’ll ask them to either rephrase or explain those words.

In other words, I’m becoming something of an investigative mathematical journalist. And I really enjoy it. I think I could do this for a living, or at least as a large project.

What I have in mind is the following: I go around the country (I’ll start here in New York) and interview people about their field. I ask them to explain the “big questions” and what awesomeness would come from actually having answers. Why is their field interesting? How does it connect to other fields? What is the end goal? How would achieving it inform other fields?

Then I’d write them up like columns. So one column might be “Hodge Theory” and it would explain the main problem, the partial results, and the connections to other theories and fields, or another column might be “motives” and it would explain the underlying reason for inventing yet another technology and how it makes things easier to think about.

Obviously I could write a whole book on a given subject, but I wouldn’t. My audience would be, primarily, other mathematicians, but I’d write it to be readable by people who have degrees in other quantitative fields like physics or statistics.

Even more obviously, every time I chose a field and a representative to interview and every time I chose to stop there, I’d be making in some sense a political choice, which would inevitably piss someone off, because I realize people are very sensitive to this. This is presuming anybody every read my surveys in the first place, which is a big if.

Even so, I think it would be a contribution to mathematics. I actually think a pretty serious problem with academic math is that people from disparate fields really have no idea what each other is doing. I’m generalizing, of course, and colloquiums do tend to address this, when they are well done and available. But for the most part, let’s face it, people are essentially only rewarded for writing stuff that is incredibly “insider” for their field. that only a few other experts can understand. Survey of topics, when they’re written, are generally not considered “research” but more like a public service.

And by the way, this is really different from the history of mathematics, in that I have never really cared about who did what, and I still don’t (although I’m not against name a few people in my columns). The real goal here is to end up with a more or less accurate map of the active research areas in mathematics and how they are related. So an enormous network, with various directed edges of different types. In fact, writing this down makes me want to build my map as I go, an annotated visualization to pair with the columns.

Also, it obviously doesn’t have to be me doing all this: I’m happy to make it an open-source project with a few guidelines and version control. But I do want to kick it off because I think it’s a neat idea.

A few questions about my mathematical journalism plan.

- Who’s going to pay me to do this?
- Where should I publish it?

If the answers are “nobody” and “on mathbabe.org” then I’m afraid it won’t happen, at least by me. Any ideas?

One more thing. This idea could just as well be done for another field altogether, like physics or biology. Are there models of people doing something like that in those fields that you know about? Or is there someone actually already doing this in math?

This is already being done. See http://www.ams.org/samplings/math-history/happening-series.

Interesting, but not what I had in mind. Those look more like stories centered around mathematical research, whereas I’m talking about exploring the landscape of fields directly.

Do you know the “What is…?” columns in the notices of the AMS? It sounds like your project.

http://www.math.cornell.edu/~whieldon/What_is….html

Oooh! This is much closer to what I’m talking about, and would serve as a good backbone to the visualization. I’d still need to make the connections though. Thanks!

Also, take a look at the Princeton Companion to Mathematics.

http://press.princeton.edu/titles/8350.html

This looks great, although the fact that it costs $99 is not great. From what I’ve gleaned by a cursory look, it is _too_ broad for my tastes – I think we need more columns on more subfields of the fields listed there to do them justice. Plus, my goal wouldn’t be to give a baby version of each field, which it looks like is being done (and is a good but different idea). Instead, I want to give a high-level vision of why people find each field compelling.

If one could convince other folks to support them, crowd sourcing like kick starter could be the way to go ..

Let me add to the list. In theoretical computer science, sara robinson use to write really informative articles at a level accessible to most non experts …. here is the link to her page – http://www.msri.org/people/members/sara/

It seems she has moved on to other stuff now, though.

As you and I have discussed in person, I strongly support such an activity.

A laudable project, as the more one becomes THE expert in one’s specialized field, the more one uses a narrowing jargon to speak to fewer and fewer interested parties, until it becomes rarely more than a few hundred throughout the world.

Crowdsourcing seems like a good way to find financing, especially if it could be done in the model of SourceForge, say as a networking coding project that is truly open source in structure. Hypertext/media would seem to be an effective display objective.

Don’t stop there. Train and encourage them to regularly blog on behalf of their professions, so they can do what you have been doing for mathematics. We did something in a similar vein with different job titles and work units at one place I worked, and the results were amazing: We found that, going in, half of us didn’t understand what the person at the next desk did for a living. We all explained, told folks what we could do for them (lots of happy surprises there), and what they could do for us (including telling us more things we could do for them).

Punditry isn’t necessarily a bad thing, and it wouldn’t hurt to be able to add to the gallery of media pundits a bunch of people who actually know and care about what they’re talking about. The public might actually become better informed, better educated. Next financial blip, I would hope the cable networks might let you chime in, instead of turning to Jim Cramer for half the “analysis”.

Gotta think about how to monetize this so that at least a few people who put effort into this can at least afford groceries.

Wow, have you lit a fuse? I hope so.

This is actually something I have thought a lot about: if you want a comprehensive map, one way to get a quick low-resolution take, would be a sort of “friend” network approach, where you asked people: name 3 important results in your field (if you have more than 1 field, pick one for the purpose of the exercise), name 3 important open problems, name the 3 best journals where work in your field gets published, 6 other researchers who work in your field who you admire, and then ask them a few questions about the fields closest to theirs. (Nothing special about the numbers 3 and 6, but you get the idea). Also, what is the name of their field, to work on the ontology. Then you look at the network! Call it “field guide to the mathematicians”

This sounds a bit like what Erica Klarreich does.

http://www.ericaklarreich.com/page3.html

I think it’s a worthy goal.

Math and Sciences Monthly. Each discipline gets a different section. The art would be KILLER. Talk to the NSF or Conde Nast?

This sounds right up the alley (or should be) of Jim Simons, mathematician, founder of hedge fund Renaissance Technologies, philanthropist, and multibillionaire. He already funds mathematical research, according to Wikipedia: http://en.wikipedia.org/wiki/James_Simons

If you can get to him, he is a high probability prospect. Good luck!

crowdfunding FTW? eg Kickstarter / Indiegogo

This sounds like a similar idea to Scholarapedia: http://www.scholarpedia.org/article/Main_Page. Definitely a worth while goal (both yours and scholarapedia)

This sounds like a great plan! As one possible precedent, I would recommend checking out the book “Fearless Symmetry: Exposing the Hidden Pattern of Numbers” by Avner Ash and Robert Gross (Princeton University Press, 2006). It’s an attempt to explain Galois Theory for laypeople in reasonable technical detail. I don’t think it accomplishes its goal terribly well, but it addresses a serious gap: although I dropped out of undergraduate math, what helped me to understand whatever things I did was other mathematicians explaining things with conceptual roadmaps, metaphors, images, etc., which are things that are mostly absent in the proof-based presentations of any theoretical math book. This book at least tries to operate in that space.

One thing I sort of saw in retrospect is that mathematicians don’t understand things through proofs, they understand structures abstractly. A proof is a confirmation of the consistency and groundedness of that abstract understanding, not the actual form the understanding takes.

Assuming I’m correct in that understanding, it would be enormously helpful for math students, mathematicians of other fields, and other scientists to have presentations of important ideas (completed or ongoing) in a way closer to how mathematicians understand it within their own minds, when those others either don’t have the time or (yet) have the ability to reconstruct understandings from proof-based presentations.

Also, again assuming I’m correct in my retrospective understanding, it would be enormously encouraging to explain to beginning theoretical math students that it doesn’t mean there’s anything wrong with them or that they are not cut out for math if they can’t reconstruct understandings from proofs alone right when they start off. I might have stayed on in math had somebody told me that.

And, while it would be an enormous service even if self-published, from Fearless Symmetry it seems Princeton University Press might be a receptive publisher.

Good luck!