Mathematicians Behaving Badly

I write this post in a state of mild panic. New York Public Library has made a margin call on When Genius Failed: The Rise and Fall of Long-Term Capital Management, and I still have a few pages left in the epilogue. Holding on to this asset is costing me, I’m losing equity, etc., etc.

Having now rushed to finish the book over the past few days, I can’t recommend it highly enough.

The story, in short, is this: Long-Term Capital Management was a hedge fund created by “geniuses.” These included two university mathematicians who could make legitimate claims to being key creators of contemporary mathematical finance. (They won Nobel Prizes for this while working for the fund.) It included key disciples of these mathematicians. There were PhDs and Ivy League degrees up the wazoo.

They quickly made a bajillion dollars. They made this money by developing mathematical models that could help them identify pairs of items that were mispriced, relative to each other. They then bet that those prices would converge. They bet this over and over gain in many, many different situations. They always won.

Then, they didn’t. They very quickly lost it all and had to be bailed out by the NY Fed and a consortium of banks.

This was happening in the ’90s. The people involved with LTCM were (if I understand correctly) early pioneers of using quantitative models to capitalize on the mathematical theories of modern finance. I know that this previous sentence is pretty vague, but my point is that this is a story about mathematics and mathematicians.

While reading about these mathematicians, I recognized an arrogance that I’ve experienced in mathematical cultures waaaay too often:

Hilibrand finally offered to dispatch Scholes [Nobel Prize winner — MP] to give the bank a lesson on option pricing, but Pflug was too smart to go head-to-head with the guy who had invented the formula. “You can overintellectualize these Greek letters,” Pflug reflected, referring to the alphas, betas, and gammas in the option trader’s argot. “One Greek word that ought to be in there is hubris.”

What hubris did Pflug divine? The partners were not arrogant in their mannerisms or even in their speech; it was more deep-seated. It was the arrogance of people who had been to Harvard and MIT — of people who really believed that they were more intelligent than others. “Do you know why we make so much money?” Greg Hawkins once asked an old friend from Salomon. “It’s because we’re smarter.” Once the Hawk even tried to lecture a colleague’s wife about molecular biology, her longtime specialty. “You’re full of shit,” she finally replied.

In particular, it seems to me this is partly the arrogance of believing that math is truly about everything. I see this in books that claim math gives you the tools for being logical, in general, or in somehow not being wrong — again, in general.

I also see it in the belief that math can give students general-purpose reasoning skills, ready to be deployed willy-nilly in any context, whatsoever.

It’s something that comes up in the belief that models can be usefully deployed on any dataset, which is one way that LCTM dug its own grave:

Characteristically, Meriwether encouraged the firm to explore new territory. Even at Salomon, the troops had always sought to extend their turf…In retrospect, such moves had been baby steps, not bold new departures. But the partners’ experience — to them, at least — seemed to belie the adage that it is dangerous to try to transport success to unfamiliar ground. Trusting their models, they simply rebooted their computers in virgin terrain.

This is an attitude I even saw in something like Cathy O’Neill’s Weapons of Math Destruction. I don’t have the book in front of me (so apologies if I get this a bit wrong) but there are various moments when she suggests that the same algorithms that are currently deployed oppressively could simply be turned towards more socially useful causes.

I don’t think that, on reflection, O’Neill would deny that deep knowledge of particular context matters, but a reader of her book could be forgiven for thinking that it’s just a matter of where you aim your weapon.

(Hannah Fry’s Hello World does a better job thinking aloud about how deep knowledge of context is necessary for making mathematical models work. So, for example, medical experts might use a trained AI to help identify likely patches of cancerous cells. But the human is the crucial bit here; AI is the tool.)

I’m rambling now, so let’s wrap this up. When Genius Failed: I recommend it. And in general I recommend looking at finance as a major site in the contemporary mathematical landscape. If we want to understand what math is in the world these days, we have to look at finance.

Advertisement