Note: I completed a PhD in Mathematics from University of Illinois under the direction of Nathan Dunfield in 2011. I worked as a research analyst at GiveWell from April 2012 to May 2013. All views expressed here are my own.
About this post: I've long been interested in ways in which mathematicians can contribute high social value. In this post, I discuss a tentative idea along these lines. My thoughts are very preliminary in nature, and my intent in making this post is to provide a launching point for further exploration of the subject, rather than to persuade.
Recessions as a serious threat to global welfare
- It’s been claimed that the cost to US taxpayers in bank bailouts was $9 trillion.
- The Dow Jones Industrial Average dropped by almost 50% and took over 4 years to recover.
- US unemployment jumped from ~5% to ~10%, and has only gradually been declining.
- Budget cuts were especially great for government support of activities with unusually high humanitarian value to those without political constituency, such as investment in global health.
It’s been claimed that recessions cause a drop in prosocial behavior.
All told, the Great Recession had massive negative humanitarian disvalue, and preventing another such recession would have massive humanitarian value.
Transparent financial analysis as a possible solution
There are actors in finance who accurately predicted that there was a housing bubble that was on the brink of popping, and who bet heavily against subprime mortgages, reaping enormous profits as a result. The most prominent example is John Paulson, who made $3.7 billion in a 2007 alone, starting from a base of less than $1 billion. There are less extreme examples that are nevertheless very striking.
It’s difficult to determine the relative roles that skill and luck played in these peoples’ success, and the situation is further obscured by hindsight bias. Nevertheless, it seems possible that the financial success of Paulson and others was a consequence of careful analysis and shrewdness, and that other people of sufficiently high intellectual caliber and rationality would have been able to predict it as well.
As is always the case in finance, those who recognized the impending pop of the housing bubble kept their analysis secret, because sharing it would have allowed others to partially close the arbitrage opportunity, reducing the potential to profit. If these people had made their thinking public, it could have resulted in other people betting against the housing bubble earlier on, popped the housing bubble when it was smaller, possibly substantially lessening the severity of the ensuing recession. While there were people who publicly voiced concern, a large number of people would have had a bigger impact
This suggests that transparent financial analysis by intellectual elites could carry massive humanitarian value.
Mathematicians as unusually well positioned to perform such analysis
In the course of my graduate school days, I became familiar with mathematical community. There’s a wide cultural gulf between pure math and finance. My experience was that mathematicians generally view finance as “dirty business,” on account of:
- Often having left-wing political beliefs
- Discomfort with the zero-sum and/or negative-sum nature of finance
- Not identifying with materialism
- Disliking messy problems that are less intrinsically interesting than problems in pure math.
I believe that this gulf has led to a potential opportunity being overlooked: mathematicians may be ideally suited to perform transparent financial analysis that reduces damage from financial bubbles.
This idea occurred to me a few weeks ago. Ideas for philanthropic interventions generally fall apart upon closer examination, and so I wasn’t too optimistic about it holding up. So I was surprised when Neal Koblitz (co-creator of elliptic curve cryptography) raised the same idea in unrelated correspondence:
If mathematicians had been noticing the dubious ways that people in the financial world were claiming to be applying mathematics, and if they had publicly and loudly criticized the misuse of mathematics, then the world might have been spared the collapse of 2008 (or, rather, it wouldn't have been as bad). If mathematicians could have played a role stopping the credit-derivatives bubble before it got out of hand, the economic value of doing that would have been in the trillions of dollars.
When an idea occurs to two people independently, the case for it being a good idea is strengthened. Moreover, Koblitz has a long history of involvement with humanitarian efforts and so can be expected to have perspective on them.
Some reasons why mathematicians seem unusually well suited to the task are:
Transferable Skills — Most mathematicians are unfamiliar with some of most important tools used in finance: statistics, data analysis & programming. But there’s a historical track record of mathematicians being able to pick up these skills and use them to powerful effect. James Simons transitioned from differential geometry to quantitative finance, and became one of the most successful hedge fund managers ever. Cathy O’Neil did a PhD in algebraic number theory under Barry Mazur’s direction, and got a job at DE Shaw, which is one of the most prestigious hedge funds. Mathematicians who are motivated to learn these skills are well positioned to do so.
There are other skills that are very important for successful financial analysis – in particular, one has to have a good eye for empirical data. This is a skill that’s not directly transferable, but it still seems likely that a nontrivial fraction of mathematicians could develop high facility with it.
Intellectual Caliber — The mathematics community has a very dense concentration of intellectual power. James Simons offers a direct point of comparison between math and finance:
Simons won the Oswald Veblan Prize in Geometry before leaving academia to start Renaissance Technologies. There are 25 living mathematicians who have won this prize. The prize is awarded exclusively for work in geometry/topology, and if one looks more broadly at all mathematical fields, one can generate a list of about 100 living mathematicians who were at least as accomplished as Simons at the same age.
After leaving academia, Simons made $10 billion in quantitative finance. What I find most interesting about this is that the situation is not that Simons succeeded where other mathematicians of the same caliber had failed – rather, Simons is virtually the only pure mathematician of his caliber to have left academia. This raises the possibility that there are a handful of elite mathematicians who could make much better financial predictions than most present day actors in finance. Less accomplished but capable mathematicians may also do very well.
Cautiousness — Mathematicians are naturally intellectually conservative, as they spend much of their time rigorously examining arguments for flaws. Thus, they’re unusually unlikely to succumb to greed and fear, which are factors that are thought to play a large role in the behavior of financial markets, and which lead to speculative bubbles. This is corroborated by some of Cathy O’Neil’s remarks on finance.
The above considerations suggest that mathematicians could contribute enormous social value by engaging in transparent financial analysis.
Many mathematicians who I know wish that they could contribute more social value. In the essay Is there beauty in mathematical theories?, the great mathematician Robert Langlands wrote:
In a letter to A.-M.Legendre of 1830, which I came across while preparing this lecture, Jacobi famously wrote
It is true that Mr. Fourier thought that the principal goal of mathematics was their public utility and their use in explaining natural phenomena. A philosopher like him should have known that the only goal of Science is the honor of the human spirit, and that as such, a question in number theory is worth a question concerning the system of the world.
I am not sure it is so easy. I have given a great deal of my life to matters closely related to the theory of numbers, but the honor of the human spirit is, perhaps, too doubtful and too suspect a notion to serve as vindication. […] Moreover, the appeal to the common welfare as a goal of mathematics is, if not then at least now, often abusive. So it is not easy to ﬁnd an apology for a life in mathematics.
A fair number of mathematicians don’t have any choice but to do pure math. Gromov wrote:
You become a mathematician, a slave of this insatiable hunger of your brain, of everybody's brain, for making structures of everything that goes into it.
I'm very sympathetic to Gromov's remark, and I think that for people who constituted in this way, it’s probably best not to try to suppress these urges, as such attempts tend to be unsustainable and result in lower contributions to global welfare rather than higher ones.
But for mathematicians who are:
- Tenured professors who don’t have to worry about career considerations
- Able to enjoy financial analysis
- Strongly motivated to do an excellent job
there may be a major opportunity to contribute enormous social value by conducting transparent high quality financial analysis.
This question warrants further investigation.