The Meaning in the (Financial) Mathematics

Having chosen death over exile after being charged with impiety and corrupting the youth of Greece, Socrates declared at his trial that the unexamined life was not worth living. Thus spawned millennia of thinkers dedicated to understanding the ways in which we do and ought to interact with each other and our world.

Aristotle told us how to live a good life. Kant taught us what it meant to be a citizen of the world. Whitman and Joyce showed us eternal aspects of the human condition. In disciplines from philosophy to literature, freshmen are engaging with these greats, thinking carefully about what a good life entails. Meanwhile, freshmen in economics are desperately trying to memorize the derivative of log x before their unit test.

When Socrates uttered his now-famous declaration, philosophy literally meant “a love of all knowledge,” and the careful examination of one’s life was the key to wisdom. As time passed, philosophy became partitioned into the natural, moral, and metaphysical realms, and somewhere along the way, the question of how we ought to live became scattered across hundreds of disciplines and sub-disciplines.

The humanities’ connection to the examined life remained clear; Aristotle’s teachings on how we should engage with the world have stayed accessible and relevant. But in many of the fields grounded in mathematics, meaning has given way to algebra.

Every student in introductory statistics knows how to substitute probabilities into Bayes’ rule, and yet many commit the base rate fallacy with gusto. Most students of economics know that the solution to the problem of optimizing consumption over time involves equating weighted marginal utilities; the same students balk at the suggestion that they should try to spend more, not less, during their broke college years. The same investment bankers who compute present values 80 hours a week for a living drop their jaws at a one-time signing bonus worth a tenth of their annual salary. There is a fundamental disconnect between the theory we learn and the way we live our lives; with apologies to Oscar Wilde and Philip Fisher, it’s all too easy to know the mathematics of everything and the meaning of nothing.

This state of affairs is not, by any means, a necessary byproduct of mathematical formalization. Arrow, Sen, and Black put the theory of how to collectively achieve social welfare on axiomatic grounds, while Bayes, Pearson, and Jeffreys laid the basis of how science, and the endeavor of knowledge-gathering as a whole, could be understood according to Bayes’ eponymous formula. But somewhere in the midst of problem set deadlines and lectures slides filled with Greek letters, the connection of these ideas to our daily lives has slowly been severed.

Such a divergence is unnatural to say the least: equating derivatives of utility functions has everything to do with how we might maximize our lifetime happiness, and the expected value of dice games can tell us much about the ways we should choose our romantic partners. The basic idea of present value can tell us both why extravagant signing bonuses shouldn’t matter (too much), and why arguments lamenting the flow of top Harvard graduates to lucrative but ostensibly soul-draining fields have less bite than their proponents might think.

Some readers may have noted that the concepts hinted at above are precisely those that underpin the theory of finance, which exists at the intersection of economics and statistics. Though perhaps more well-known for giving rise to a vampire squid-like industry with its tentacles wrapped around the face of humanity, these notions can also help us understand how we might better live our lives. And as we do, I hope that any cephalopod-based conceptions of the financial industry will begin to give way to one of a sprawling, complicated, necessary, and admittedly imperfect human endeavor, built upon some of the most beautiful and elegant of ideas.

The links between financial theory and how we ought to approach the world around us are plentiful and applicable, so long as we take the time to look. The only challenge that remains is to examine our lives not only from the perspective of the humanities but also the more dismal sciences, as we search for the meaning in the mathematics.

Marshall Zhang ’16, is a statistics and mathematics joint-concentrator with a secondary field in philosophy. He lives in Mather House.