The second-rate mind of an expositor


Exposition, criticism, appreciation, is work for second-rate minds.

At least, so says Godfrey Harold Hardy, the godfather of stuffy mathematicians everywhere. To Hardy, the intellectual world is divided into two camps: Those who create, and those who commentate. The creators are artists, scientists, and politicians. The commentators are art-critics, expositors, and bloggers. The creators possess a first-rate mind, sharp enough to forge connections heretofore unseen. The commentators merely have second-rate minds, just capable enough to understand what the greats do.

Like any respectable gate-keeper, Hardy makes sure that his preferred activity is placed in the most prestigious category. Professional mathematicians are not only creators, but creators of the highest order. “Immortality may be a silly word,” says Hardy, “but probably a mathematician has the best chance of whatever it may mean.”

Hardy is onto something here. Mathematical immortality is alluring. Finding “the truth” or being a swell teacher is nice, but the real game is showing everyone, for all time, just how great you really were. Why publish papers? Why prepare talks? Why bash your head against difficult problems? Because if you are successful, then you get to put a new bullet point on your CV, and if you get enough bullet points in the right places, then you get respect, possibly forever.

As Hardy puts it, “a man’s first duty, a young man’s at any rate, is to be ambitious.” I am in total agreement with Hardy on this point. It is refreshing to read such a blunt statement of purpose. Another excellent example of this honesty is Richard Hamming’s “You and Your Research”, wherein Hamming states that a scientist ought to desire great discoveries and the prestige that they bring. Sure enough, both Hardy and Hamming produced their share of amazing research.

And yet, for all the wonderful work that Hardy’s first-rate mind produced, being a moderately well-known mathematician does not merit even a footnote in any account of human history. He is less known to the man on the street, and has made a smaller impact on their life, than the town barber. Occasionally a mathematician stumbles into true immortality, like Euler, Newton, and Euclid, but even then no one but mathematicians has more than a passing knowledge of their names, much less what they did. Hardy himself wouldn’t rank in the top fifty English historical figures, even of just the 20th century. He would be lucky to be an answer on Jeopardy!.

In contrast, who are the most famous mathematical people alive today? They are the mathematics communicators. People like James Grime and Matt Parker, both featured in Brady Haran’s excellent Numberphile series. They are the mathematical spokespeople, like Po-Shen Loh, who calls himself an “educator and coach” before “academic and researcher.” They are pop-mathematics authors like Eugenia Cheng, who writes New York Times bestsellers. They are textbook authors like James Stewart, who wrote one of the most popular calculus texts of the past twenty years. Even my famous advisor is at least as well known in the mathematics community for his opinions as he is for his research. Expositors may have “second-rate minds,” but they also have first-rate impact.

Lost in his pontificating, Hardy forgot that no one cares what mathematicians do. Even other mathematicians barely care. Of all the academic disciplines, mathematics has got to be one of the most obscure and meaningless to the average person. Therefore, the greatest impact a mathematically-inclined person might have on the world is to explain mathematics to the public, or to work in some area that uses mathematics.

There is no greater demonstration of Hardy’s absolute disconnect than the following passage, where he describes how a person might defend what non-mathematical they do:

“I do what I do because it is the one and only thing that I can do at all well. I am a lawyer, or a stockbroker, or a professional cricketer, because I have some real talent for that particular job. I am a lawyer because I have a fluent tongue, and am interested in legal subtleties; I am a stockbroker because my judgment of the markets is quick and sound; I am a professional cricketer because I can bat unusually well. I agree that it might be better to be a poet or a mathematician, but unfortunately I have no talent for such pursuits.

Let’s do as Hardy suggests and pick a famous, contemporary athlete. Who is better remembered by the world, Hardy or Babe Ruth?

I have great professional admiration for Hardy. The mathematical community surely owes him a debt of gratitude. However, I must remind his spirit that, outside of this small cult of strange people called “mathematicians,” he will soon be forgotten. The tiny chance that he has to be remembered by the world is not for his research, but for his reluctantly-written Apology.

Fortunately we do not need to pick favorites. The aim of research is not new facts, but interesting stories. In this sense, expositors and researchers are two sides of the same coin: A mine is of little use to the world without a refinery to process the minerals. Together, researchers and expositors produce stories for experts and non-experts, which lets everyone share in the joy of human ingenuity. Amen.