# The second-rate mind of an expositor

** Published:**

*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.