remembered for any sort of spectacular success in my later years; maybe
I can be remembered for a spectacular failure, like Comte or Newcomb.
After all, we live in a society in which notoriety and fame are often con-
fused.
Besides, mathematics is an area in which a really good question can
achieve so much publicity that its eventual resolution, and those who re-
solve it, almost become historical footnotes to the question itself. Pierre
de Fermat, Bernhard Riemann, and Henri Poincaré are among the greats
of mathematics—but Fermat is almost certainly best remembered for
Fermat’s last theorem, Riemann for the Riemann hypothesis, and Poin-
caré for the Poincaré conjecture. Fermat’s last theorem fell a decade ago
to Andrew Wiles, who was denied a Fields Medal for his accomplishment
because he was too old (Fields Medals are reserved for thirtysomethings
and twentysomethings, and Wiles missed it by a year or so). The Poincaré
conjecture succumbed more recently, and argument still exists in the
mathematical community as to who should get the lion’s share of the
credit, with the Russian mathematician Grigori Pereleman in the lead.
The Riemann hypothesis is still just that—a hypothesis. Besides, one can
go into the annals with a great conjecture, even if one is not a great math-
ematician. Most mathematicians would be hard-pressed to name a single
one of Christian Goldbach’s mathematical accomplishments,^1 but every-
one knows Goldbach’s conjecture—the elegantly simple “every even
number is the sum of two primes”—a conjecture understandable to
grade-school children but still standing unproved after more than a quar-
ter of a millennium of effort.
The Impact of Age
There is a perception that mathematicians and physicists do their best
work before they are thirty. That’s not necessarily true, but it is true that
the young make a disproportionate contribution to these subjects. This
may be because the young are less willing to accept the generally accepted
paradigms. Unquestionably, age confers both disadvantages and advan-
tages.
Sometimes these disadvantages force practitioners into other areas. It
is said with some truth that as physicists age, they become philosophers.
They tend to pay less attention to discovering the phenomena of reality
than to ref lecting on the nature of reality. With the possibility of multiple
dimensions and the nature of quantum reality still unresolved, there is
no question that there is considerable room for ref lection.
When I was young, like most boys growing up in my era, I was ex-
238 How Math Explains the World