Being obsessive by nature, my recent encounter with the CAT
exam has reignited my curiosity for all things mathematics. My shrink has
recommended me not to feed my obsessions, but if I was the kind of guy who took
his shrink’s advice, I wouldn’t need a shrink in the first place.
As often as math is claimed to be interesting by those who live, eat, and drink mathematics, it can
always be made more interesting for the rest of us with bits of curious
factoids peppered over it from time to time. Factoids can range from anywhere
to anything to anybody, but, to me at least, they carry a special significance
if they have to do with the history of a problem or history in general. History,
again to me, is like a story. As repugnant as I found it in school, not unlike
math itself, my interest in history was reignited after school and has grown
exponentially since. This love of history combined with a gathering enthusiasm for math
took me to digging out some remarkable stories about mathematicians both great and
amateur, their discoveries both significant and trivial. The deeper I dug,
however, the more tragic stories that came to life. Some mathematicians who had the godseed in
them to turn mathematics inside-out, upside-down and rebuild it bottom-up, and did to
some extent, sadly couldn’t reach their prime years. I write this blogpost both to keep
their memories alive and to obsess myself more against my shrink’s
recommendation.
G. H. Hardy, Ramanujan’s Cambridge mentor and father-like figure who discovered him, wrote a memoir
in 1940 called A Mathematician’s Apology that is often considered a classic in math
circles and one of the best writings on the inner working of a mathematician's mind. One particular sentence in it caught my attention:
I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.
I present six mathematicians who departed before turning that now-dreaded 40, in descending order of their ages of death:
6. Bernhard Riemann (September
17, 1826 – July 20, 1866; aged 39)
One can dig up several mathematicians who died between 35 and 40, but Riemann holds a special place in mathematics to this day because of a problem that he posed – the Riemann hypothesis – which as of this writing is considered the most important unsolved problem in mathematics, more than 150 years since it was first posed by Riemann, then 33. Although Riemann himself did not anticipate the importance the implications of his hypothesis would have, and in fact it was almost forgotten for 40 years after he died, mathematicians everywhere slowly woke up to it and made it their primary purpose in life to solve it. Alas, no one has. This obsession was documented in a very engaging non-fiction book for the layman by John Derbyshire called Prime Obsession: Bernhard Riemann and the GreatestUnsolved Problem in Mathematics.
One can dig up several mathematicians who died between 35 and 40, but Riemann holds a special place in mathematics to this day because of a problem that he posed – the Riemann hypothesis – which as of this writing is considered the most important unsolved problem in mathematics, more than 150 years since it was first posed by Riemann, then 33. Although Riemann himself did not anticipate the importance the implications of his hypothesis would have, and in fact it was almost forgotten for 40 years after he died, mathematicians everywhere slowly woke up to it and made it their primary purpose in life to solve it. Alas, no one has. This obsession was documented in a very engaging non-fiction book for the layman by John Derbyshire called Prime Obsession: Bernhard Riemann and the GreatestUnsolved Problem in Mathematics.
If you want to become a
millionaire, solve this problem. There’s a prize of $1 million for anyone who
does, and it’s currently listed in the 6 Millenium Prize Problems. The
hypothesis has such profound implications for mathematics that I remember
reading a mathematician saying if he was frozen today and woken up 100 years in
the future, the first question he would ask is, “Has the Riemann hypothesis
been proven?”
Some of Reimann's
contributions to math were key to the development of Einstein’s theory of
relativity. He died at 39 years of age
due to tuberculosis.
5. C. P. Ramanujam (January
9, 1938 – October 27, 1974; aged 36)
No, this is not the
other Ramanujan. The similarities between both, however, are striking. Besides
the similarity in name, both worked extensively in number theory and died in
their 30s. While his contributions may not be as long-lasting, deep-reaching or
mind-bending as Ramanujan’s, there is little doubt that he would’ve been one of
India’s pride possessions had he lived longer. (Coincidentally, the
mathematician he frequently collaborated with, David Mumford, recently won the
Fields Medal – the equivalent of Nobel Prize in mathematics.)
He committed suicide at
the age of 36 due to chronic depression and schizophrenia.
4. Srinivasa Ramanujan (22
December 1887 – 26 April 1920; aged 32)
The crowning jewel of
Indian mathematics, Ramanujan lived a life that can only be compared to his
own. Of all the personalities of history worth their helmet, I find no man as
endlessly fascinating as Ramanujan, and the loss to mathematics because of his
premature death is, simply put, incalculable. Ramanujan had a bent for mathematics from an unusually young age, and it’s ridiculous to even try to
list his theorems, considering that there are 3900 of them, but one of his most
prodigious examples that come to mind: While a teenager, he independently discovered Euler’s identity,
widely considered to be the most beautiful equation in all of mathematics.
When Hardy, himself an
accomplished mathematician and the first westerner to recognize Ramanujan’s
genius, was asked by Paul Erdos what his own most signification contribution to
mathematics was, he replied that it was the discovery of Ramanujan. Hardy once
ranked all the great mathematicians of his time with a score out of 100, and
while he gave himself a 35, he placed Ramanujan at the top with a score of 100
and said that he has never seen a mathematician like him, comparing him to the
likes of Euler and Gauss.
The movie Good Will
Hunting is loosely based on the relationship between Hardy and Ramanujan. This
quote by Hardy adds more light to the fact:
The tragedy of Ramanujan was not that he died young, but that, during his five unfortunate years, his genius was misdirected, side-tracked, and to a certain extent distorted. He would have been a greater mathematician if he could have been caught and tamed a little in his youth; he would have discovered more that was new, and that, no doubt of greater importance.
Reminds you of Matt
Damon’s character? Me too. Ramanujan was a very difficult person, often
bad-tempered, easily irritable, and notoriously stubborn. This is a letter
written by his dad to The Hindu, notifying the editor of a missing person’s notice to be
published in the newspaper after a quarrel between him and Ramanujan, and Ramanujan ran away from home with tempers burning
He died at the age of 32 of malnutrition and related causes. A biopic film on Ramanujan is currently in the making, although I think it will be a shit film. There is, however, an outstanding Ramanujan biography called The Man Who Knew Infinity written by Robert Kanigel.
Hardy called his collaboration
with Ramanujan as “the one romantic incident in my life."
3. Frank Ramsey (22 February 1903 — 19 January
1930; aged 26)
Unlike other mathematicians
on this list, Ramsey is the only one who was much more than just that. Being an economist and a philosopher, he was
also a good friend of that insurmountable Austrian genius, Ludwig Wittgenstein,
and translated Tractatus Logico-Philosophicus into English – one of the most
important works of 20th century philosophy (logic).
The work Ramsey did in
mathematics though, starting with Ramsey’s theorem, was so significant that it
opened up a whole new branch of mathematics called Ramsey theory that deals
with some very important properties in combinatorics.
He died at the age of
26, due to postoperative jaundice contracted after a surgery gone wrong.
2. Niels Henrik Abel (5
August 1802 – 6 April 1829; aged 26)
The list of
mathematicians who died at 26 is very populous (Ramsey, Pavel Urysohn, René
Gâteaux), but this Norwegian prodigy, reminiscent of that recent chess prodigy
who made news, being poor as shit all his short life, concocted so many groundbreaking
theories that Charles Hermite, another legendary mathematician, was noted to
have said: "Abel has left mathematicians enough to keep them busy for five
hundred years."
In his honor, the
Norwegian government and the King of Norway annually present a mathematics
prize – Abel Prize – to an international mathematician of reputation. Along with the Fields
Medal, Abel Prize, too, is called the Nobel Prize of mathematics. The current head of Indian Statistical
Institute, S. R. Srinivasa Varadhan, has won the Abel Prize.
He died at the age of
26, succumbing to serious illness. His life was encapsulated in his biography, Niels Henrik Abel and his Times: Called Too Soon by Flames Afar by Richard
R. Daly.
1. Evariste Galois (25
October 1811 – 31 May 1832; aged 20)
Don’t let that pretty
little fag face fool you. Galois (pronounced Gal-Wa) was radical of his political
views during the French Revolution and died of gunshot wounds sustained in
a duel over a girl.
Galois did most of his
important work as a teenager. He solved a long-standing problem in the
solutions to polynomials, and founded the Galois theory. Of particular interest
is the fact that Galois fields and Galois groups were instrumental in proving Fermat’s Last Theorem – the deceptively simple-looking conjecture that has the Guinness record of being the most difficult problem in the history of mathematics and that remained
unsolved for 300 years until Andrew Wiles solved it in 1993, for which he was knighted
and a comet was named after him.
Galois died at the age
of 20, from being a chronic asshole.
All these men left
behind a legacy at a very young age that lasted centuries and will inspire
mathematicians for millennia to come.
Which raises a troubling
question best avoided: When are you going to change the world?
