25 April 2020 | New Scientist | 21S
RINIVASA RAMANUJAN
was a mathematician like
no other. He had almost
no formal training yet produced
some of the most stunning
mathematical results of all time.
This month marks the 100th
anniversary of Ramanujan’s death.
Yet his extraordinary ideas and
remarkable life story are still
highly influential in mathematics,
including in inspiring both of us
to pursue mathematical research.
Ramanujan was born in 1887
and became obsessed with
mathematics as a teen. He spent
so much time making original
discoveries in mathematics that
he flunked out of college – twice!
In 1913, he sent a now-legendary
letter to G. H. Hardy, a
mathematician at the University
of Cambridge. In pages upon pages
of dense formulae, Ramanujan
seemed to report from a parallel
universe. He later said he saw the
equations in his dreams.
The formulae lacked
explanations. Some were well
known, yet presented as original
results; some claims were
impossible but displayed a wildly
creative flair; and some formulae
were so breathtaking that Hardy
wrote: “They must be true
because, if they were not true,
no one would have had the
imagination to invent them.”
Hardy was beyond intrigued,
and invited Ramanujan to join
him in Cambridge.
When Ramanujan arrived in the
UK, Europe was at the edge of war,
JOSand seismic shifts were taking
IE^ F
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Over the next five years,
Ramanujan and Hardy
would introduce a host of
groundbreaking ideas in the field
of number theory. From advances
in our knowledge of partitions –
ways to split up numbers, which is
surprisingly complicated – to the
powerful circle method that is
now a ubiquitous tool for
mathematicians and physicists,
the pair’s results sent shock waves
through mathematics.
For his advances, Ramanujan
became the first mathematician
from India to be elected afellow of the Royal Society, in 1918.
Ramanujan returned to India
in 1919 a national hero, but he
was in failing health, diagnosed
with tuberculosis, which is
now believed to have been a
misdiagnosis. Reunited with his
family and wife, the 32-year-old
number theorist made his most
profound discovery, even as his
health worsened.
In a letter to Hardy dated
12 January 1920, Ramanujan
sketched details of an enigmatic,
previously undreamed-of theory
of “mock theta functions” –
strangely symmetric equations.
Before Hardy could reply, hereceived the news that Ramanujan
had died.
In the century since
Ramanujan’s final letter to Hardy,
mathematicians have stretched
their collective mind to
understand the underlying
theories he didn’t write down.
In probing the consequences of
Ramanujan’s work, Jean-Pierre
Serre and Pierre Deligne
discovered Galois representations,
and the latter was awarded a
Fields medal – a sort of maths
Nobel prize.
Work in this direction sparked
a chain reaction of advances in
20th-century mathematics,
culminating in the 1995 proof by
Andrew Wiles and Richard Taylor
of the almost 400-year-old
conjecture known as Fermat’s
last theorem.
The sphere of Ramanujan’s
influence continues to expand:
modern fields building on his
formulae range from signal
processing to black hole physics.
It is only in the 21st century that
his mock theta functions have
come to be understood and appear
to describe stringy black holes.
Contemporary mathematicians
are still fleshing out the details
of the theories in Ramanujan’s
dreams. ❚Dreamy mathematics
Srinivisa Ramanujan’s mathematics seemed to come from a parallel universe
and we are still tr ying to understand it today, say Ken Ono and Robert Schneider