About a year ago I was talking to some of my residents (I
was an RA for two years) about their classes when two of them, Rob and Lucas,
presented me with an interesting conjecture. Rob and Lucas claimed that 1 + 2 + 3 + 4 +…. = -1/12. I was not convinced, but the boys set about
demonstrating the mathematical veracity of their claim and eventually succeeded, and down the rabbit hole I fell.
It turns out that the sum presented to me by Rob and Lucas
has a name. It’s called the Ramanujan summation and it’s not so much a sum in
the traditional sense as it is a method of assigning a numerical value to an
infinite divergent series which is important if you’re interested in studying
such series. I am most definitely not interested and if you are, then now is the time to leave this corner
of the Internet and find a more mathematically informed one. What I became
interested in was not infinite series, but the mathematician Srinivasa
Ramanujan who developed the Ramanujan summation.
It turns out that Srinivasa Ramanujan was a really interesting guy and I don't mean footnote interesting. I mean "this guy's life could be a Hollywood movie" interesting. Ramanujan was
born in 1887 in colonial India. He excelled at but did not enjoy primary or
secondary school and flunked out of two different colleges before living in extreme
poverty while independently pursuing mathematics. Ramanujan’s work began to
draw attention from other Indian mathematicians, but there were doubts about
his real abilities.
It was in 1913 that Ramanujan’s life took a fateful turn
that would ensure his mathematical legacy would long outlive him. In a
nine-page letter, Ramanujan wrote to renowned British mathematician G.H. Hardy,
a professor at Cambridge. Ramanujan sought validation of his mathematical
theories and abilities, but Hardy was skeptical at first, wondering if
Ramanujan was a fraud. However, Hardy came around as he further studied
Ramanujan’s work. Ramanujan’s letter to Hardy included some rediscoveries of
mathematical theorems that were new to Ramanujan but old to the western
mathematical world, but some of them were wholly new and incredibly innovative.
Hardy wrote back to Ramanujan, which resulted in Ramanujan’s
travel to England to study under and work with Hardy and his colleagues at
Cambridge. Ramanujan died tragically at age
32 after several years of battling mental and physical illness, but in those three decades he produced over 3000 original theorems and his
work remains invaluable to modern mathematicians. Hardy once remarked that his
collaboration with Ramanujan was “the one romantic incident of my life.”
Ramanujan has been on my mind a lot lately because he drives
home an important point for me. Genius can come from anywhere and everywhere. Ramanujan
was gifted not only with incredible mathematical talent, but also with a set of
highly fortunate circumstances that allowed him to share his talent with the
world. Many students who are just as intelligent and innovative are not given
such a chance. That is why the work of Teach for America and education
professionals across the country and world is so important. Just as Ramanujan’s
incredible work on infinite series could have remained locked away in the mind
of a poor mathematician from Madras, the keys to curing cancer or reversing
climate change or achieving peace in the Middle East could remain locked away
in the mind of a student in a failing school in the Bronx or central LA or
rural Mississippi. It’s up to everyone to ensure that that is not the case.
Certainly the world owed Ramanujan better 100 years ago and certainly we owe
our students better today.
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