TITLE: The Scientific Value of Reading Old Texts
AUTHOR: Eugene Wallingford
DATE: November 20, 2015 6:02 PM
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BODY:
In
Numbers, Toys and Music,
the editors of Plus Magazine interview Manjul Bhargava, who won a
2014 Fields Medal for his work on a problem involving a certain
class of square numbers.
Bhargava talked about getting his start on problems of this sort not
by studying Gauss's work from nineteenth century, but by reading the
work of the seventh century mathematician Brahmagupta in the original
Sanskrit. He said it was exciting to read original texts and old
translations of original texts from at least two perspectives.
Historically, you see an idea as it is encountered and discovered.
It's an adventure story. Mathematically, you see the idea *as it
was* when it was discovered, before it has been reinterpreted
over many years by more modern mathematicians, using newer, fancier,
and often more complicated jargon than was available to the original
solver of the problem.
He thinks this is an important step in making a problem your own:
*
So by going back to the original you can bypass the way of thinking
that history has somehow decided to take, and by forgetting about
that you can then take your own path. Sometimes you get too
influenced by the way people have thought about something for 200
years, that if you learn it that way that's the only way you know
how to think. If you go back to the beginning, forget all that new
stuff that happened, go back to the beginning. Think about it in a
totally new way and develop your own path.
*

Bhargava isn't saying that we can ignore the history of math since
ancient times. In his Fields-winning work, he drew heavily on
ideas about hyperelliptic curves that were developed over the last
century, as well as computational techniques unavailable to his
forebears. He was prepared with experience and deep knowledge.
But by going back to Brahmagupta's work, he learned to think about
the problem in simpler terms, unconstrained by the accumulated
expectations of modern mathematics. Starting from a simpler set
of ideas, he was able to make the problem his own and find his own
way toward a solution.
This is good advice in computing as well. When CS researchers tell
us to read the work of McCarthy, Newell and Simon, Sutherland, and
Engelbart, they are channeling the same wisdom that helped Manjul
Bhargava
discover new truths
about the structure of square numbers.
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