[FOM] Manjul Bhargava: A nice exception to a rule

David Roberts david.roberts at adelaide.edu.au
Fri Aug 15 20:19:49 EDT 2014

Regarding Bhargava, Tim Gowers writes [1]

>But the first of his Fields-medal-earning results was quite extraordinary. As a PhD student, he decided to do what few people do, and actually read the Disquisitiones. He then did what even fewer people do: he decided that he could improve on Gauss. More precisely, he felt that Gauss’s definition of the composition law [DR: taking 20 pages or so] was hard to understand and that it should be possible to replace it by something better and more transparent.

>I should say that there are more modern ways of understanding the composition law, but they are also more abstract. Bhargava was interested in a definition that would be computational but better than Gauss’s. I suppose it isn’t completely surprising that Gauss might have produced something suboptimal, but what is surprising is that it was suboptimal and nobody had improved it in 200 years.


>In this way, Bhargava found a symmetric reformulation of Gauss composition. And having found the right way of thinking about it, he was able to do what Gauss couldn’t, namely generalize it. He found 14 more...

[1] http://gowers.wordpress.com/2014/08/15/icm2014-bhargava-laudatio/



On 14 August 2014 22:04, Colin McLarty <colin.mclarty at case.edu> wrote:
> On Wed, Aug 13, 2014 at 3:13 AM, Harvey Friedman <hmflogic at gmail.com> wrote,
> among much else, that among mathematicians in general when a
>> solution uses considerable machinery (t)his is considered an extreme plus
>> over it being solved by extremely
>> clever special methods.  There is rationale for this, mainly that if big
>> machines are used, then that promises
>> further solutions to further problems more than an extremely clever
>> special method.
> Yes that is common.  But the Fields Medal to Manjul Bhargava shows clever
> methods without heavy machinery can sometimes also promise further solutions
> to further problems.
> Bhargava cites some mathematicians who use heavy machinery (Langlands, de
> Jong) but I don't know if he cites the heavier parts of their work.  And
> what people like about his work is how light weight the machinery is, yet
> vastly productive, and suggestive of much more.  People compare his work to
> Gauss's.
> Colin
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Dr David Roberts
Research Associate
School of Mathematical Sciences
University of Adelaide
SA 5005

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