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

[Timothy Y. Chow]

Colin McLarty 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.

What I think is really going on in all these cases is that people are 
primarily impressed by how "smart" someone appears to be.  Secondarily, 
they are impressed when someone's work opens up vast new vistas for 
research.

If someone scores high in both categories then they'll rack up more points 
than someone who scores high in just one category.  To that extent I agree 
with Friedman.  However, I don't think that heavy machinery per se 
improves your chances of scoring high in both categories.  Both heavy 
machinery and special techniques can make you look "smart."  I would also 
argue that heavy machinery is much less correlated to subsequent 
fruitfulness than Friedman (or even McLarty, who seems to accept that it 
is a rule with few exceptions) suggests.  Bhargava's work is a pretty good 
illustration of lightweight machinery being fruitful (though my opinion is 
that his work uses more machinery than you might think if you just read 
the press releases), but actually if you look around you can find plenty 
of examples.  The reason they get overlooked is that they are often so 
simple that they don't look "smart" and hence lack glamor and prestige. 
Similarly there are lots of papers that introduce heavy machinery that 
solves just one problem and hence get ignored.

Tim