[FOM] Prove something weaker!

[Timothy Y. Chow]

On Mon, 13 Jul 2015, Joe Shipman wrote:
> My worry is that emphasis on the "big" conjectures might retard progress 
> by discouraging people from working on much weaker questions, especially 
> with techniques that might not be promising for generalization to the 
> "big" conjecture but which would still represent a major advance in what 
> we know.

It's hard for me to believe that this is anything to worry about.  The 
standard mechanism is, post a big conjecture as an advertisement to 
attract people to the field, and once they're in the door, direct them to 
the current frontier, complete with all the mini-conjectures that are 
not completely out of current reach.

The only real drawback I see is that this mechanism has a tendency to shut 
out individuals who lack social access to the community of experts.  But 
that's a much more general problem that won't be solved by greater 
publicization of weaker conjectures.

> Schanuel's conjecture is an interesting case because it is basically 
> saying that a certain structure is free, so it's hard to think of what a 
> partial result might look like (maybe "no nontrivial relations of 
> syntactic length N" for some small N?).

There are plenty of partial results, such as Baker's theorem, and weaker 
conjectures, such as the four exponentials conjecture.

Tim