Technology for Which Mathematical Activities?/1

[Timothy Y. Chow]

Kevin Buzzard wrote:

> I would naively imagine that computers will be better at good 
> conjectures than good definitions.

There are two examples that I know of; I would be interested in hearing 
about others.

Siemion Fajtlowicz wrote a program in the 1980s called "Graffiti" to 
generate graph-theoretic conjectures.  It was mildly successful; it came 
up with several conjectures that were new and sufficiently interesting 
that graph theorists spent time on them and published papers proving them. 
I'm not sure what the best reference is, but one reference is Fajtlowicz's 
1988 paper, "On conjectures of Graffiti," Discrete Math. 72:113-118.

The "Ramanujan Machine" has generated some conjectural continued fraction 
identities.

https://arxiv.org/abs/1907.00205
http://www.ramanujanmachine.com/

These folks got off on the wrong foot with the number theory community 
because they committed several faux pas (claiming that certain things were 
new without checking with an expert first; advertising their results using 
language that traditional mathematicians find crass or distasteful; etc.). 
But I think that some genuinely new conjectures have emerged.  How 
interesting the conjectures are is of course debatable; probably number 
theorists need to get involved in order to steer the project in a more 
mathematically interesting direction.

Just to be clear, I'm intentionally omitting standard "experimental 
mathematics" stuff such as using PSLQ or similar algorithms to search 
numerically for interesting evaluations of integrals or infinite series; 
these don't seem to be quite in the spirit of what I think Kevin is 
talking about.

Tim