Technology for Which Mathematical Activities?/1
Timothy Y. Chow
tchow at math.princeton.edu
Wed Mar 10 20:42:27 EST 2021
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
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