Comment by contubernio
3 days ago
We research mathematicians are still learning how to use AI in research and how to deal with the output. I drafted eight papers last weekend. This week I advanced on none. AI still gets stuck at the key point on a problem where there isn't already a lot of work done. What falls is where techniques not known to the researcher are available and profitably employed - ai brings them into the fray fast - and someone with experience immediately sees where to go with it - and the dominos fall.
So far AI still doesn't make definitions. It tries but it doesn't really see structure - only patterns on which it can impose (by brute force) known structures.
What's not clear is how the professional infrastructure will survive. Journals seem likely to die. The arxiv is swamped. A human can't assess the volume of the output. Serious conjectures have fallen and serious people have checked them.
We are looking for constructive and productive and socially useful ways forward. One reflection is that a lot of what we have been doing was maybe not so interesting as we thought.
> where techniques not known to the researcher are available and profitably employed - ai brings them into the fray fast - and someone with experience immediately sees where to go with it
> So far AI still doesn't make definitions. It tries but it doesn't really see structure - only patterns on which it can impose (by brute force) known structures.
Insightful and nicely phrased!
Mathematicians are victims of their own success, by systematizing Formalism which made AI possible in the first place.
Paradoxically, they should also be indicted for removing the Human element by deemphasizing the study of Philosophy of Mathematics (i.e. ontology/epistemology/discovery/invention) and its mapping to Reality, but focusing only on formalization as an end in itself.
As you point out, the "definitions" (i.e. conceptual theory) are what is the critical aspect of discovering/inventing/doing mathematics and this has been forgotten in mathematics education since the Formalists gained ascendancy.
I think it is time to go back to the foundations of Mathematics and its Teaching viz. various types of Logical Reasoning, discovered/invented structures and their relationships based on Reality (the ontology and epistemology), with the final goal of understanding Nature itself.
Only a minor in mathematics here. That's interesting that it struggles with definitions. Maybe unsurprising given the different ways they're chosen and written (motivational, aesthetic, pedagogical, etc)? A big lever to keep hold of.