What’s the most impressive research-y feat interpolating AIs can theoretically do, fixing their training data to (say) today?
I don’t have a good sense of this in general, but in pure math it’s probably at least Fields medal-tier, if laudatios like that of Akshay Venkatesh are anything to go by:
Akshay Venkatesh stands out for the startlingly original way he has connected number theory problems to deep results in other areas. Far from using them as “black boxes” to crank out solutions, Venkatesh brings fresh insights to the results and highlights their unexpected connections to number theory. In this way he has made striking advances in number theory while also greatly enriching other branches of mathematics.
This, and the rest of the laudatio, reads like a very souped-up version of what OpenAI’s recent internal model did with Erdos problem #90 (itself a souped-up version of what GPT-5.4 Pro did with problem #1196), give or take a few Gowers-hints. One of Venkatesh’s advantages over other top-tier mathematicians is his sheer range, the thing frontier models do vastly better than humans at.
And I can imagine, for instance, 2 years of advancements enabling a frontier model to skillfully deploy the late legendary Jean Bourgain’s toolkit. Bourgain was regularly spoken of by other world-leading mathematicians as “effectively a god”. Terry Tao:
When I was a graduate student in Princeton, Tom Wolff came and gave a course on recent progress on the restriction and Kakeya conjectures, starting from the breakthrough work of Jean Bourgain in a now famous 1991 paper in Geom. Func. Anal.. I struggled with that paper for many months; it was by far the most difficult paper I had to read as a graduate student, as Jean would focus on the most essential components of an argument, treating more secondary details (such as rigorously formalising the uncertainty principle) in very brief sentences.
Tao goes on to describe Bourgain’s style and toolkit:
I began to realise that Jean had a certain collection of tools, heuristics, and principles that he regarded as “basic”, such as dyadic decomposition and the uncertainty principle, and by working “modulo” these tools (that is, by regarding any step consisting solely of application of these tools as trivial), one could proceed much more rapidly and efficiently. By reading through Jean’s papers, I was able to add these tools to my own “basic” toolkit, which then became a fundamental starting point for much of my own research. Indeed, a large fraction of my early work could be summarised as “take one of Jean’s papers, understand the techniques used there, and try to improve upon the final results a bit”.
In time, I started looking forward to reading the latest paper of Jean. I remember being particularly impressed by his 1999 JAMS paper on global solutions of the energy-critical nonlinear Schrodinger equation for spherically symmetric data. It’s hard to describe (especially in lay terms) the experience of reading through (and finally absorbing) the sections of this paper one by one; the best analogy I can come up with would be watching an expert video game player nimbly navigate his or her way through increasingly difficult levels of some video game, with the end of each level (or section) culminating in a fight with a huge “boss” that was eventually dispatched using an array of special weapons that the player happened to have at hand.
Imagine unleashing thousands of Bourgain-toolkit interpolators math-wide in 2028. I think I’m being conservative here, not assuming continual learning or whatever, not even assuming anyone else’s toolkit, and yet I still find it hard to imagine how transformative this would be. And this is just for pure math.
I was researching ontology of mental states. Gestalt therapy distinguishing mental process between figure and ground where both as part of the conscious landscape. Freudian models distinguish between conscious, pre-conscious and unconscious.
I had a previous chat about the gestalt therapy model and was asking a model (I think 5.0) for the Freudian categories. On it’s own it suggested to have a figure / ground / pre-conscious / unconscious model for my work, without me even explicitely asking it to do a synthesis. It did seem to understand where my research was going after asking it to explain both frameworks to on it’s own suggest the ontological synthesis that as far as the model is concerned nobody else made previously.
However on the other side, the models do have some trouble with adopting the new ontology to use it for reasoning. The models seem to be good enough to come up with ideas for improving the ontology but you need a new training run to actually integrate new ontology into the model.
What’s the most impressive research-y feat interpolating AIs can theoretically do, fixing their training data to (say) today?
I don’t have a good sense of this in general, but in pure math it’s probably at least Fields medal-tier, if laudatios like that of Akshay Venkatesh are anything to go by:
This, and the rest of the laudatio, reads like a very souped-up version of what OpenAI’s recent internal model did with Erdos problem #90 (itself a souped-up version of what GPT-5.4 Pro did with problem #1196), give or take a few Gowers-hints. One of Venkatesh’s advantages over other top-tier mathematicians is his sheer range, the thing frontier models do vastly better than humans at.
And I can imagine, for instance, 2 years of advancements enabling a frontier model to skillfully deploy the late legendary Jean Bourgain’s toolkit. Bourgain was regularly spoken of by other world-leading mathematicians as “effectively a god”. Terry Tao:
Tao goes on to describe Bourgain’s style and toolkit:
Imagine unleashing thousands of Bourgain-toolkit interpolators math-wide in 2028. I think I’m being conservative here, not assuming continual learning or whatever, not even assuming anyone else’s toolkit, and yet I still find it hard to imagine how transformative this would be. And this is just for pure math.
I was researching ontology of mental states. Gestalt therapy distinguishing mental process between figure and ground where both as part of the conscious landscape. Freudian models distinguish between conscious, pre-conscious and unconscious.
I had a previous chat about the gestalt therapy model and was asking a model (I think 5.0) for the Freudian categories. On it’s own it suggested to have a figure / ground / pre-conscious / unconscious model for my work, without me even explicitely asking it to do a synthesis. It did seem to understand where my research was going after asking it to explain both frameworks to on it’s own suggest the ontological synthesis that as far as the model is concerned nobody else made previously.
However on the other side, the models do have some trouble with adopting the new ontology to use it for reasoning. The models seem to be good enough to come up with ideas for improving the ontology but you need a new training run to actually integrate new ontology into the model.
Interesting. Seth’s comment seems relevant.