More thoughts on benchmarks

On progressive defeatism and its implications

Seen at Colorado State University in Fort Collins, CO, site of this year’s Summer Research Institute in Algebraic Geometry

I started writing this at one of the numerous international conferences that structure the mathematician’s agenda, especially during the summer. Even after COVID forced these meetings online, revealing to their participants that much of the benefit of attendance was preserved in virtual mode, any mathematician who is active in international collaboration will tell you that nothing beats gathering in person as a way to share the latest news in the field and create social cohesion. The hypothetical mathematician referenced in the last sentence may not remember to mention, but I will, how the exchange of vague and unstructured thoughts that is a feature of such conferences, often in response to questions raised by the audience at the end of (or even in the middle of) a talk, plays an indispensable role in the subsequent development of the field.

The history of the series of conferences to which this one belongs gives an outstanding example of this phenomenon. The series began in 1964 with a legendary conference in Woods Hole, MA, followed by one in Arcata, CA in 1974¹, and then every 10 years starting in 1985, always under the auspices of the American Mathematical Society until this one in Fort Collins, CO. Woods Hole has been memorialized in the history of mathematics by the Woods Hole Fixed Point Theorem, proved by Atiyah and Bott, who learned at the Woods Hole conference that a version of the theorem had been conjectured by Shimura. Would there have been a Woods Hole Fixed Point Theorem if the mathematicians hadn’t met face to face in Woods Hole?²

During my four days in Fort Collins I saw nothing to suggest that robots or any other manifestations of artificial intelligence were attending the talks, though I’m not completely sure about the online participants. By the time algebraic geometers meet again in 2035, this won’t be possible, if you believe what Eric Schmidt calls the “San Francisco consensus” in an article published the other week in Forbes:

The consensus timeline is breathtakingly compressed:

1. Within months: Programming jobs and skilled roles begin vanishing faster than Taylor Swift concert tickets, transforming labor markets overnight.

2. Within 3-6 years: Widespread artificial general intelligence (AGI) emerges, with machines rivaling our brightest minds across intellectual domains.

3. In a decade [my emphasis]: Artificial superintelligence (ASI) arrives. AI systems make discoveries beyond human comprehension. Picture explaining quantum mechanics to your golden retriever. Now imagine you are the retriever!

It turns out that more than a few colleagues at the Fort Collins meeting, and not only the younger ones, have been directly involved with the corporate interests³ behind this San Francisco consensus. A few of them even participated in designing benchmarks to industry specifications, rather than benchmarks that might have intrinsic interest for mathematics, like those in my previous post.⁴ This surprised me, since none of these colleagues strikes me as an ideologue, so I asked them what they thought they were doing. One expressed an interest in “seeing how the sausage is made,” while another used the word “bulldozer” to refer to the arrival of AI in mathematics, suggesting that it would be better to claim a perch on top of the bulldozer than to stand in its path.

Such answers, coming from colleagues who could hardly be more lucid, and expressing no particular enthusiasm⁵ for the enterprise to which they were contributing, are symptomatic of what I would like to call progressive defeatism, the sense that, however unpleasant our immediate prospects may seem, there is nothing we can do to avoid them; therefore, we must do our best to make peace with whatever is coming our way. “Progressive” alludes to the judgment that such a strategic retreat provides the best hope for preserving some fragments of the values that supposedly unite us, even in the face of scenarios like the one outlined by Eric Schmidt.

The administration and trustees of my own Columbia University would run away with this year’s progressive defeatism prize — if there were such a prize — in recognition of the Agreement they signed a few weeks ago with the federal government. In the rationalizations I heard in Fort Collins of colleagues’ involvement with the tech industry I heard echoes of Columbia’s Acting President’s account of the thinking that led to that Agreement, specifically when she invoked

an unwavering commitment to the mission, values, and future of Columbia University.

This is not the place to second-guess my university’s decision to adopt progressive defeatism as its strategy for dealing with its current crisis. Anyone who wants to see where the strategy may lead should instead consult this analysis. Regarding engagement with the tech industry, on the other hand, alternatives to the attitude of progressive defeatism are easy to find, for those who make the effort to look. I’m waiting impatiently to see mathematicians’ vision of The AI We Deserve — the title of a forum published last fall in the Boston Review — and their plans for making such a vision concrete rather than acquiesing to a world where we are either stuffing the sausage or being stuffed.

1. To which I hitchhiked from Boston after my first year as a Harvard graduate student. The official history of the present conference also mentions the 1954 meeting by Oscar Zariski, but this was probably a much smaller affair.

2. If you know the statement of the theorem you will probably answer that, yes, there would have been such a theorem, although it would not have had that name. But there’s no reason to think the theorem would have been formulated in quite that way, or would have been limited to just that domain.

3. Since U.S. law attributes “personhood” to these interests, the question of whether robots attending the 2035 algebraic geometry summer institute will enjoy the same rights and privileges as any stray human attendees seems to have been resolved in advance.

4. This is probably where I should confess that I have actually been thinking about a few of the benchmark problems since I published them. In the unlikely event that some of them are solved between now and next year’s deadline I promise to replace them.

5. It is of course perfectly possible that the individuals in question preferred to conceal from me their genuine enthusiasm for the technology, because what they know of the present Substack newsletter might have led them to expect that I would otherwise subject them to an unwelcome and interminable harangue. Please be reassured that nothing of the sort would have happened!