A faster answer is useful. But is it all mathematics is for? Steven Strogatz and Alex Townsend, two applied mathematicians, take up that question as AI systems begin solving open problems and mathematicians worry about what might be lost along the way.
Their example is compressed sensing, the mathematics behind reconstructing a signal or image from surprisingly few measurements. It did not spring from one isolated puzzle. Work on Fourier analysis, wavelets, statistics, optimization and seismic imaging converged with rigorous proofs by Emmanuel Candès, Terence Tao and David Donoho. That understanding could then be put to work on MRI: the authors describe a pediatric scan cut from eight minutes, with sedation, to just over a minute with the child awake.
An AI that found an opaque shortcut to a faster MRI would still help patients, they readily concede. The question is what else the conceptual route produced. Knowing why a technique works makes it possible to test its limits, recognize the same structure in another field and build on it there. An output-only measure of progress does not count those future uses.
The essay adds an applied-math angle to Amit Sahai’s recent argument for funding more mathematicians who can understand AI-produced ideas. Neither history nor the MRI example proves AI cannot help develop such understanding. Strogatz and Townsend’s narrower warning is against treating the solved problem as the whole achievement.
Read via a September 24 archived snapshot of the NYT essay.