I have long been exasperated by mathematicians regarding numerical computation as some kind of an engineering add-on to their subject rather than part of mathematics itself. To fully understand and advance mathematics, surely we must apply and explore its ideas, and that means computing. What could be more obvious? Yet many mathematicians seem to believe that, although algorithms grind out numbers usefully for applications, one need hardly pay attention to all that.

Awkwardly, this narrow-minded view about numerical computation and mathematics parallels the view I have held about machine learning and science. All around us, ML is transforming our capabilities. Protein folding, weather prediction, design of materials, discovery of drugs — it’s amazing. I don’t deny the power, but my feeling has been that these new ML tools have little to do with true scientific understanding.

The analogy isn’t perfect, but I think it’s good enough that I should change my opinion. Provisionally, going forward, I shall take the view that machine learning is a true and indispensable part of science.

[29 December 2023]