The creativity of mathematical conjectures
In a recent perspective in Nature, Thomas Fink of the London Institute for Mathematical Sciences makes an interesting case for why the creativity of (good or great) mathematicians is, and will remain for some time, central to progress in mathematics. Famous conjectures (Fermat's last "theorem", the Riemann hypothesis, Hilbert's problems among many, many others) have been the driving force behind extraordinary mathematical discoveries and unlikely connections between subfields of science. These conjectures are formidable engines of progress that have been created by humans. They are unique in an infinite universe of possible conjectures of no interest for their ability to contribute to multiple domains and be relevant to countless problems. hashtag#genAI can help accelerate the production of many conjectures, perhaps filter out the obvious losers, but the mathematician's eye will be the final arbiter of meaning.
I love Fink's citation of Hardy: "In his 1940 essay A Mathematician’s Apology, G. H. Hardy explains that a good theorem “should be one which is a constituent in many mathematical constructs, which is used in the proof of theorems of many different kinds”.
Creating important conjectures is a talented human's work of art. For now.