“We are transitioning from an era of proof scarcity to proof abundance. For thousands of years proofs were hard and… it required understanding and expertise and a bit of luck and talking to people and knowing the literature. It was universally valued because everyone who found a proof of a difficult theorem had to do all this difficult work and this helped grow the field. And now we found the shortcut. We found machines that can get these proofs for us and now we’re drowning in proofs, but we’re not getting all the understanding that we used to get.
“I guess we are seeing the end of the romantic era of mathematics — the age of heroes — which happened in other disciplines centuries ago as early as the industrial revolution. But somehow mathematics held on and we had our idiosyncratic traditions. For example, we all use blackboards, as you can see, and I’ve got this special Japanese-Korean chalk.” – from Terence Tao Talks to Numberphile About AI
Today it’s an uncommon reflection that in industrialization, a discipline’s practitioners change the way they work. We are mostly past that time of industrialization. So the emotional reactions from mathematicians to recent AI proofs speaks to their discipline’s changing norms.
I was struck by the degree to which notions of romance, respect, civility, fear, and more factored into those reactions. I had found similar reactions in other disciplines of the past (see the anti-tech Luddite movement list), but compared to historical accounts, like the impact of the sewing machine on tailors and the tractor on farmers, it is more powerful to witness changes in real time. Continue reading “The Chalk and the Airplane”
