Terence Tao's slide from the lecture he gave yesterday evening at Caltech “Math 2.0”
AI can now crack open problems that were once out of reach, and he says that is the wrong thing to celebrate on its own.
Basically he says chasing problem-solving alone is hurting math.
“Further blind optimization of problem-solving alone is now actively harmful to the long-term health of mathematics.”
“Contrary to popular opinion (or some of our own marketing), mathematicians are not singularly focused on solving open problems.”
“Particularly in pure mathematics, open problems serve as “lighthouses”: not destinations to be reached in and of themselves, but as useful guides to explore the mathematical landscape around these problems.”
“The lessons learned while attempting to solve these problems — whether they succeed, fail, or achieve partial progress — are often more valuable than the final solution to the problem itself.”
“Reaching these lighthouses prematurely by automated tools can disrupt the exploration of the paths not taken, and sterilize the surrounding field.”
“Indiscriminate use of AI to solve problems in a non-renewable fashion damages the long-term health and progress of the field, as well as safe transfer to messier, real-world applications.”