“ In mathematics, it’s not a cliché that the journey matters more than the destination. Problems are posed not so much because their answers will be practical and important, but because they represent interesting journeys. The hope is that as mathematicians struggle to solve a problem, they’ll come up with intriguing tools and connections, stumble on novel ideas and directions, take fruitful detours, and answer new questions they never would have thought to ask.
“It was never about the theorems,” Goh said. “It’s to carry on a tradition that has benefited society despite not having any market value. To reason deeply, to understand the world … and to spread that knowledge.”
It breaks our system. It just takes it to its absolute limit and destroys it.
Tasmin Chu, California Institute of Technology
AI models skip to the end. At the moment, their proofs are nearly impossible to read. They elide salient details and waste pages on irrelevant concepts. They fail to demonstrate how the new work builds on or connects to other results in the mathematical literature. Mathematicians know that the proofs are true — they’re verified by a system that checks their logic(opens a new tab) — but have no idea why. What’s missing is understanding, the currency that mathematicians trade in. If there is a journey, humans are not invited along for the ride.”
Not everyone will succumb. Those who truly love what real learning requires will not be enticed by shortcuts. Rather, they will either eschew AI or use it as the assistant it’s meant to be, and they will continue on the forefront of thought and human advancement.
The problem I see is AI’s potential to widen the divide between those who maintain rigorous mental muscles and those who atrophy resulting in an even deeper chasm between the haves and the have nots.
A quick scan of that paper demonstrates to me what I posited above – those who think deeply will continue to think deeply, challenging AI not deferring to it. This is a hopeful example of strong minds analyzing and revealing the limitations of the machine. (The paper concludes with the mistakes AI made in the Navier-Stokes translation.)
I am not competent to judge the paper either, but it seems clear that the authors were able to undermine if not completely disrobe the AI proof (shortcut), and that is no mean feat in the case of the complexity of AI reasoning that needed to be reviewed to find the fault in the AI logic.
Faculty have nowhere to go. Quite as many people won’t join PhDs and it’s not the worst thing for them. All those people are mostly hoping for academic jobs, and there aren’t as many (never were) academic jobs.
You can search for recent articles that discuss AI’s effect on the future of academia and mathematics (I used Chat to pull up a few), but it seems the most immediate threat to faculty retention and advanced curricula/degrees is the current dearth of funding. AI may change the academic landscape in ways we can’t yet quantify, but current funding cuts are starving our programs and encouraging our brain trust to move elsewhere. The combined effect of AI and funding cuts does not bode well for the future of academia in general in the U.S.