If Math Is Running Out of Problems, Will AI Help Out the Humans?
July 26, 2024
This essay is the work of a dinobaby. Unlike some folks, no smart software improved my native ineptness.
I read “Math Is Running Out of Problems.” The write up appeared in Medium and when I clicked I was not asked to join, pay, or turn a cartwheel. (Does Medium think 80-year-old dinobabies can turn cartwheels? The answer is, “Hey, doofus, if you want to read Medium articles pay up.)
Thanks, MSFT Copilot. Good enough, just like smart security software.
I worked through the free essay, which is a reprise of an earlier essay on the topic of running out of math problems. These reason that few cared about the topic is that most people cannot make change. Thinking about a world without math problems is an intellectual task which takes time from scamming the elderly, doom scrolling, generating synthetic information, or watching reruns of I Love Lucy.
The main point of the essay in my opinion is:
…take a look at any undergraduate text in mathematics. How many of them will mention recent research in mathematics from the last couple decades? I’ve never seen it.
New and math problems is an oxymoron.
I think the author is correct. As specialization becomes more desirable to a person, leaving the rest of the world behind is a consequence. But the issue arises in other disciplines. Consider artificial intelligence. That jazzy phrase embraces a number of mathematical premises, but it boils down to a few chestnuts, roasted, seasoned, and mixed with some interesting ethanols. (How about that wild and crazy Sir Thomas Bayes?)
My view is that as the apparent pace of information flow erodes social and cultural structures, the quest for “new” pushes a frantic individual to come up with a novelty. The problem with a novelty is that it takes one’s eye off the ball and ultimately the game itself. The present state of affairs in math was evident decades ago.
What’s interesting is that this issue is not new. In the early 1980s, Dialog Information Services hosted a mathematics database called xxx. The person representing the MATHFILE database (now called MathSciNet) told me in 1981:
We are having a difficult time finding people to review increasingly narrow and highly specialized papers about an almost unknown area of mathematics.
Flash forward to 2024. Now this problem is getting attention in 2024 and no one seems to care?
Several observations:
- Like smart software, maybe humans are running out of high-value information? Chasing ever smaller mathematical “insights” may be a reminder that humans and their vaunted creativity has limits, hard limits.
- If the premise of the paper is correct, the issue should be evident in other fields as well. I would suggest the creation of a “me too” index. The idea is that for a period of history, one can calculate how many knock off ideas grab the coat tails of an innovation. My hunch is that the state of most modern technical insight is high on the me too index. No, I am not counting “original” TikTok-type information objects.
- The fragmentation which seems apparent to me in mathematics and that interesting field of mathematical physics mirrors the fragmentation of certain cultural precepts; for example, ethical behavior. Why is everything “so bad”? The answer is, “Specialization.”
Net net: The pursuit of the ever more specialized insight hastens the erosion of larger ideas and cultural knowledge. We have come a long way in four decades. The direction is clear. It is not just a math problem. It is a now problem and it is pervasive. I want a hat that says, “I’m glad I’m old.”
Stephen E Arnold, July 26, 2024
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