Random thoughts on AI

What follows are some reflections on "AI and Math". Many of them will be very banal, some very controversial, none set in stone. They might change on a moments notice. If you don't like them, feel free to tell me! Happy to incorporate feedback and learn.

Math vs. human vs. AI

  1. AI in Math is here to stay and mathematicians need to find ways to grapple with this development.
  2. "Math without AI" will be a theoretical possibility, but will be closer to math without computers or the internet.
  3. I respect the efforts of "Math without AI" groups, such as AHM, but I simply cannot imagine a long-term future, in particular in its most ambitious form.
  4. What "Math with AI" means is in the eye of the beholder. Each person and community needs to find their own response.
  5. I sometimes hear about "Math without Human", which is the idea that AI will advance so much that humans will become redundant.
  6. I acknowledge this is a possibility, but a world with such an AI would be very different from even current AI. It would not just reshape math, but also many other things. So to me "Math without Humans" is not primarily a math question.
  7. I hence don't think preparing for "Math without Humans" is the constructive path for mathematicians. We should rather focus on "Math with AI": mathematicians need to have a response to that.

Who pays for math?

  1. Research math never had a supply problem: There are always excellent smart dedicated people interested in doing math research.
  2. Research math does have a significant demand problem: There is basically no market for research mathematics, and public funding is always limited and will probably be more so in the coming years.
  3. That is precisely why many talented people I have met over the years are now data scientists, actuaries, ... .
  4. This demand/supply dynamic will persist in an "AI with Math" environment.
  5. In particular it is underdiscussed who is supposed to pay for AI, even if it is technically capable.
  6. Currently we are in a rare moment where big AI companies are subsidizing AI in Math, hence there are no supply constraints and we are seeing massive results (good or bad).
  7. I will not pretend to know their motivations. Probably something about publicity and some vague idea that "doing Math" is particularly smart.
  8. Broadly speaking the influence of these companies on mathematics has been destructive. This is unsurprising given these are companies with little understanding of the research world.
  9. My guess is they will lose interest once the "next big thing" hits the market and market logic pulls in other directions.
  10. At that point, AI will be one additional resource next to all others competing for limited supply. Then it's more about the technology and less about the companies.
  11. Ideally the mathematics community will have plans in place to respond how to allocate resources meaningfully. Instead it appears the focus is on much more extreme scenarios.
  12. To be fair, there are efforts. One I know about: AI.MATH

Young researchers

  1. The one context where "doomer" attitudes seem reasonable is for PhD students/early-career people.
  2. Unfortunately, the main math voices politics/society hears are Fields Medalists/established professors. The ECM perspective has not received the same level of attention.
  3. This does not appear to me to be some sort of conspiracy. Rather there is simply no "math government" that can give more representative responses.
  4. To be clear, I am not saying established mathematicians cannot be hurt by these developments (in particular the way AI solutions are announced). Just that they have more opportunity to stabilize.
  5. I am concerned that many young people will either despair or go for AI-Maxxing, neither of which is a good outcome.
  6. To me this outcome, where math research changes but continues for established figures and, at the same time, young people are harmed/pushed out, is quite likely, and underestimated.