It seems like AI has become a huge deal. OpenAI has announced major progress in certain parts of math, including subfields I’m personally interested in. More concerningly, the computers have been autonomously hacking websites (including government ones).

Unlike some people that are more technologically averse, I am fine with using AIs myself to assist my understanding. I made ample use of Anthropic’s Claude Opus model in my preparation for my algebra qualifier. This was primarily due to the fact that I was injured, so I was unable to attend the university’s qualifier preparation classes myself, so instead I would write exam solutions myself and talk to Claude to ask it for assistance on topics and ideas I didn’t have much experience with. It was… shockingly effective. I passed my qualifier with (relatively) flying colors.1

It’s not at all doubtful that AI is extremely effective in tasks it’s well suited for, especially in finding counterexamples for problems from a field as well-codified as math. However, I think the popular imagination is jumping the shark, and I fear this will end up really bad for the field of math as a whole.

There’s so much discussion on the web from technology chauvinists2 essentially cheering the likely degradation of mathematics from a field focused on developing understanding into a bunch of Lean slop (for lack of a better term). I’ve seen a number of memes from AI wrapper company CEOs putting Terence Tao in McDonald’s crew uniforms, effectively gloating at the idea of being able to obviate the “egotistical” mathematicians who tortured them by giving them a B in Calculus 2.

It’s kind of sickening to me, honestly. I can’t really pinpoint exactly why I love math, but what I do know about math is that I am constantly trying to learn more about it. I just think about it all the time, even when other things are going on around me, even when I’m just relaxing at my apartment, even when I’m teaching other math. Hardly does it leave my mind. I’ll occasionally open up documents to read about one concept and spend 20–30 minutes trying to digest it. Thinking about math is, essentially, a base state of mine.

Similarly, I love teaching math. I love sharing my thought process and perspective on topics ranging from limits in Calculus 1 all the way up to and through ideas in operator algebras. There’s a baseline urge within me to learn and share perspectives, and not just in math. It’s why I edited for my undergrad’s school newspaper for four semesters. It’s why I post so often on Twitter. It’s why teaching is so rewarding for me.

Fundamentally, I think that the ability to relate to humans — share perspectives, develop new ones, improvise on their communication, etc. — is what separates us from the AIs. There was a great YouTube video by VSauce about reasoning from five years ago, mostly focused on climate (Bill Gates’s issues aside, it’s a great watch). What I’m afraid of with the advent of extra-powerful AIs is that in the minds of many, they will obviate the need for reason itself. In a sense, reasoning is a social process, where the goal of truth qua truth is essentially secondary to the goal of relating to others and developing a shared reality. A modern Rene Descartes may have said something along the lines of “I relate, therefore I am.”

I don’t believe that AIs are human, or even human-lite. I don’t think they are capable of the rich depth of reasoning that humans engage in regularly. I believe AIs can think, and certainly we as a society believe that thinking is the fundamental part of humanity, but personally I don’t believe that thinking is what separates humans from other creatures (AIs included). Joseph Henrich’s book The Secret of Our Success explains what really separates humans apart is our ability to develop cultural knowledge. That is, shared understanding passed down through generations; society itself is the thinking organism, rather than the individual human. AI agents can imitate this to an extent, but I don’t think that they have developed the novelty that human society has developed through its millennia of societal enrichment.

Humanity as a whole will have to reorient ourselves around the fact that what separates us apart isn’t our ability to think, but rather our ability to relate to each other in such a broad way that other animals cannot replicate. I think it will be imperative in the future that we assert this part of ourselves regularly. To an extent, that will require strict pushback against the corrosive nature of technology chauvinists that seek to destroy the organs of reason and collective knowledge and replace it with their dystopian ideas of what productivity and knowledge really mean. If their vision comes to pass, then we will not only see an end to math, but our entire society.

  1. It did help that the exam was really easy and had very few curveballs, but even then I felt like I was largely prepared for those curveballs that might have had a chance of coming up. ↩

  2. Usually they are called “tech bros,” but I get the sense that this is a descriptive double entendre. ↩