After Math

I think as a civilization we need to postulate a new term: “purpose death”

Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence.

I truly think because of the pace of innovation this will be a universal feeling for every human for the rest of existence.

As a software engineer, I myself have only recently recovered from it. So, it’s really interesting to watch a prominent figure in their industry publicly go through “purpose death” and the related grief. It’ll be a useful case study to re-read his written meditations through this cycle.

I’d say Terrance has recently left the denial phase, the anger phase I’m sure he wisely kept off the Internet, and is currently in the bargaining phase - ie scrambling to change the goal posts. I wonder if he will wisely keep the depression / burnout phases also off the internet.

However, soon as the goalposts keep falling, I think like most humans he will accept, retool, and come out of this grief with renewed purpose with larger expectations of himself and mathematics. This recent post even starts towards some of that - but sadly is slightly off the mark.

“The important question is, therefore, not whether AI will defeat mathematicians, but which mathematical ends we want AI to serve.”

He still thinks there is controlling AI. AI will run and trample anything that stays in front of it. He needs to one day find acceptance in letting AI run while he learns how to suggest it minor course corrections which it may or may not accept, and when it doesn’t accept quickly learn from the AI why he was right or wrong.

I maybe wrong, but I think this is the cycle of “purpose death” we will all have to contend with in our own time.

I feel like, to different degrees, we’re witnessing the same effect seen in image generation or text generation. People who don’t know better about art or writing would be impressed by what gen AI can produce and will find it indistinguishable from a human-produced equivalent. This admittedly is good enough for most business endeavors that cared only about the process, and would gladly avoid the cumbersome (to them) process that leads there. But art or writing is not just about the product as much as it is about the human process itself. That is true for all creative forms, even the ones that are normalized in business. Now with the advancements of the frontier models, we’re seeing this in growingly complex fields like mathematics. It does seem to produce results, but the process is equally important. Yet we pretend to measure its ability only based on the result. It’s as if these tools grow to become better at pretending to be top of the crop in increasingly complex fields, which makes it harder and harder for people that actually have a deep grasp of those fields to explain why that’s not exactly what’s going on.

The authors of this piece are Silvia De Toffoli and Eamon Duede. It is hosted at Terence Tao's blog, but he did not write it.

You even notice that with the recent opus and fable models by Anthropic.

If you give them a wide open problem statement, they'll start talking a lot of semi intelligible gibberish.

My guess is that this happens because that's not what they are evaluated on anymore for these kinds of tasks. The generated code is evaluated (in this case the lean code). So talking a bit of gibberish in the language part so you have more test time compute is not punished.

Grigori Perelman rejected the Fields Medal and the Clay prize among other things for what he considered unjust decisions and lack of ethics and proper attribution to other mathematicians. I find it surprising that he hasn't been mentioned yet, given it involves another Clay prize (ironically another lack of attribution, I guess). There is a long tradition of mental problems among great mathematicians, but maybe this was not the case, or maybe in a Lovecraftian way the observation of deep truths has a terrible toll.