What's a mathematician to do? (2010)

LLM models can only predict the next token.

The can't predict the consequences of an action predicting one token after another. They can't solve a Rubik's Cube unlike a 7 year old human who can learn to do it in a weekend. They can't imagine the perspective of being a human being unlike a 7 year old human if asked to imagine they where in the position of another human.

“Comparison is the thief of joy.”

Do the math because you enjoy doing the math and if you do it long enough you may well do something of value to someone else. Same goes for most intellectual and artistic pursuits I think.

I’ve learned for myself that as soon as enjoyment is based on some future achievement or ranking my work against others the day to day satisfaction dries up.

So I've got a gut feeling that math (like human languages (like programming languages)) is best learned in service of some greater end.

I look at some truly impressive projects like CLASP which sprang into existence not because of someone noodling around, but because they had a bigger goal which required the team build it.

So my advice to any mathematician who feels lost, like they don't know what to work on, would be to go collaborate with someone who has an actual goal, to look for inspiration in the kinds of math they need.

Today, there are a lot of opportunities to jump forward that only get capitalized on through coincidence (e.g. two people bump into each other at a conference, or researcher happens to have a colleague working on a related problem through the lens of a different discipline). If AI does nothing but guarantee that everyone will have such a coincidence by serving as that expert from a different discipline, that will still be a massive driving force for progress.

The question of "whats a mathematician to do" is still clear: you need to find and curate and clearly express interesting and valuable problems.

Living culture is a concept that I think is quite unintuitive to modern minds. Examples of it are all around us... but it's usually blatantly missing from our "big picture" thinking.

For example. Take a modern country with a modern economy. Flatten it. Destroy all the factories. Bankrupt all the companies. You can get back to a fully modern economy again quite quickly. WWII demonstrates it.

Taking an unindustrialized country through the development process... that's very tricky. It can't really be rushed.

For a long time, economic development was seen as mostly capital and technology. You need time to develop all the capital needed. Roads, factories, etc. But... development efforts underperformed. Then the idea of "human capital" got popular as a way of explaining the deficit. Education, mostly. Development efforts still underperformed.

I think the "living community" thing is the answer to this. It' ecology. You can't make a rainforest by just dumping all the necessary organisms into the right climate. It's the endlessly complicated relationships between all those organisms that make the rainforest.

This is one of the things that worries me about the pace of modern change. When writing and literacy resurged in classical antiquity... we totally lost all the ways of (for example) doing scholarship orally. Socrates (through Plato) wrote about some of the downsides to this.

...and we did completely lose oral scholarship. We have no idea how to do it. Once the living culture died... it stayed dead. All the knowledge contained within it went away.

Could work in a patent office or something.