Right, but my point is that’s still what mathematicians do. That has never changed. Grothendieck was a great mathematician, but the difference is not that other mathematicians don’t approach problems with sufficient curiosity. I would go as far as to say Grothendieck’s strength was a heavier time commitment very early in his career to just publish less “deep” results, because that time investment allowed him a very deep understanding of the objects he was working with, which is the key to making real insights. Directing mathematicians away from investing time on more boring proofs to only work on fun theory is misguided.

Saying mathematicians don’t focus enough on curiosity and novel discoveries is completely at odds with all of my experience in math research. That’s the fun part of math! For everyone! It’s throwing aside that the amount of time and effort Grothendieck put into producing “ordinary” results beforehand was completely necessary in developing schemes. Dismissing the kind of results Grothendieck had published earlier on as not theory-crafting destroys theory-crafting, because deep insights don’t pop out of thin air and thinking outside the box, they come from years of familiarity with the objects you’re working with. It’s also throwing aside that he himself saw toposes as much deeper than schemes, but those did not catch on to the same degree, and that most mathematicians who have been in it for a few decades have their own body of work like that that could be easily dismissed from the outside as not “theory crafting” because the audience is niche in the same way it is for toposes. There’s no “need to reinvent” towards “theory crafting”, and saying that there is is misunderstanding the crisis by misunderstanding how math research has worked in reality.

You and I have a similar workflow. One thing AI solved for me is not having to hunt obscure specific documentation or wade through unhelpful forums. It also helps make a test script for when I want to see if something’s working without another 20 minute sidequest.

I’m mainly referring to the people who want the AI to do all the work, which has unfortunately become a common expectation lately. Some people want to feel like programmers without ever reading or writing any of the raw code.

I’d say I actually fall in that camp. Right now I’m trying to set up an open source AI assistant that’s like, a little dumb but can still help me while I’m coding.

My ideal relationship with AI is this image:

No. Some are, that’s my point. And probably not even close to the majority of us.

The loudest economists use economic theory as a cudgel. You are right to find them infuriating. They assert certainty where economics does not, and cherry pick exceptions to hold up as rules. They are to economics as RFK Jr is to medicine.

The math of economics is more like the math of epidemiology or fluid dynamics than the math of mechanical linkages. It describes how things tend to interact within a system, but a given element or interaction is unpredictable. Even concrete sections, like price theory, have contradictions like the velvet rope effect. It describes probable outcomes in a chaotic system running on irrational humans.

Meteorology is still a math-based science that makes useful predictions, even though it cannot say with certainty whether a particular tropical depression will become a hurricane.

There is an element of this, because the people using it for policy or writing headlines always disregard a ton of caveats and qualifications in any field (including actual hard science like physics), but most economics texts I’ve read hide a ton of complexity behind “rationality” that doesn’t exist and are implicitly describing the system that we have (capitalism) without acknowledging that we could do it any other way - which frees them from any ethical conflict with capital/exploitation and lets them pretend they are describing a natural system.

The truth is we are irrational both as individuals and as groups with outside influences, and the economy can function in whatever way we want it to function. In that lens economics quickly turns into psychology, ethics and philosophy. Which, to be clear, would be a useful thing to study in any economic system (all of which have incentives and pitfalls), but it is not nearly as objective or concrete as it currently pretends as it fiddles with interest rates while billionaires run roughshod over our entire society.

There’s a famous quote about economics that goes something along the lines of “the market can remain irrational longer than you can remain solvent,” which I think summarizes everything pretty nicely. Humans are chaotic and largely unpredictable creatures, and economics is a science devoted to trying to pull deterministic data out of inherently nondeterministic people. Sometimes they’re even pretty on point about it. But in all cases it is, best case, an educated guess.