spectrums_coherence

I wouldn’t even listen to it for money (unless it is a lot of money

Mathematics, and really any other subject, are not just about solving formalized problem. It is much more important to understand what question to ask.

One of my colleague once said the definitions in a good (computer science) paper should be the most interesting part, theorem statements should be the second interesting, and the proofs should be obvious.

Formal proof means nothing if it cannot give us insight in other proofs.

Same with open problems, Mathematician love open problems because given that no expert are able to solve them, their solution likely involves novel mathematical ideas. Fermat’s last theorem on its own is no where near as interesting as the mathematics that leads to its soluion.

Given that AI have yet to be able to wield the mathematical corpus effectively in solving large projects (or even fully autonomously improve large software), it would need human guidence, and by that, human experts are needed to understand the problem.

To qoute another one of my colleagues, people orchestrated AI to solve an open problem are simply the apple falling on Newton’s head. Apple “knows” about the existence of gravity, because its motion follows it, but it takes a Newton to formulate and explain gravity that leads to a number of technological advancement later. Without the question “why do apple fall”, apple will keep falling, we will keep noticing it, but we would never turn that observation into useful technologies we enjoy today.

Suppose we had a library filled with proofs of every theorem [in mathematics], as well as excellent guides that could, given a question, take us to the answer and explain it. What would a mathematician do in such a library?

If you ask the question this way, the answer becomes clear: they would be unbelievably excited, and immediately get to work. They would immediately start asking questions: how does one prove the Riemann hypothesis? The Hodge conjecture? Their own pet obsession (in my case, the Grothendieck-Katz p-curvature conjecture)? Then they would work until they understood the answer. The job would not be done, not even close.

This paragraph by Daniel Litt feels to me like hubris coming from someone in the position of power. Many tech-optimistic mathematician are not at the risk of being replaced by AI because they are either on the tenure track or already tenured.

We need to acknowledge that mathematics is a subject of more human importance than economical importance. In this hyper profit driven world, field without a primary economical drive will necessarily shrink significantly.

Mathematics have no doubt experienced that: in the cold war, mathematics is behind most of the technological advancement that lead to concrete economical output. Later, as many of these fields stablized, engineer and computer scientists takes the place of mathematician, and mathematics shrunk significantly.

Now mathematics still holds importance because people believe it still encapsulates important ideas that have the potential to be the next generation of economical driver force. And mathematicians are important to preserve and disseminate such knowledge.

So if such truth oracle described above can develop and articulate any mathematical idea better than (or even close to the quality of) any mathematicians, it would be fun for established mathematician to flip through the answer sheets of their puzzle, but it would kill the financial driver and wipe out most of professional mathematics with it.

Framework said that even LPCAMM2 cannot support the desired ram speed of strix halo.