Math is an incredibly broad field. I mean, you don't expect a traffic engineer to understand anything about nuclear reactors, do you? Yet, they are all 'career engineers'.
>And then -- the kicker -- something that I personally spent a couple years on in grad school, leading to some of my proudest work: quantum parallel repetition theorems
...
>Is there some broader context or theory within which this would've been the obvious thing to do? What other results can be proven using these techniques? What is it telling us about quantum information or operator theory? I have no idea
https://bsky.app/profile/henryyuen.bsky.social/post/3ms2jpch...
That guy has been featured in quantamag too, btw
I saw another expert on Ehrhart express their bafflement (but I can't find that link now)
PP (actually the "broad career mathematicians" themselves) were being slightly disingenuous... But the specific domain experts seem to be understating how much over their head it actually was. We're in totally unknown territory here..
we can however be optimistic, oddly. If you believe Feynman when he says that you can't explain to a child something you don't understand.. then we can see that ChatGPT has no idea of just what it has done!
(Steel Manning:
1. maybe any chatbot would need 1000x more tokens than were used to arrive at the result to understand it to its own satisfaction.
2. It's possible that Einstein did not fully understand General Relativity
Why would that be optimistic? Seems like the pessimistic reading to me, if anything. Or are you having a bout of Schadenfreude?
Compare the various summaries that humans have written on the Jacobian counterexample, to the chat logs that were archived.
I'm not guessing that they aren't working on this aspect or that chatbots won't be able to do it in the futute. It just seems that we do have an advantage for now.
I might have overstated a bit, but by 9th grade (15 year old) this is what was taught to us back then.
What you learned, was it more like:
1. "You need to slow down neutrons so they can react"
or 2. "Here's the graphs of how the neutron absorption and scattering cross sections vary with neutron temperature for H-1, H-2, H-3, Be-9, C-12, O-16, Fe-54, Fe-56, Fe-57, U-233, U-235, U-238, Pu-239, …"
If it was the former, you didn't learn "nuclear engineering".
(which is a simplification in itself, but that's best left until 2nd-3rd year in uni)
But for general understanding, .. there is stuff that slows neutrons. some is more effective, some less. There is also activation. It is why tanks and ifvs were lined with polyethylene or similar on the inside back in cold war - it had lots of hydrogen. But for controlling a power plant that is not enough - why?
and then we answer why.
It turns out that the "more CO2 = more warmer" model is hilariously simplified, and the real modelling gets into the weeds to put it mildly! There's a NASA database of the super-high-resolution absorption and emission spectra of every isotopic combination of every common molecule and ions, excited states, and more! It turns out that most of the forcing is determined by the behaviour of the upper atmosphere at high latitudes where the air is so thin that exotic excited states can persist for appreciable durations, and are made in large amounts by absorption of UV light. The "glancing angle" of the sunlight near the poles also means that even minor constituents participate in the exchange of IR radiation. Then, then, the simulation has to be run in many thin slices because air is so opaque to IR radiation that it bounces many times on the way up and down, and of course, the isotopic mixes (and excited fractions) are inconsistent between layers.
An insanely complex supercomputer model is required to come up with even a rough estimate of the actual warming.
Only those who try to maximize profits while skirting the risk of a revolt care whether global average temperature will be 1.2 or 1.8K above pre-industrial average in ten years. For the rest it's already too warm, the damage is already plainly visible.
We don't need better models to predict future warming; we dragged our feet long enough that we can now look at historic data to see where it's going.
Newton's laws of motions are not hard. Making a rocket that doesn't kill the occupant, is.
For the 2026 version of me out there, please ignore. It is nerd posturing, and as real as the boomers at your gym claiming to have benched 225/315/405 in high school, despite having terrible form while doing 185.