pfdietz

What do you mean by that?

All that needs to be checked to avoid that is the statement of the main theorem. Any divergence further inside means you proved the main theorem differently than you thought you did -- but you still proved it.

This assumes the Lean kernel itself isn't bugged, but getting it correct is a matter that affects all uses, not just this one, so the cost of making it correct is spread over all those uses.

It's being sunk 20 miles offshore, which is out of Florida control (that extends only nine miles there; which is kind of odd since for most US states the control only extends three miles).

Indeed; one cannot copyright mathematical ideas, only their specific expressions. And the formalization is a different expression.

It's possibly the longest open source project of any kind (depending on whether you count comments and white space in Linux).

The proof was of such complexity and length there were lingering doubts. This dispels them.

Wind certainly helps, but there's a question of what will happen to the relative cost of wind and solar in the future. Solar seems to have a steeper experience curve.

The formalization is 43.1M lines of Lean.

Oh European colonial mindset, don't ever change.

Even better than that: the thermal time constant is proportional to the square of the radius. There's the square/cube effect that causes a factor of r ratio in the volume to surface area, but there's also a factor of r from the temperature gradient (which, from the center of the pile to the surface, is inversely proportional to r).

I think part of what's getting the goat of some mathematicians is not that OpenAI is getting results, but that OpenAI is telling mathematicians that priority isn't something they care about. The indifference is more threatening to the current traditions of math than if they were actually fighting for priority. The indifference gets reinterpreted as them trying to "steal glory" but that's not what they're doing. They're bulldozing glory.

x/sqrt(log(x)), I believe.

Just low-hanging Fields Medal worthy results. Nothing to write home about, right?

Kind of reminds me of work that's done in the drug industry to produce custom enzymes for specific synthesis steps.

https://www.science.org/content/blog-post/chemical-biology-e...

> The real question whether OpenAI's machine has contributed something others will in turn build on.

This has already happened.

> experimentally disproved

Those damned protons refusing to decay.

Yes, you're right, a world where all mathematicians link arms, sing Kumbaya, and agree to not use AI is a much more plausible future. /s

Attribution is a way to pay knowledge workers in ego boost rather than currency. It's a kind of exploitation.

Some recognize this.

"No man but a blockhead ever wrote except for money." — Samuel Johnson

Well, Father Strickland seems to have kept his name off it.

Society has already settled the question of whether it's ok to render someone's job obsolete.

The cavalcade of illogic from the critics has been quite revealing, hasn't it?

This sort of argument becomes increasingly ludicrous with time. It requires that all sorts of results were made unknowingly by mathematicians but they somehow didn't realize it. It's actually a stunning indictment of mathematicians.

No, what is happening is that the AI is really good at connecting the dots and human mathematicians aren't.

OpenAI is explicitly not taking credit, btw.

I think there's a good chance we will actually see decentralization of industry due to very cheap solar. We may also see a movement of industry to sunny locations. This is bad news for northern Europe, and perhaps for all of Europe.

The scale will be set by how large long term storage has to be, which could be as small as 100s of kW. The future grid might be a constellation of loosely connected microgrids. This will do wonders for resilience.

Note that the thermal time constant of a given geometry scales as the square of the radius. This is why subsurface geothermal heat is there even though it was "charged" gradually over millions of years. So it's not hard to achieve very long time constants just by making the pile a bit larger. They've done these computations. The result is the minimum practical size is a pile that provides ~100 kW(th) constant output.

So the idea is not practical for storage for an individual home, but could work on the scale of a village or small industrial enterprise. It would allow a solar microgrid to be completely disconnected from the larger grid, even at high latitude (assuming one could get a sufficiently good heat engine to work at that scale; it's a bit small for steam turbines.)

If you look at very large piles of dirt, like large earthen dams, if arranged in a suitable geometry they would have thermal time constants (assuming no fluid flow through them) in the thousands of years.

A computation for you: compute the cost of a given R value per m^2 for various materials. Dirt is very cheap, so even if it's not the best insulator it comes out on top. You need the thing being insulated to be large enough that you can fit the thick dirt layer around it, of course.

At 600 C one can use stainless steel, but things rapidly become expensive and problematic beyond that. 1000 C would require Inconel or something.

Solving Kakeya in three dimensions was worth a Fields Medal.

The insulation is just more dirt.

That is wrong, and I already explained why.

They appear to be focusing on Europe, and have raised $11M (or maybe 11M euros, I'm not sure which). There is some favorable buzz in Germany, which makes sense because natural gas has become quite expensive there.

https://www.cleanthinking.de/thermischer-erdspeicher-erdhueg...