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The development of physics and mathematics have gone hand-in-hand for hundreds of years. "Pure" math is pure until it is applied to something. The key parts of the mathematics used in Special and General Relativity existed as "pure" math until it was used in Einstein's theory and atomic bombs...

As a casual amateur, I like the analogy of a stone thrown into water. It could be continued to the waves hitting sand on the shore. If a wave is a small ripple, sand pebbles are nudged a little but fall back into place, and the ripple does not lose energy. If the wave is strong enough to...

IMHO: LLM = "Garbage in, garbage out." Agentic AI/LLMs = automatic, unreviewed actions based on garbage.

That is where "infinity" begins. It is the size of the smallest infinite set. It's size is denoted by ##\aleph_0##. There are larger infinite sets of size ##\aleph_1##, ##\aleph_2##, ... etc. Yes. Good question. The subject is interesting. You might be interested in the work of Georg Cantor...

A real problem with AI-generated code would be verification. Generated code is often very hard for a human to read and review. If the results need to be reliable (like safety-critical code) the AI system would have to be certified and tested. That is a demanding (impossible?) requirement. Even...

At that page I did a search for "AI System" and it took me there. The address looks identical to the OP link. I see that the address in the OP is not the same as the text displayed. It was pasted twice. Try this: https://seas.harvard.edu/news/ai-system-automates-coding-scientific-research

Appear to who? To a stationary observer, every process in the moving frame are slowed. On the other hand, to an observer in the non-accelerating, moving reference frame, he can assume he is stationary and all physical processes measured in his reference frame behave as though he was stationary.

Good question. Yes. It is time itself that a "stationary" observer thinks is distorted in a fast-moving reference frame. Every process that depends on time appears to be slowed in the moving reference frame. The talk about "clocks" includes any process by which the progress of time can be...

"guaranteeing" translates to finding the minimum result as a function of the problem parameters. * Maximizing the guaranteed result translates to maximizing the minimum result. A min-max problem solution is a fixed result, given the solution parameters. * ADDED: a "guarantee" usually allows a...

This problem is a problem to maximize the minimum payoff. I am trying to see a simple, conceptual way to interpret that as the equalities of the OP, but I can not see it. Is there a simple way?

Different companies may have different reasons. It's my understanding that Meta is transferring a lot of its Metaverse resources to AI. That is to put some of their useless Metaverse equipment to a different useless purpose. In my opinion, the resulting AI-generated fake videos will be about...

Good point, and I expected that in the problem statement, but it's not there. That being said, I agree with the OP interpretation of the problem although I think the wording of the problem statement could be improved, as I said in my post,

IMO, if this is really the intent of the question, a better way of phrasing it would be "with the largest guaranteed win". That would be a "min-max" problem, where you are maximizing the minimum possible winnings. Otherwise, I would interpret problems like this to be talking about maximizing...

The quantum computers use networks of entangled qubits.

If possible, can you please post a link to the article so others who have the same question can understand. I am just a casual amateur and would appreciate it.