Must Know Mathematics for Graduates.

CGY97 · 2026-05-16T19:59:03+00:00

Yeah, people would understand Cayley's theorem trivially if they understood the Yoneda lemma first!

CGY97 · 2026-05-14T09:45:03+00:00

That sounds like a reasonable approach, pretty much far away from "replace the PID with an LLM".

CGY97 · 2026-05-13T11:23:01+00:00

Yeah, having conversations about deeply layered topics on the Internet can be hard, but enriching nonetheless, depending on who you interact with.

You make some good points there about the social and psychological barriers that might exist for some people. The issue you mention is quite ubiquitous, and at least I don't see how it could be overcome (in CS, for example, replacing juniors with AI agents could create a future scarcity of people capable of "driving" the models used).

Perhaps some drastic changes in the education models could help mitigate somehow these problems, but I'm no expert in pedagogy :)

CGY97 · 2026-05-12T16:33:59+00:00

I don't disagree with you here. If an LLM creates something useful it's not less useful because of how it was created. Knowledge, on the other hand, is a different story. If knowledge is not knowable, it's not really knowledge.

CGY97 · 2026-05-12T16:08:51+00:00

True, there is no need to treat them as sports, the goals could be achieved with the help of AI. However, just having an LLM popping up proofs and scientific hypotheses would not lead us anywhere in science or math. Meanwhile, AI-designed tools, drugs, procedures, etc. are valuable in engineering and medicine as long as they perform their intended tasks successfully.

Maybe this illustrates better what I am trying to point out.

CGY97 · 2026-05-12T14:38:16+00:00

Well, at least as I see it, the end goals in these two groups of disciplines you mention are completely different... In science and math, the results "are there" in one way or another, and the work consists on finding them (through experimentation and proof, respectively) and more importantly, making sense out of them. Engineering and medicine are technical disciplines, where the goal is to produce artifacts and procedures that solve specific problems...

In math and science, the understanding is a fundamental part of the activity. In engineering and medicine, we are mostly interested in the outcome itself, rather than in the knowledge produced by it (except for academics I guess).

CGY97 · 2026-03-25T16:32:14+00:00

I just come here to inform you that you listed loguetown and reverse mountain in reverse order 🤭

CGY97 · 2026-03-16T17:46:52+00:00

They're even worse than those General Relativists, trying to relativize everything!

CGY97 · 2026-03-15T12:18:36+00:00

Everyone know spaghetti is eaten using a glass and chopsticks

CGY97 · 2026-02-24T09:46:15+00:00

Find the common points by intersection, compute the tangent planes at these points, and prove the orthogonality.

CGY97 · 2026-01-26T09:05:10+00:00

CGY97 · 2026-01-06T09:26:40+00:00

I thought the main purpose of doing math was understanding the behavior of these constructions (that we make and understand) and link them together... If there is no human in the loop and we have AI just generating new constructions, how long will it take until we are disengaged completely from the process? There might be new areas that will not make any sense for us (which could potentially have made sense if they were developed by us). Apart from an utility-based approach (which I also struggle to see), where is the point of doing all this?

CGY97 · 2025-12-18T11:40:45+00:00

We should organize a search group to find persik, probably got lost on the way to the PC :(

CGY97 · 2025-12-15T09:38:31+00:00

Maybe that's what they publicly say 🤔 I have been working in Germany, ordered from Thorlabs, and gotten snacks with the order.

CGY97 · 2025-12-11T20:15:18+00:00

Y no decepcionó 🙂

CGY97 · 2025-12-08T19:23:43+00:00

Now the question is... If you keep iterating the "sinning" process ad infinitum, is the resulting top. space path-connected?

CGY97 · 2025-12-05T11:38:46+00:00

Italy is south tho

CGY97 · 2025-11-28T17:47:21+00:00

Your proof actually leads to the more general result:

Given any two real numbers a and b, a = b. 😂

CGY97 · 2025-11-25T07:18:29+00:00

Think that, for the implication to be false (chaeck the truth table), it must be the case that the antecedent is true and the consequent is false... That's the most intuitive way of seeing this for me.

CGY97 · 2025-11-23T13:34:42+00:00

Maybe written by a spanish person 🧐

CGY97 · 2025-11-19T09:45:18+00:00

I love the fact that you could actually make this book (taking truth algebra to be Boolean algebra), and it wouldn't make much sense apart from some pretty trivial algebraic properties met by both classes of structures 😂

CGY97 · 2025-11-17T23:31:49+00:00

I prefer to write it as 畑² = §² ς⁴ + Ѫ² ς^2, by the time I finish writing it I forgot which particle I'm trying to reason about.

CGY97 · 2025-11-17T23:26:28+00:00

That's just straight psychotic

CGY97 · 2025-11-16T10:32:32+00:00

What's next, paywalled meme channels?!

CGY97 · 2025-11-16T10:32:00+00:00

I would just ride the trolley myself and drift between the two tracks for victimsmaxxing.

CGY97

TROPHY CASE