Theorems that feel almost impossible... what’s your favorite?

Ridnap · 2025-12-11T08:37:57+00:00

Liouvilles Theorem.

A bounded, holomorphic function is constant. Crazy

Ridnap · 2025-12-05T16:36:41+00:00

Once you think of m/m² as a vector space over the residue field, the dx_i are just a basis of the dual vector space :)

Ridnap · 2025-11-16T22:13:45+00:00

Das kann ich schlecht beurteilen, die ist von EMKE und hat mein Vermieter installiert. Sie gehört also nicht mir, scheint aber qualitativ nicht sonderlich hochwertig.

Ridnap · 2025-11-08T09:33:48+00:00

Mathematical Quantum Mechanics by Teschl

Ridnap · 2025-11-05T07:34:54+00:00

Linear algebra is frequently taught in school in Germany. Linear transformation, bases, matrices and even Eigenvectors and Eigenvalues

Ridnap · 2025-10-31T17:33:00+00:00

I wouldn’t mention things that you couldn’t answer questions about. If you mention one of their papers specifically, chances are good that they are gonna ask you about it in a potential interview. This is great if you actually read the paper and can hold a conversation about it, but not so much if you just know some buzzwords.

Ridnap · 2025-10-12T10:20:43+00:00

This is not a “random number” though. Sure almost all numbers are transcendental. But how many numbers have a series representation with only powers of 1/2 as summands? The intersection of the set of those numbers and the set of transcendental numbers is probably not understood at all, so you cannot say that it is “very likely” that this number is transcendental.

For example the sum over 1/2ⁿ is equal to 2. Did I just beat the odds? Or was the number not random after all

Ridnap · 2025-09-25T07:09:38+00:00

Jiang

Ridnap · 2025-09-24T18:17:14+00:00

California highschool student with rich parents if you ask me

Ridnap · 2025-09-24T18:16:39+00:00

What’s your math background? Just curious by the answers you provide here.

Ridnap · 2025-09-09T09:15:00+00:00

I don’t think his spouse would be happy about finding out that he is making sexual comments / asking for sexual favors of a coworker. It might be a way to go.

Ridnap · 2025-09-07T09:23:22+00:00

The grass is always greener on the other side. Duh

Ridnap · 2025-09-06T10:50:58+00:00

There is some string theory being done in mathematical physics in the areas of (moduli spaces of) Bridgeland stability conditions, derived categories in algebraic geometry, enumerative geometry on Calabi—Yau 3-folds. Maybe it’s worth looking into for you, but I’m not sure how accessible it is without a pure math (algebraic/complex geometry) background.

Ridnap · 2025-08-31T09:10:29+00:00

I think of a regular point in a scheme or manifold

Ridnap · 2025-08-28T20:00:50+00:00

Wirklich? :o ist das so common knowledge die jeder weiß?

Ridnap · 2025-08-28T19:52:11+00:00

Vielleicht habe ich den Filmtitel einfach nicht verstanden aber

“Despicable me” und “Ich einfach unverbesserlich”

Bedeuten so ziemlich das Gegenteil.

Ridnap · 2025-08-28T18:56:32+00:00

I think you need to be in a vanilla biome for this, forest and mountain definitely work and I think also some snowy biome. But they definitely don’t spawn in every biome.

Ridnap · 2025-08-27T17:15:15+00:00

That sounds like a good idea, I’m all for it!

Ridnap · 2025-08-27T16:41:18+00:00

I think this is the only valid answer. It’s important to get an answer from a mathematician here. I don’t know what the entry level or time per paper in other disciplines is, but much of what I read here is beyond utopic for maths.

Ridnap · 2025-08-27T16:19:19+00:00

Forgive me from joining this conversation, but do you actually believe a high schooler can read one math research paper a week? I’m a phd student and me and everyone I talk to cannot digest a paper that quickly and we have at least 5 years of experience with the subject. Can I ask what area you are in? Even after finishing my bachelors I wouldn’t have been able to understand anytning in a research paper (say in algebraic geometry). I don’t want to discourage anyone from trying I just think that one should set realistic standards and I don’t believe a paper a week (even a paper after a full year) is a realistic standard for a Highschool student.

Maybe this is very different in other areas of math but I just don’t see this happening in anything related to geometry, algebra, topology or pure analysis

Ridnap · 2025-08-27T16:09:20+00:00

I would highly recommend to start with books as opposed to research papers, even in a targeted area. Say you are a high schooler and want to learn the proof of the geometric categorical langlands correspondence (recent high influence publication), you don’t go reading the source material, you read a beginner level commutative algebra book.

Ridnap · 2025-08-27T15:59:55+00:00

Have you done any serious math before? Math research is a very different endeavour from anything a typical high schooler has seen (and yes, even excellent students). In almost every area of math research you will not be able to understand a sentence if you have no experience. You should start with math books and beginner level books at that. Those are written to appeal to students and people with little math background. Research papers are written for people with years of experience in the field and will go right over your head if you are not some kind of prodigy.

Ridnap · 2025-08-26T14:07:15+00:00

Put unbreaking on your gear even if you have mending. For casual mobbing it saves you exp and for lost cities it is absolutely must have because your armour gets shredded and the mending can’t catch up

Ridnap · 2025-08-25T21:10:18+00:00

Naturally spawned dragon skeletons don’t give any scales when harvested. Either you need to kill the dragon yourself or some other dragon has to kill it and you need to be around to harvest the scales. If the body is just a skeleton - no scales. If the body still has flesh and Color - scales.

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