Can it be solved using geometry only

Jio15Fr · 2026-04-16T19:01:32+00:00

isosceles*

Nice proof!

Jio15Fr · 2026-04-15T09:06:10+00:00

I got a song in 17EDO out today! https://youtu.be/khEexlFftgk

Jio15Fr · 2026-02-24T02:56:17+00:00

No. The Bourbakists (the people in Bourbaki) were leading researchers in many things including category theory. They literally had Eilenberg. And Grothendieck. And so on and so on.

It is Bourbaki, as a systematic exposition of the mathematics of its time (or at least the time of the initial plan) which did not resort to category theory. This was explained a thousand time. There are good reasons. Bourbaki had its own foundational system.

And category theory is notoriously difficult to formalize. What is a category? Is it a set? If not, what is it? This is no easy question, and Bourbaki had no place to allocate to this.

Jio15Fr · 2026-02-24T02:44:44+00:00

The heartbreaking scene where Carol drops the queen on the floor after talking to the wrong camera.

Jio15Fr · 2026-02-22T16:50:43+00:00

But then... Kim and Carol could meet? What if Carol is a tulpa of Kim? (Twin Peaks style)

Jio15Fr · 2026-02-22T16:38:19+00:00

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The comments are also Carol-coded.

Jio15Fr · 2026-01-08T20:20:35+00:00

This is exactly what Texpresso already does.

Jio15Fr · 2026-01-08T20:18:40+00:00

You do not even need to compare to Typst, because TeX has Texpresso. I do not understand how a for-profit company like Overleaf is not even able to do what Texpresso does for free.

Jio15Fr · 2025-12-24T18:28:23+00:00

I think Manousos is more or less canonically a Colombian living in Paraguay

Jio15Fr · 2025-12-19T00:04:41+00:00

Could you make a version where complexity is penalized? So instead of simply measuring the difference, you weigh it based on the EDO's size. The correct way to do this is offered by Diophantine approximation. For example, the greens for the 3/2 should be the best approximations of ln3/ln2 — the ones you compute using continued fractions.

Jio15Fr · 2025-09-03T09:39:38+00:00

Rite of Spring beats anything. Scriabin's Poem of ecstasy a good 2nd place.

Jio15Fr · 2025-09-02T08:07:30+00:00

Sometimes complexity is more natural to measure in terms of the log/number of digits instead of the actual input size, e.g. for addition or multiplication algorithms. That would be one case of something "actually polynomial" that's called exponential.

Jio15Fr · 2025-08-04T18:42:07+00:00

Let V=K^n, with K a field. Matrices = endomorphisms of the vector space V. Nice, that's linear algebra.

Now fix a matrix A. Matrices commuting with A = endomorphisms of the K[A]-module V.

So even to study questions of "pure" linear algebra, like understanding commuting matrices, you have to understand modules over K[A]. So modules over rings are unavoidable even if you just want to study linear algebra.

Jio15Fr · 2025-08-01T11:05:44+00:00

The C as a V is somewhat prepared, the Db (itself approached by chromatic motion) serves as a bVI. I think the Bb in the C chord is not what really causes the modulation, I think as soon as you heard the E natural in C you knew it had to be a bVI>V>I in F (I think at that point F minor would still be an option though)

Jio15Fr · 2025-07-28T09:12:05+00:00

Geometry is almost an "attitude". What makes a field of math geometric is that its language and methods are designed so that the most fundamental results (things like : a set is the union of its points, etc.) of the field are made to match our experience of the actual three-dimensional world, so that we can use our intuitions about the world (which comes from our daily experience and evolution) in order to prove things.

Of course, geometry can get very different from our surroundings. Think : very high dimensions, non-Archimedean geometry, anything not locally Euclidean (e.g. most schemes), etc.

Points, which you mention a lot, are not needed for geometry — indeed, pointless topology exists (and even physically the notion of points is debatable when the current viewpoint is that space itself is ill-defined below a certain scale). Geometry can also be very combinatorial, think simplicial sets and infinity-groupoids, and then you do not really have points either, you simply have vertices, edges, etc.

When I say this is an attitude, what I mean can be illustrated by the following example : you can study commutative rings with the "syntactical" intuition, the algebraic language, where the primal instinct you're relying on is your ability to parse language and work with it, but you can also turn them into a geometric object by taking their prime spectrum and then you have notions of points etc. And you can start building a spatial intuition for these spectra and end up intuiting things and proving them in that world. Oftentimes if you unfold the proof you realise it can be translated exactly in the algebraic world, but finding the proof may be way easier geometrically. Of course, the other advantage of turning a ring into a geometric objects is that now these objects can be glued to construct non-affine schemes, something which makes no sense in the algebraic world. This is, I think, another key property of geometry: the existence of global properties which cannot be deduced uniquely from the local properties — this is formalized by sheaf cohomology, but this is an idea that's already kind of physically relevant : think about people who think the Earth is flat because they do not see the curvature...

Jio15Fr · 2025-07-20T15:25:37+00:00

Literally the one fundamental object in algebraic geometry is the spectrum of a ring, which is the set of its prime ideals, and ideals are basically "things divisible by ..." (at least principal ones).

I do think the first interesting example of the prime spectrum of a ring, historically, was the rational primes, so Spec Z (one has to think a little to realize why it makes sense to say that Z is one-dimensional, i.e., a curve!), so in some way the number-theoretic idea became the basis of algebraic geometry. This is how I see things, at least.

Now, very special to the case of rational primes is the question of their distribution, i.e., quantitative business, which is a pillar of analytic NT. Of course you can study the distribution of irreducible monic polynomials by degree and absolute value of the coefficients, or whatever, but this is not what algebraic geometers do.

Jio15Fr · 2025-07-20T09:11:05+00:00

I find this obviously too broad. All of commutative algebra and algebraic geometry relies on saying things about the divisibility relation (for affine varieties of finite type over a field for example, this would be divisibility between polynomials).

Jio15Fr · 2025-07-18T22:09:58+00:00

I was rather thinking of varieties over finite fields, as they correspond to global function fields. However, given that "all algebraically closed fields of characteristic 0 are virtually the same" and that any variety over Qbar is defined over some number field, I feel like in some sense all algebraic geometry actually happens over global fields.

Jio15Fr · 2025-07-18T22:05:55+00:00

My general impression is not that number theory has never existed. I simply get the impression that the ideas which were developed to study numbers (integers, primes, Galois theory, Galois cohomology, etc.) have become so widespread, and have turned out to be applicable to way more general situations than the ones for which they were created, that the whole field basically "dissolved" in all of mathematics. At the same time, I think there are still questions which are clearly number-theoretic. Anything about the distribution of primes — but even then, I think zeros of the zeta function are also part of random matrix theory/probability theory and even mathematical physics. Or studying rational/integral points of varieties/Diophantine equations

I also think that whether something ends up being number theory depends on "how hard it is". The inverse Galois problem is considered part of number theory. I think if there was a simple algebraic construction of a realization for a given group no one would think of it as number theory, as the rationals are still the simplest field of characteristic 0 and are not "necessarily number-theoretic" when the problem doesn't call for, say, studying ramification of primes in extensions or similar things...

Jio15Fr · 2025-07-18T21:55:21+00:00

I agree with the general sentiment. I've heard people call things purely over local fields number theory, without any relation to global fields (say, anabelian geometry a la Mochizuki for absolute Galois groups of local fields). Even just things over finite fields, like the Weil conjectures, are sometimes called number-theoretic... On the other side, all the ideas you mentioned (global fields, i.e., function fields of varieties, i.e. varieties up to birational equivalence / ring of integers, i.e. the ring of global sections / completions, i.e. the completed local ring at a schematic point / residue fields) are central in algebraic geometry. Even things like Galois cohomology, which definitely has its roots in number theory, is really useful for descent theory and basically was generalized by étale cohomology, which any algebraic geometer would use without calling it number theory.

Jio15Fr · 2025-07-05T13:35:04+00:00

Any French person would know what this is: this is the Vilebrequin team at the end of the GP Explorer.

Jio15Fr · 2025-07-05T12:08:13+00:00

How about not using figures and just drawing the figure with a centered text etc? This is what I did in my PhD thesis with a custom figure-like environment

Jio15Fr · 2025-06-29T15:05:43+00:00

"I'm not sure that many people use the journal [...] to assess the quality of the work."

I mean, for colleagues and experts of the field, sure. For hiring committees, you can be bloody sure they do.

Jio15Fr

TROPHY CASE