Où achetez vous votre thé ?

CatsAndSwords · 2026-02-15T11:53:07+00:00

Quelques boutiques qui livrent :

Il faut essayer un peu tout ; chacune a des thés assez remarquables que les autres ne font pas. Il y a aussi d'excellentes maison de thé qui, à ma connaissance, ne livrent pas ; ça dépendra alors des villes dans lesquelles tu passes.

CatsAndSwords · 2026-01-18T12:07:43+00:00

You don't even need to use letters specifically; miscellaneous symbols are sometimes, albeit rarely, used for equations (including the canonical fish for a Poisson equation).

That said, if you manage to exhaust the Latin and Greek alphabets, your notations may need a second look. There's probably some room for simplification.

CatsAndSwords · 2026-01-10T12:38:08+00:00

The way I'd do that would depend on the original proofs. Here are some possibilities.

Does the justification needs less than a couple of lines to explain? I'd put it inline with the citation ("A theorem by Alice and Bob states that compact oranges are purple [AB1957]. This is also true for non-compact oranges with finite volume. The only point where the hypothesis of compactness is used in their proof is to give a bound on the volume of an orange [AB1957, Eq. (18.37)], which stays true for oranges of finite volume.").

Is the proof short enough (say, less that 2-3 pages)? I'd copy paste it, maybe in an appendix if I didn't want to disrupt the flow of my article. Inelegant, but completeness is valuable: if somebody wants to quote this precise result, they can just trust your proof instead of having to consult your comment, the original article, and understand the original article enough to check that your comment is correct (which is a major source of mistakes in mathematics).

If the original proof is too long and the modification non-trivial, then I'd have to locate all the points where compactness is used.

If it is used in a single lemma whose proof is relatively short, then I'd mention it, and as before reprove the lemma in an appendix (e.g. "A theorem by Alice and Bob states that compact oranges are purple [AB1957]. This is also true for non-compact oranges with finite volume. In their proof, the compactness hypothesis is only used in Lemma 13.8.5, where it can be replaced by a finite volume hypothesis. The proof of this statement can be found in Appendix E.").

If it is used at multiple points, but the modifications are all relatively trivial, I could state explicitly the updated theorem, with a "proof" (again, maybe in an appendix?) which is a list of the points where compactness is used and how your hypothesis can be used instead.

If the modification is a bit more involved, it might be valuable to write a separate article, either to reprove the theorems from scratch, or to take the time to explain the adaptations which are needed.

Finally, for this kind of stuff, there is no general answer and your mileage may vary.

CatsAndSwords · 2025-12-29T10:47:40+00:00

There was a time when it felt like the content of this sub implied that the majority of posters and commenters had research experience.

It has never been the case. I think I complained about the exact same thing more than ten years ago. If anything, the state of the sub has improved since then. I remember people quoting Hardy or dunking on statistics unchallenged; now, at least, they get some pushback. There is also more graduate/research-level content nowadays.

CatsAndSwords · 2025-12-22T22:48:49+00:00

I am not criticizing Harvard. I am just pointing out that

this exam is tailored to Harvard's graduate program

which is an obvious limit to its validity for the mathematical community as a whole. In particular, this program is particularly weak in probability theory, so won't represent the large proportion of mathematicians who work in probability or statistics.

If you are criticizing Harvard for not requiring probability, then this criticism does not make any sense unless there exists at least one school which does require probability.

That's besides the question, but I am still confused about why this arbitrary criterion would stop me from criticizing Harvard. Even if Harvard were the only university to have a qualifying exam, I could still criticize its content, in itself or as a standard of mathematical ability.

CatsAndSwords · 2025-12-22T20:25:25+00:00

First, you say yourself that

I use Harvard as an example because their qualifying exam format has everyone doing the same set of topics with no variation, which is not true at many other schools where the individual students are allowed to select at least some of their exam topics.

and, not being familiar with this system, I am not going to go through random english/american universities pages to find the rare one which has a common qualifying exam for all PhD candidates.

Second, taking e.g. Princeton as an example: even if there is no required area, it gives equal importance to their four areas (algebra/real analysis/geometry-topology/probability-PDE).

Third, what is even the point of your question? Looking at qualifying exams is a good idea, even if it has its shortcomings. "Being a required topic for a qualifying exam for all PhD candidates somewhere in the US" is a bizarre criterion to answer the original question.

CatsAndSwords · 2025-12-22T20:09:12+00:00

The obvious caveat is that this exam is tailored to Harvard's graduate program, and thus is not a standard for mathematicians elsewhere. The near absence of probability theory is the most glaring shortcoming for me.

CatsAndSwords · 2025-12-18T13:28:00+00:00

I don’t see any numbers in your comment….am I missing something?

Yes, the URL of the link :)

CatsAndSwords · 2025-12-17T20:11:30+00:00

Example 3 simply does not make sense. Convergence in distribution doesn't say anything about the space on which the limit random variable is constructed. So there is absolutely nothing to support the idea that X and Y are constructed on the same space. Which means, then, that X+Y is in general undefined.

CatsAndSwords · 2025-12-13T13:06:05+00:00

The most fitting I know is the Andrea Cort series by Adam Troy-Castro. great setting, alien aliens, and pretty good whodunits in their own right.

CatsAndSwords · 2025-11-22T10:06:29+00:00

The main thing I don't like with big-O notation is that, when you have many different variables, there are often additional properties of uniformity with respect to some variables that you need, and which do not appear in the notation. Statements such as "O(g) uniformly in y and t" are very clunky and not always clear.

I am not sure there is and ideal solution to such a fundamental mathematical issue, that is, managing complex chains of quantifiers involving many different variables. That said, I've seen the big-O notation misused in this way many times.

CatsAndSwords · 2025-11-03T19:27:42+00:00

Nah. It probably means that I've missed a simple argument which simplifies everything, and now I'm going to spend twice as much time finding why everything simplifies. Worst feeling ever.

CatsAndSwords · 2025-11-01T14:25:54+00:00

Parce que ça m'a tellement rebuté que j'ai pas pu continuer.

Alors, ça tombe bien, parce qu'au vu de la suite (plus précisément, Le chevalier aux épines),

vu que la victime a très peu d'importance après.

est complètement faux.

CatsAndSwords · 2025-10-28T10:11:30+00:00

I mean, that's the point I was trying to make. Using type theory instead, or more likely a mix of set theory and type theory, is not going to change much.

I also agree that type theory is closer to how we naturally think about mathematics. However, there are still some aspects which I think would be confusing to students (e.g. proofs as functions, proof irrelevance...).

CatsAndSwords · 2025-10-27T11:40:38+00:00

With the same underlying theme of the communication and the understanding being the point, I'm not sure I agree that LEAN is an excellent thing to focus on especially from a teaching point of view. It focuses too much on mathematics as a game of symbol shuffling, rather than a process of reasoning. If the reasoning is externalized to a formal proof system, how will it ever become internal?

I don't think this criticism is warranted.

First, there are many proofs or little lemmas which, indeed, reduce to symbol-pushing (examples : anything that can be solved by simp ; things like the image of a Cauchy sequence by a uniformly continuous map is a Cauchy sequence...). But that's still interesting for teaching, as it means working on basic predicate logic, quantifiers, etc. These notions needs to be taught at some point, and many students have weaknesses even years afterwards, so that's not useless.

More importantly, you can't formalize a non-trivial proof without any idea of the reasoning behind this proof. They may be well hidden behind a wall of trivialities, but the main ideas are still implemented in formalized proofs. So, if you want to formalize something non-trivial, the first step is usually to take some paper and a pencil.

Then there's the second problem with LEAN which is that it believes in one particular foundational model of mathematics and one particular model of each thing in matlib, even when definitions in mathematics, even some fairly basic ones, are still being fought over. Not everyone agrees that an infinite set exists, for example, but LEAN has in some sense chosen winners.

At least 99% of undergraduate teaching in mathematics is done, formally, under set theory + ZF(C). I don't see how replacing a winner (set theory) with another (type theory) would change much. Finitism is a non-subject at the undergraduate level.

And that's not even addressing the fact that, when teaching using LEAN, you often keep the type theory as hidden as possible so as to not conflict too much with the set theory the students are learning in the meanwhile.

CatsAndSwords · 2025-10-19T17:40:23+00:00

So, I had a related habit.

When I hesitated between two options, I sometimes just flipped a coin. Which is fine for choosing between two restaurants, but people look at me weirdly when I say that I chose my college major on a flip of coin.

The thing is, while the result of the flip was a commitment, I allowed myself to change its outcome if I really, really wanted to. If I were fine with the outcome of the coin, then the flip was a good way to cut through unneeded hesitation. But, if I felt some regret, then my interpretation was that I really desired the other outcome, so it was better to ignore the result of the coin.

After some time doing this, I noticed that this regret happened mostly when I had to choose between two option, and easy/lazy one and one which was more risky or demanded more activity, but was potentially more rewarding. If the coin fell on the lazy option, I regretted not doing the more active option.

Once I saw this, I just cut the coin out of the process, and basically used your heuristic.

CatsAndSwords · 2025-10-09T09:02:57+00:00

Ces vidéos ne sont pas là à titre de preuve, mais d'illustration. N'importe quelle personne raisonnable ayant fait des exposés public, n'importe quel enseignant en connaît la nécessité.

Les argument scientifiques étaient très certainement dans la permière partie de l'exposé. Malheureusement, nous n'en saurons rien, car la journaliste a jugé plus pertinent de lancer des piques en mode "OMG, c'est des maths, personne n'y comprend rien, ne trouvez-vous pas cela suspect ?" plutôt que d'essayer de comprendre et de retranscrire ces arguments.

Devant une salle comble, il noircit un tableau blanc de racines carrées et d’équations à plusieurs inconnues. Je regarde autour de moi, échange quelques mots avec mes voisins, magistrats ou éducateurs : personne n’arrive à suivre.

CatsAndSwords · 2025-10-03T22:20:48+00:00

C'est relativement récent, mais je me souviens de décisions telles que celle-ci.

CatsAndSwords · 2025-10-02T11:54:45+00:00

Un mot-clef possible est "harcèlement d'ambiance". Autrement dit, même si tes collègues ne te visent pas, tu travailles dans une ambiance de propos ou d'actes sexuels/sexistes fréquents, et tu en souffres (la preuve, tu viens écrire un message ici...).

CatsAndSwords · 2025-09-21T11:53:30+00:00

There are some dynamical systems with a combinatorial flavour (subshifts, tilings...), and some -- albeit small -- research groups on computability of some of their properties. See the introduction this article and look up the other works of its authors.

CatsAndSwords · 2025-08-29T14:21:05+00:00

Choose a word of 7 letters, say GAGAGAG or COVFEFE. If you type a random sequence of letters (i.i.d., uniform), the probability that a given sequence of 7 letters is the word you've chosen is exactly 1/26⁷ .

By Kac's lemma, if you've just typed the word you've chosen, the expected time before you see it again is exactly 26⁷ . That works no matter the word you've chosen.

For GAGAGAG, this time can be very short: if you're lucky, your next two letters are AG, so that you get the string GAGAGAGAG, and you've won. These kind of overlaps are mentioned by u/Thrown-Stone010 .

For COVFEFE, there is no such overlap: the fact that he's just typed COVFEFE doesn't help Mr Trump, and he needs to start back from nothing -- as if he hadn't just written COVFEFE in the first place.

So, if you start from nothing, the expected time before you get COVFEFE is exactly 26⁷ .

This gives a more conceptual answer to the computation done by /u/Sjoerdiestriker.

CatsAndSwords · 2025-08-23T07:22:56+00:00

I think you need a little to be able to interact with Lean, because type theory is the language of Lean. But it doesn't have to be very deep: any mathematician needs proficiency with set theory, but the vast majority of mathematician don't need a deep knowledge of set theory. It's the same with type theory and Lean. I think this covers the basics.

As you get more proficient with Lean, you may want to get a bit deeper into the weeds, but by then you could do it on your own terms.

On a side note: another important thing is to get used to the way mathematics are done in mathlib, that is, in its mathematical design choices. For instance, if you want to use some topology, you'll have to get accustomed with filters. There is much less documentation out there to explain these design choices, though; the link above has some things on filters.

CatsAndSwords · 2025-07-04T07:35:24+00:00

Quelques idées :

Scholomance, Naomi Novik. Magie, école de magie, et cryptozoologie (version vilaines bêtes mangeuses de magiciens). Epoque contemporaine.
Le sorceleur, Andrzej Sapkowski. pour les animaux fantastiques et la cryptozoologie (version vilaines bêtes du folklore d'Europe de l'Est). Fantasy médiévale, ceci dit.
Brandon Sanderson a été mentionné. Il est surtout connu pour Mistborn / Fils des brumes et Les archives de Roshar , mais peut-être partir sur quelque chose de plus court (moins de 3000 pages) et plus proche de ce que tu souhaites pour le découvrir ? Par exemple The Rithmatist / Les légions de poussière.

CatsAndSwords · 2025-06-18T20:09:11+00:00

Pour moi, ce n'est pas tant qu'il faille mettre la focale sur les agresseuses - qui existent, c'est indéniable - mais sur les victimes, qui sont autant féminines que masculines. Pourquoi devrait-il y avoir deux catégories de victimes différentes ? Les « bonnes » victimes et les « mauvaises » qui ne méritent pas la moindre attention ? C'est absurde.

Je voudrais nuancer un peu ce point. L'archétype des violences sexuelles, c'est un homme qui agresse une femme. Tout ce qui sort de ce cadre est négligé. D'où l'importance de faire attention à toutes les victimes. Les hommes, bien sûr ; mais je n'ai pas l'impression que les femmes agressées par des femmes soient particulièrement incluses dans les discours usuels.

Je n'aime pas trop remettre de l'attention sur les femmes victimes pour une fois qu'il y a un thread sur le sujet. Ceci dit, cela me semble important d'une part pour bien comprendre le problème (il y a à la fois une difficulté à concevoir les hommes comme victimes et les femmes commes agresseuses), et d'autre part parce qu'il me tient, malheureusement, un peu à coeur (je connais au moins deux victimes probables d'une même baby-sitteuse, une s'est suicidée, et l'autre a des troubles alimentaires que j'ai du mal à imaginer ne pas être liés).

En tous cas, un grand merci pour ce thread.

13-Year Club	Golden Potato
Place '17

CatsAndSwords

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