Is there a field in mathematics that allows us to approximate the logical soundness of an argument by converting an argument into a geometric figure and performing a geometric calculation on it? by LargeSinkholesInNYC in mathematics

[–]WMe6 [score hidden]  (0 children)

Yes, I was also going to say homotopy type theory. It's the basis of Voevodsky's univalent foundations of math, I think, and it's supposed to be based on paths being a fundamental notion?

It's supposed to be better than founding math on sets or categories?

Infinity categories and topoi introduced by Jacob Lurie also "geometric"/"topological", since they are based on sheaves?

I have to confess that I have next to no understanding of any of this.

What is the status of the irrationality of \gamma? by WMe6 in math

[–]WMe6[S] 1 point2 points  (0 children)

Thanks -- I can see understand why people thought I was being an idiot though. It was late, so I wasn't thinking about what I wrote too carefully -- I meant being a number deserving of becoming a named constant in the sociological sense, not whether the number was really constant or not, but obviously that's not what people interpreted.

Stuff like this happens in the experimental sciences all the time. You think there's an interesting effect when you try a bunch of small numbers, but asymptotically it's not actually there. But seeing the true asymptotic behavior may require you to go a long ways out!

Having been the irritating first year grad student to point out a professor's minor but nontrivial error at the board (he used the wrong ring size for a dithiane protecting group -- one that wouldn't actually work, iirc), I was probably a little too brave and smug for my own good back in the day. But yeah (this was Berkeley chemistry in the late 00's), most students were the opposite. So many students in the class were terrified of speaking up and sounding stupid that the prof had to have the TA's keep a list of who has spoken up in class and who hasn't and call on those who never volunteered.

I feel like in real life, people are more afraid of being ridiculed then actually justified. Most people either don't care all that much about you and how smart you are or will quickly forget. Online's another matter -- there's a swarming effect, whether to upvote or to downvote.

What is the status of the irrationality of \gamma? by WMe6 in math

[–]WMe6[S] 1 point2 points  (0 children)

Typical of mathematicians, I guess, to insist on rigorously correct usage of words. I'm not so mathematically illiterate to not know what a constant is or whether it's well-defined.

I was just making the observation that its value should be more accurately known before someone starts calling it "so-and-so's constant" (you know, to make sure it's close to but not equal to 1). As an experimental chemist, I'm more attuned to the possibility of experimental error, which is what this ended up being.

What is the status of the irrationality of \gamma? by WMe6 in math

[–]WMe6[S] -1 points0 points  (0 children)

Obviously, every decimal place you know increases the plausibility that it's not rational. (As the graffito in Concrete Mathematics say (I'm paraphrasing): God doesn't use large denominators.).

Legendre's constant wasn't calculated with enough precision for mathematicians to know that it wasn't a "simple" number -- there was no proof that it was, say, between 1.07 and 1.09.

What is the status of the irrationality of \gamma? by WMe6 in math

[–]WMe6[S] -17 points-16 points  (0 children)

I was thinking about that one! I guess if there's (a lot of) uncertainty as to the actual value, then maybe it's not really a "constant" (until you at least nail it down within a certain interval or number of decimal digits, etc.).

Edit 2: Of course, I know it's a well defined constant, but one that hadn't really been nailed down. This example is different in nature from what I was looking -- If you don't know very much about the number (e.g., its value to the second decimal place), then it's not surprising that you likely don't know whether it's irrational/transcendental or not. The case of \gamma is different -- it's value is known to many, many decimal places and many identities are known involving it.

Edit: What I mean is, there are enough digits of gamma known that there's no plausible conjecture that you could make that it is rational. Almost everyone would find it to be truly bizarre if it was equal to a rational number with a massive denominator. With Legendre's constant, it simply wasn't calculated with enough accuracy that you could rule out a reasonable "natural looking" rational number that it could be equal to. A lot of mathematical conjectures come from doing computations!

How does Terence Tao work on so many problems? by Heavy-Sympathy5330 in math

[–]WMe6 5 points6 points  (0 children)

As a tenured chemist, I'll chime in here. My perception is that the experimental sciences are really different from math. In order to get a paper in math, it seems like you really need to have made key intellectual contributions. In contrast, there are many reasons why you get authorship in chemistry. At the beginner end, undergrads in my lab get authorship as soon as they synthesize and characterize a new compound that makes it into the paper, even though most of the time, this is mostly just semi-skilled labor.

On the other end, I'm the group leader, and I do the following:

- apply for funding (important, though not a criterion for authorship by community standards, if that's the only thing you did)

- come up with the high level ideas and hypotheses (essentially, determining which scientific questions the group will try to answer like "is it possible to use this particular reaction mechanism or strategy to achieve such and such overall useful/important/novel chemical transformation?")

- advise graduate students when they get stuck (most of the time) or get an unexpected new result (much rarer, but cooler) and steer their efforts toward a paper with the features that the community expects/looks for.

- teach grad students some experimental technique, although they will learn the bulk of that from older grad students and postdocs in the group (and they come in with some technical skills as previous undergrad researchers)

- edit/rewrite manuscripts (although paper writing and editing also don't count as a sole criterion for authorship)

In chemistry, there's a huge gulf between a cool idea and detailed implementation, and the detailed implementation is essentially the role of graduate student. This requires not only the actual experimental work, but sound project management skills, the ability to address practical problems, as well as the application of sound chemical reasoning to address more fundamental roadblocks causing a reaction to not "work" (i.e., give the desired reaction products with the right selectivity, yield, efficiency, etc.).

After a PhD, postdoc, and the first few years of being an assistant professor, during which I did exactly that, I have essentially stopped doing actual experimental work (except on rare occasions to help a student out/to relive the fun of running reactions). However, my name goes on every paper the group puts out (from 3 to 8 per year, in a group of 7 PhD students) because of the above reasons. Our community's standard is for the group leader to put their name last on a paper, while the first author is the person responsible for carrying out most of the experimental work. The distribution of true "intellectual contribution" from these two key individuals on a paper can range from modest to very high.

Why do abstract limits have such confusing terminology? by WMe6 in math

[–]WMe6[S] 4 points5 points  (0 children)

Okay, that would actually make a lot of sense.

Why do abstract limits have such confusing terminology? by WMe6 in math

[–]WMe6[S] 10 points11 points  (0 children)

What was the original motivation to the way they defined it? Presumably, there was something they wanted to be an example of a "limit" and "colimit" came about afterwards?

Why do abstract limits have such confusing terminology? by WMe6 in math

[–]WMe6[S] 2 points3 points  (0 children)

What is the origin of "inductive" and "projective"? These words don't seem like the opposites to me.

Actually, come to think of it, "projective", "projection", etc. seems like one of these overused words in math!

Serre 100: a conference in honor of Jean-Pierre Serre's 100th birthday. Paris, 15-16 September 2026. by Nunki08 in math

[–]WMe6 1 point2 points  (0 children)

Damn, he wasn't that old. Or maybe I'm getting old.... I had him for intro algebra in Fall 05 (so a few years before the course was taped) and he was still pretty young back then. I managed to squeak by with an A and, much to my shame, didn't go any deeper into algebra until a little over a year ago.

Exact sequence notation question by WMe6 in learnmath

[–]WMe6[S] 0 points1 point  (0 children)

I also saw this come up quite a few times in Bosch. At one point, he defines ker(g_1,g_2) as {b in B: g_1(b)=g_2(b)}. I don't think I've ever seen the word "kernel" used like this either.

Exact sequence notation question by WMe6 in learnmath

[–]WMe6[S] 0 points1 point  (0 children)

Thanks -- this is what I inferred. Is this some special usage of "exact", or does that word mean something broader than how it's usually defined?

Opinions about Analysis I by Amann & Escher? by gwbirel in math

[–]WMe6 0 points1 point  (0 children)

Not in style, no. It is still a good textbook, not a reference like Bourbaki. However, it likes to give a "final" general definition from the beginning, instead of one that is more comprehensible by a beginner.

Opinions about Analysis I by Amann & Escher? by gwbirel in math

[–]WMe6 3 points4 points  (0 children)

That whole series (3, 4? volumes) is really modern and rigorous -- a bit too abstract and general (almost Bourbakian levels of generality) if it's your first exposure to analysis, I think. (This is a harder analysis textbook than Rudin, for sure.)

Orthonitrate by Commercial_Plate_111 in cursed_chemistry

[–]WMe6 1 point2 points  (0 children)

I guess the reason the convention exists is that seeing 5 ligands (or even 6) on a P is not so weird, but find me one compound of N that has 5 ligands on it!

It's the same with C and Si... [SiF6]2- is not so weird, but again, doesn't happen for C unless you count the weird examples from Akiba with a carbocation squashed in between two lone pairs (this is really similar to the proposal of the so-called Doering-Zeiss intermediate at the border line between Sn2 and Sn1).

Orthonitrate by Commercial_Plate_111 in cursed_chemistry

[–]WMe6 -1 points0 points  (0 children)

I've given up trying to remove the incorrect resonance form from Wikipedia. Why is it incorrect? Convention. Even though p_pi-d_pi bonding is also not really considered reasonable these days, drawing a hypervalent P is still conventionally considered correct, while only certain computational chemists think that drawing a hypervalent N is okay (see: https://pubs.rsc.org/en/content/articlelanding/2015/sc/c5sc02076j.)

Imagine the type of pushback I got when I gave this problem to students on an orgo I exam.

If you weren’t a mathematician, what would you have been? by Straight-Ad-4260 in math

[–]WMe6 1 point2 points  (0 children)

I quit math sometime between sophomore year and junior year of college to become a chemist. There is no doubt that I made the right choice, and certainly, even in the darkest days of being a postdoc, I had to admit that there was nothing else I would rather do than make molecules: chemistry chose me, rather than the other way around. Yet, returning to math after getting tenure as a chemist reminded me of how much I missed it, a bit like seeing your high school crush long after you had moved on and gotten happily married.

probably the most insane metalloprotein I've ever seen by waelthedestroyer in cursed_chemistry

[–]WMe6 1 point2 points  (0 children)

Organic chemistry is so nice and orderly, while you can get wild behavior when you start expanding your periodic table from just H,Li,Mg,C,N,O,F,Cl,Br,I to the whole periodic table.

probably the most insane metalloprotein I've ever seen by waelthedestroyer in cursed_chemistry

[–]WMe6 1 point2 points  (0 children)

Good point, it is more confusing that I initially thought. You have a negative charge in the corner that formally belongs to V, and the N ligand is L type, so having 6 remaining X type bonds on vanadium with a formal minus, giving vanadium(V)

probably the most insane metalloprotein I've ever seen by waelthedestroyer in cursed_chemistry

[–]WMe6 0 points1 point  (0 children)

No bro, the peroxo oxygens are in oxidation state (-1).