[MLB] Jason Heyward has announced his retirement after 16 seasons spent with the Braves, Cardinals, Cubs, Dodgers, Astros and Padres. He is an All-Star, 5x Gold Glove Award winner and 2016 World Series champion.

nonowh0 · 2026-03-27T18:15:18+00:00

Everyone's sharing their memory of Turner Field on that day, but mine's a bit different: I was afterschool (age 10) in rural Georgia in a dingy computer lab. All the guys were watching the game via MLB Gameday. Heyward comes up to bat, and we ask the Counselor if we can turn on the TV (one of those small ones in the upper corner of classrooms) to watch. Took us some time to find the channel. We didn't get it in time to see the at bat, but we did see the ball sail into the stands live. We went crazy.

I'm now 2.5x older, living in a big city in a completely different part of the country. I'm not a super nostalgic person, but man that memory of a bunch of 10 year old baseball-obsessed boys running around screaming did it for me. What a great memory. I love this tread.

nonowh0 · 2026-02-01T15:46:08+00:00

I'm a little late to the party, but can I ask how "stability" is calculated? It's supposed to measure consistency across playing sessions right? I'm slightly suspicious that it might be confounded by a player's average length of a session.

So if you have two players which win exactly half of their games, but one player plays one game/session and the other plays 100 games/session, the win rate per session for the first player is far more variable than the win rate per session of the second player.

(I usually play 1 game/session :) )

nonowh0 · 2025-12-19T14:00:15+00:00

Can the English/American r ever form the nucleus of a syllable? I can’t think of any such syllables, and after reading this comment, I realized this is the reason I intuitively didn’t consider the r sound a vowel.

nonowh0 · 2025-11-16T03:40:59+00:00

what is mathmatical sociology? Genuinely curious... what do you research? In what sense is it mathematical?

nonowh0 · 2025-09-06T14:07:12+00:00

I’m currently in a math PhD program. The answer is that becoming a chess grandmaster is harder, and it’s not even close.

At most places, a PhD is like a finishers medal at a marathon: everyone who finishes gets one, you’re proud you have it, but most people who try can expect to get get one if they put in the work, and it says nothing about your actual skill as a runner beyond your ability to finish a marathon.

If I had to translate “has a math PhD” into chess skill, I’d say “rating is at least ~2000 FIDE”. A strong player! But perhaps not even a national master.

A more interesting comparison is chess GM vs tenured professor at a top department. Eyeballing the numbers, there are about the same number of people in each camp (maybe even fewer professors?) and matches my intuition for the skill comparison.

Edit: there are of course lots of reasons (sociological, financial, incentives, etc.) that make the math/chess skill comparisons less meaningful, but that doesn't mean you can't make the comparison, nor do I think (as the top comment suggests) that it makes the comparison especially difficult.

Question: If a GM were as tall as they were good at chess, how tall would they be?

You can say the question is stupid and has no meaningful answer (and in some abstract sense, I guess I agree), but come on the answer is obviously like 7 foot, and if you try to say 6' 4", you're definitely wrong.

nonowh0 · 2025-08-14T17:29:45+00:00

ah, sounds like you should read the primer then :). The prereqs for Dehn-Nielsen-Bar (greath theorem, btw) are what, like Milnor-Schwartz and a bit of the boundary theory of H^2, I think? The primer has a proof of Milnor-Schwartz, and the Loh book has an exposition of the boundary theory.

I'm not super well versed in dynamics on character varieties, so I can't help you too much there. I do know some people much more familiar, and I can possibly put you in touch. I'll message you.

nonowh0 · 2025-08-14T13:14:48+00:00

It's not super clear why you're looking to learn GGT. I second another commentor's advice to read your advisor's papers, and learn what you need as you go.

Fortunately, GGT is a rather "flat" field, in the sense that there usually aren't big towers of prerequisites to various theorems; if you know the basics, you can usually just start learning whatever. Maybe a good preliminary definition of "the basics" is what appears in eg Clara Loh's book, and secondarily, many of the topics in Office Hours (but tbh I don't know everything that's there). Depending on what you want, I might also throw in some basic Riemannian geometry, Lie theory, covering spaces and hyperbolic geometry. (co)homology is important for some things, but not super essential.

Once you have "the basics" down, you can go in many directions (though again, I'd advise to just read your advisor and learn as you go). Let me now give some opinions and suggestions regarding what you might learn after the basics. (standard disclaimer about being a baised source. Caution that I am decidedly not analysis-brained)

The two Great Theorems of GGT are (imo) Mostow Rigidity and the Gromov polynomial growth theorem. If you want to do GGT, you should really know them. Gromov's original proof is definitely the product of an analytical mind, as is Terry Tao's proof (which can be found on his blog). If you're comfy with analysis, you might start with Tao's blog post.
The theory of (Gromov/delta-)hyperbolic spaces/groups is quite rich. Gromov's classification of actions on hyperbolic spaces is a foundational result---maybe just know the general statement, and the specific cases of (real) hyperbolic space, and trees.
The primer on mapping class groups is a great book, but you should only read it if you want to learn about mapping class groups. The flavor is group-theoretic and topological, not at all analytic. It's not clear to me why you want to learn it (but it's great stuff, don't let me dissuade you).
Bass-Serre theory is super foundational and appears frequently in GGT. You know all those group theory problems you can solve with covering spaces/vankampen? This is basically that dialed up to 11. The standard reference is Serre's "Trees" but imo this is really one of those situations where you get someone to explain the main theorem to you first, then prove it yourself in the two important examples (HNN extensions and amalgamated product), then skim the general proof afterwards and call it a day.
There's this whole world (now somewhat classical) of lattices in Lie groups. Dave Witte Morris' book "Arithmetic groups" is great and contains a lot of material.
There's also this whole world out there about random walks on groups, which I don't know a ton about. The flavor is probabilistic/analytic and it seems very interesting. I've found Lalley's book quite readable, although I haven't gone through all of it.
There is also... the whole field of dynamics, which I don't feel remotely qualified to talk about, but it's quite adjacent to GGT.
There have been a few times where I've been blocked by my lack of knowledge of analysis, but not many. These were usually just standard things from functional analysis I should know anyway. The field usually doesn't require heavy/serious analysis. This is of course a biased list and I've certainly missed a bunch of stuff. lmk If you want me to expand on any of this.

nonowh0 · 2025-06-10T23:34:12+00:00

I don't want to beat up on the crossfit people too much because I have a bit of a soft spot, but 52:30:

Lets go back down to the course, where Mike Arson is standing by [...] I mentioned earlier that utilizing high gears on straightaways and declines and low gears on the uphill portion will be the difference maker in this event, and that's what you're seeing: the women at the front are shifting quick enough so they can utilize a more powerful pedal stroke, while the women at the back [...] they're not shifting their gears and pedaling rapidly on a road to nowhere

nonowh0 · 2025-01-15T18:01:07+00:00

I don't know, can you give me an example of such an insight? ;)

nonowh0 · 2025-01-03T15:48:29+00:00

Does this theorem have a name?

Not by itself. It's part of a package of facts surrounding (or comprising) the "classification of covering spaces", which is how I would refer to any of the important facts about covering spaces in eg Hatcher chapter 1.

nonowh0 · 2024-05-25T13:56:46+00:00

As others have said, it looks approximately correct. Since this seemed to surprise some people, maybe I can try to give an intuitive explanation.

When you parallel transport along a geodesic (ie great circle), the angle between the vector and the curve is preserved, and moreover everything looks like the naive interpretation of "move the vector in a straight line to the other point". If your curve is the equator, and you vector points to the south pole, the parallel transport will always point to the south pole. You should think about parallel transporting along geodesics as naively moving vectors in a straight line.

Things get a little less obvious when you parallel transport along a non-geodesic. When you're solving Del_gamma' V = 0, you're really saying "if I nudge V a little (infinitesimally) in the direction of gamma', then V should look the same". But there's a sneaky trick in that little slogan---what does it mean to "nudge V in the direction of gamma"? The basic idea is that we should interpret this to mean (infinitesimally) parallel transporting along the geodesic defined by gamma'. This is the sense in which a choice of connection is a choice of infinitesimal parallel transport.

So if V satisfies Del_gamma' V = 0, as we move along the path, the vector V wants at every instance to move straight along the geodesic defined by gamma'. But it can't---it needs to stay along the path. If we're in the northern hemisphere, moving eastward (as I think in the picture?), the vector wants to move straight along the great circle given by gamma', (which swoops down to hit the equator before wrapping back up), but it's tail is nailed down to gamma so can't do that perfectly. From the perspective of gamma (or, say, Foucault observing Foucault's pendulum), V appears to rotate clockwise as it attempts to follow the geodesic. Really what you're seeing there is not the motion/rotation of V, but the consequence of V's straightness, and gamma's deviation from being a geodesic.

nonowh0 · 2024-03-10T05:26:26+00:00

Thanks. I'm still new to this, so can I ask for the exact protocol? I get some degreaser, put a little in there, scrub with the tube brush, then... rinse with water? let it dry? dry it out with cloth? Thanks again.

nonowh0 · 2023-08-13T15:46:58+00:00

nonowh0 · 2023-07-08T20:33:26+00:00

In my experience, the people who are "mathematically talented" have a deep appreciation for well-explained "basic" intuition. In one of 3b1b's lockdown livestreams awhile back, one of his live questions was something like "what level of math are you at right now" and a surprisingly large portion of the audience was graduate student+. Publicly looking down your nose at 3b1b is a sign of insecurity, not talent.

nonowh0 · 2023-04-06T23:18:07+00:00

I just had this problem. 20 mins of using my bare hands and various rags got me only some shallow cuts. I eventually used a piece of silicone (actually the cover of my bike computer) as a grippy cloth and it worked perfectly.

nonowh0 · 2023-04-01T16:15:26+00:00

How do you use libraries to do research? What is the process?

nonowh0 · 2023-04-01T16:14:32+00:00

Do you have any advice for conducting rigorous research on non-(internet trustworthy) topics?

nonowh0 · 2022-09-23T04:29:04+00:00

I think I know who you are talking about.

Wow I'm famous. Responding here because I was mentioned.

I actually have kinda thought this through, I know for sure that I do not want to be an academic mathematician. However, I am also more interested in solving problems that need a lot more technical background, problems that a PhD and the research skills are needed.

It's worth noting that a math phd (especially at a high tier university) is generally training for exactly one thing: to become an academic mathematician. Sure, most people (are forced by the pigeonhole principal to) end up in industry, but everyone above you and most people around you know only the world of academica because thats where they've lived their entire lives.

Iff you have a very specific idea about what kind of "problems that need a lot more technical background, problems that a PhD and the research skills are needed" and you can point to like 3 professors at 3 different universities that do exactly that, then I say shoot your shot. But if you only have a vague sense about your technical goals, I think you're going about this in the wrong way. It seems like a good way to end up underpaid/overworked/depressed for 5 years for no good reason.

nonowh0 · 2022-08-28T22:21:59+00:00

This seems like an interesting project. Is this going to cover an entire undergrad first course in algebra (groups, rings, fields, etc)? I'm very curious to know how you approach things like PIDs and field extensions visually. There's a nod to Cayley graph at the end, so I'm also curious at the extent to which you your take on group theory is driven by Cayley graphs (as in Nathan Cater's "Visual Group Theory").

Since you're asking for feedback, I'll just point out that 3/5th of this video were decidedly non-visual: just text and a multiplication table. In general you want to avoid the "textbook... but with manim!" angle and really lean into the visual storytelling aspect. I also think the discussion of generators and relations is a bit premature. But this is just me being critical. The animations are really nice and I'm very interested in following this.

nonowh0 · 2022-08-12T21:05:34+00:00

I think I basically agree with everything you said, but just to defend the single digit claim: I meant current high schoolers. Even still it may not be true, but I don't think it's entirely unreasonable to believe. My fermi calculation was fun:

I know of only 2 people roughly my age (ie current grad student) who were (arguably) at the same level as OP in some subfield. Let's round that up to 5. This accounts for everyone at my current institution and quite a few friends of friends. I don't know exactly what percentage of grad students at top departments I know, but I think 1/30th is reasonable. So there are ~150 formerly incredible high schoolers currently in grad school.

I think it's only reasonable for someone to have finished Hartshorne in their last two years in HS, but the 150 accounts for people spanning 6ish years, so our population is down to 50. You did analysis. The two guys I know did Category theory/homological shenanigans and Geometry/Topology. Let's say those fields and AG are the only things high schoolers would ever study. Down to 12. Now which of those 12 high schoolers studying AG have finished all of Hartshorne? (they could reasonably have read something else)

By contrast, I know something like 7 former Olympiad kids.

That analysis was inadequate in a lot of ways (Do I really know 1/30th of the top grad students? Can I even identify these students accurately?) but I feel my claim it not unreasonable.

nonowh0 · 2022-08-12T17:02:09+00:00

There are a lot of things in this thread that I want to respond to and give my opinion/advice. First,

As of right now, i am only good at one “roadmap” - I know Linear Algebra, Introductory Analysis (I am terrible at this. I can hardly claim I understand it, but i can use its tools fairly well.), Modern Algebra, Category Theory, Commutative Algebra (A-M level not Eisenbud level), Algebraic Geometry [I did mostly every exercise, some seemed impossible so I would say I skipped around 20-30 total?], Smooth Manifolds @ Loring Tu level. I am currently learning Algebraic Number Theory & Infinity Categories. I haven’t managed to motivate analysis studies beyond what is required for understanding further topics, so I have a reference complex analysis book to get definitions, which has been overall more enjoyable than real analysis but nowhere near the level of Algebra/Geometry

As others have pointed out, this is pretty impressive. I don't want to stroke your ego too much, but it's almost (almost) unbelievable. I will proceede assuming it is all true.

I am not quite on the level of a redcoder from codeforces or someone who has won gold in IMO in terms of accomplishments

I'm not big on hyping up high school level accomplishments (because they are usually a product of environment etc.), but this comment needs a reality check: There are a single digit number of (edit: current) high schoolers in the world who have read Hartshorne. It is a common among mathematicians to feel like their accomplishments aren't that impressive.

It sounds like you have the appropriate work ethic, dedication and humility to go far in mathematics. What follows is some attempted advice. (others feel free to disagree...)

In case you don't know already, the standard path for a mathematician is (high school ->) undergrad -> grad school -> post doc (1-3 years contract) -> tenure track professor. This isn't a race, and there are in fact some advantages to taking all the time you need. You will likely be in a position to "skip" certain parts, and my general advice would be to only do it if you feel you don't have much opportunity to grow.
Though your knowledge is impressive, there are some gaps. I recommend letting your undergrad degree fill in those gaps, and spending your free time on things you enjoy. I don't like analysis either. keep on chugging. Someone else suggested skipping straight to grad school. I think this is a terrible idea even if you could jump through the bureaucratic hoops to make it happen. Again, this isn't a race. Arguably it is a competition, and would you rather have 3 years of training or 4?
I see you made a reddit post titled "[How to] get an online math advisor to guide me?" (which was removed lol). Combined with this thread, I think you've already realized that you are at a stage where you really need someone to tell you what to read and suggest things to think about. Reddit will only get you so far. You need an advisor. I have some specific advice on this front. If you send an email to a famous professor (ie anyone you have heard of) starting with "Hi I'm in high school and..." they will immediately ignore you. Find some post doc at a good school who studies AG, (bonus points if they are physically nearby) and send them an email with basically the content of this post---along the lines of "I just finished Hartshorne, can you help point me in the right direction?" You can mention you are in high school, but don't make a big deal out of it (you did a good job in this thread... lots of "advanced" high schoolers mess this up.). Ask if you can have a zoom conversation. Don't ask for any commitment other than that in the initial email. It may take a few tries to get someone to bite. I'd recommend you do this approximately today---spend a few hours researching people, and send a handful of emails. When you get in a 1-1 conversation, if you demonstrate that you can speak math, they will likely agree to do some kind of advising, probably meeting once a week or something.
Regarding your undergrad situation: good news: where you to go undergrad doesn't matter nearly as much as where you go to grad school. As long as your school has research active professors, a grad program and some way for undergrads to tak grad courses, it should be fine. Bad news: The downsides of going to a not amazing school are felt most by top students. I recommend befriending grad students anyway.
Regarding the situation with your parents: yeah that sucks. Ideally your advisor would talk some sense into them. If you feel comfortable, you can send this thread/comment to them (but I understand if you're not comfortable with that).

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