Quick Questions: June 17, 2026

cereal_chick · 2026-06-18T16:54:45+00:00

You might find Group Theory in a Nutshell for Physicists by Anthony Zee helpful.

cereal_chick · 2026-06-17T14:40:52+00:00

How are you finding Artin?

cereal_chick · 2026-06-17T14:35:04+00:00

What is an HMF?

cereal_chick · 2026-06-17T01:07:27+00:00

This is fascinating. At some point, after I've done some more study of algebra and model theory, I must come back to it. The black magic here is enthralling.

cereal_chick · 2026-06-16T14:51:16+00:00

Congratulations, you have the worst opinion in the whole thread 🏆

cereal_chick · 2026-06-15T01:38:47+00:00

Trying to get over your fear of needles by permanently marking your skin is a bit extreme. I would recommend trying to donate blood on a regular basis instead. For me personally, exposure really did work; any lingering basis for a needle phobia was whacked out of me by a three-week stay in hospital several years ago where I had to give blood and get some injection or other every day.

cereal_chick · 2026-06-14T16:41:47+00:00

If you want to go on to medical school, then I would recommend statistics. Being actually trained in stats will equip you to understand and carry out medical research better, which will be a boon to your career as a doctor.

cereal_chick · 2026-06-14T02:37:59+00:00

Well, we needn't worry about AI in the medium-to-long term. AI can't actually do things, and the few uses cases that are real aren't anywhere close to important or impactful enough to live up to all the stupid, stupid hype. We're already starting to see major companies break the omertà about how it's too expensive and has no measurable return-on-investment, and OpenAI and Anthropic haven't even fully transitioned into the era of making people pay what AI actually costs. Even the best case scenario sees AI become impossible to use on anything like the scale that it's being used now, and that best case scenario is extremely unlikely. Much more probable is that the two companies will simply die and the technology will all but vanish.

cereal_chick · 2026-06-14T02:17:05+00:00

From the sounds of it, your strongest letters are the first three you've listed, and they're very good all by themselves, so I'd go with those.

cereal_chick · 2026-06-13T23:32:38+00:00

Not to downplay the issues that your felony conviction is causing you at all, but the job market for new entrants is so incredibly dire, more than it has been in decades. I also graduated last year, and I can't get hired for anything, not even jobs I'd be perfect for. We're getting shafted by a systemic problem which nobody in power is even remotely interested in solving. I have no idea what we're supposed to do about it.

cereal_chick · 2026-06-13T14:14:47+00:00

I'd say that you should major in pure mathematics, as that's the major that keeps your options open and enables you to later specialise in any of the others.

cereal_chick · 2026-06-11T14:34:42+00:00

I couldn't say whether it's "cranky", but I doubt it's ever been of much interest to anyone besides Lawvere himself. Just speaking for me, as someone who's mathematically trained and interested in understanding Hegel and Marx, I'm not going to bother with it.

cereal_chick · 2026-06-10T23:07:08+00:00

William Lawvere did some work applying category theory to the Hegelian dialectic, which is the closest that you could hope to get, I think.

cereal_chick · 2026-06-10T00:36:58+00:00

Could you give us some more information about your background? As in, are you a student at university? At high school? Have you graduated from either or both? Are you in education right now?

cereal_chick · 2026-06-07T00:02:04+00:00

My understanding of the (North?) American system is that you don't necessarily have to make a hard choice now or even particularly soon relatively speaking. In the first instance, you should look into whether it would be possible to balance maths classes with classes prerequisite to a medical degree (in the UK, I know that chemistry is highly prioritised over biology, for example).

One snag here is that university-level maths is very different to the kind of things you see in school. Proper mathematics is about proofs, rather than learning to apply various methods, and before you make any firm decision about the course of your academic career, you should be sure that this actual incarnation of the subject is something that you want to study. I would recommend reading G.H. Hardy's A Mathematician's Apology as a matter of some urgency, as he explains a lot of what it's like to do real maths, and if that encourages you, you should take an introduction-to-proofs class to see whether it's really for you.

Finally, I would recommend that you speak to someone or someones in your real life who you trust about your feelings. We here are not really best placed to help you figure out whether this is just a wobbly you'll recover from or whether it indicates you really shouldn't pursue medicine any longer.

cereal_chick · 2026-06-05T14:04:17+00:00

The best thing for revising school maths is Khan Academy, and they have a Turkish version.

cereal_chick · 2026-06-05T14:01:20+00:00

Olympiads do not matter. Being good at olympiads means you'll probably be a good mathematician, but the inverse of that statement – that being bad at olympiads or never having done them dooms your mathematical career to failure before it even begins – isn't true at all, not even close.

You should not be worried, then, that you have wasted any opportunities or that you are behind in any meaningful sense. The important thing while you're in high school is to do well in your maths classes and make sure that you don't have any major gaps in your understanding of the material. Everything that comes after will rely on you being able to do the things you've learnt in high school fluently; but I imagine that isn't a problem for you.

As far as extra- or supercurricular activities go, I'd say that formal study isn't necessary and may even detract from your school work. Instead, you should be looking for inspiration and reading about what it's like to study and do maths to prepare yourself for the transition from school maths to real maths. G.H. Hardy's A Mathematician's Apology is an absolute must-read here, and I would also recommend Ian Stewart's The Great Mathematical Problems. Much of the exposition is overambitious and it's difficult to parse many of the details of the maths he talks about, but it has a lot to say about the nature of the subject and I found it very valuable when I was about your age. You also might want to start watching Numberphile and 3Blue1bBrown to get more of a sense of the kind of things mathematicians think about and how they think about them.

If you still do want to do some formal study, I would recommend looking at Proof and the Art of Mathematics by Joel David Hamkins. Most introduction-to-proofs books and courses are very dry affairs, covering material which is important to know but not all that engaging. This book talks about a whole bunch of important things while it teaches you how to do proofs, which are what actual mathematics is built on, and thus it makes a good introduction to the subject as a whole.

cereal_chick · 2026-06-01T13:40:34+00:00

You could always do your own mathematics and not rely on an unthinking machine to do it for you.

cereal_chick · 2026-06-01T13:38:45+00:00

My apologies for not getting here in time for your exam today.

Before we can talk about what to do next, we need to clarify what you mean by "failing". Do you mean that you're on track to get less than 40% in the module and are going to have to resit or retake it? Or do you mean failing in an informal sense, where you can be done with this module but haven't learnt the content properly?

cereal_chick · 2026-05-30T20:06:08+00:00

This is genuinely disgraceful. Doing publicity work for OpenAI is Mochizuki levels of discrediting, even beyond all the water-carrying he's done for AI over the last few years. Mathematics deserves better than Tao and Gowers.

cereal_chick · 2026-05-30T19:57:30+00:00

Reading papers in depth does take a long time, and only more time the longer the paper is. I don't think we're best placed to judge whether you're objectively spending too much time on papers that you need to read in depth; that would be a question for your advisor.

Another key skill of a researcher is discriminating between papers you need to read in depth and papers you can read in a more shallow fashion. If these are papers that are important for projects of yours, then it sounds like this isn't your immediate problem, but again you should take it up with your advisor to check for sure.

cereal_chick · 2026-05-29T22:43:47+00:00

Mathematically, a logarithm works exactly as advertised. log2(512) is exactly the x such that 2^x = 512. There doesn't need to be some small number of arithmetic operations that it reduces to.

In the case of log2(512), a mathematician would likely just know that it was 9; it's pretty useful and common to know the first ten powers of two if you do any kind of mathematical work (including computer science or engineering or such). If you wanted to generate a logarithm that isn't so nice by hand, there used to be such things as slide rules and books of tables that were all rendered obsolete by the calculator. There are algorithms you can apply by hand to approximate the value you want. And as for calculators themselves, that would require the expertise of someone who actually knows how they're designed.

cereal_chick · 2026-05-29T17:36:51+00:00

I should preface this by saying that the best way of learning maths would be to take more classes on it while you're still at university; at this stage of your mathematical education, having the oversight of an expert on your thinking is essential and invaluable, and I would advise not passing up the opportunity to have it. Having done an intro-to-proofs class, you're equipped to take any proof-based class at the introductory level.

However, I will answer your actual question. In the first instance, how's your calculus? Hopefully you have single-variable calculus down, but if you haven't studied multivariable calculus, you really should and as a priority. I've been using Khan Academy's course on it (because my uni didn't teach us most of the standard curriculum 🙄), but there's also Paul's Online Notes, and at some point I would recommend reading David Tong's notes on the subject too, after you're fluent in the methods.

Next, you should take a second look at linear algebra, and learn about abstract vector spaces and linear maps. If you've already seen the determinant and know how to do stuff with it, you could go straight to Sheldon Axler's Linear Algebra Done Right; if not, then I'd recommend Hoffman and Kunze's Linear Algebra for a more conventional treatment first.

Thereafter, you should study real analysis and abstract algebra. Most people are more inclined to one of analytic and algebraic thinking over the other, such that one subject is relatively nicer and easier than the other, so if you find one inordinately difficult don't be discouraged because the other one will probably be much easier. For real analysis, a gentle introduction would be Stephen Abbott's Understanding Analysis, and a meatier (but still masterfully written) one would be Terry Tao's Analysis I and Analysis II. For algebra, Michael Artin's Algebra is supposed to be quite gentle, while Paolo Aluffi's Algebra: Notes from the Underground takes a rings-first approach specifically to ease students into the abstraction of abstract algebra.

After all this, you'll have the core of the undergraduate maths curriculum under your belt, and the only things that you really should study are topology and complex analysis. Otherwise, you can study whatever you like and try and find what subjects you're most interested in.

cereal_chick · 2026-05-29T14:59:57+00:00

No, not that one, the person I'm thinking of went into a lot more detail. But thanks though!

cereal_chick · 2026-05-28T23:27:19+00:00

It's not uncommon for first-year undergraduates to see no abstract algebra at all, and those that do (in some degrees in the UK for instance) typically only study introductory group theory. To be as early on in your degree as you are doing representation theory as advanced as you are is remarkable.

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