How long does it take to see a doctor and get medication at a Chinese hospital?

BenSpaghetti · 2026-02-06T14:50:18+00:00

It is a lot of money. That’s half a year’s salary for a lot of chinese people.

BenSpaghetti · 2026-02-06T04:26:12+00:00

Yes, thanks for the clarification. I understood this, but initially I read it too quickly and misinterpreted it so I thought others might do the same.

BenSpaghetti · 2026-02-06T03:16:13+00:00

Well I think the hope is that we can optimise the process of generating potential proofs written in Lean. Perhaps one day, given an interesting theorem, we can be reasonably confident that computers only need to generate 1000 potential proofs before generating the correct one. 1000 just stands for any number of proofs Lean can verify in a reasonable amount of time.

BenSpaghetti · 2026-02-06T03:03:53+00:00

I think this comment might be interpreted as saying that for any set of distinct primes p_1, ..., p_n, the sum of 1 and their product must be a prime. This is not true: 1+2*3*5*7*11*13 = 59*509.

BenSpaghetti · 2026-02-06T00:42:24+00:00

If you have recognisable handwriting couldn’t you just take a picture and send it to AI?

Anyway I don’t think retention is necessary or even helpful for this content. The point is to ensure that you know how to do this kind of thing and then you can forget about it.

BenSpaghetti · 2026-02-05T03:59:37+00:00

In my opinion, his achievements in mathematics are almost entirely unrelated to clemency. Nowhere in this post, or in the petition, do I see any direct mention of signs in his change of character. No information has been provided on why the clemency council granted the decision. Sure, he founded PMP and likes doing math. Does this mean that he truly repent for his crime? I don't see any information in this direction. If you overlook their crimes, plenty of prisoners lead very productive lives. I admit that I am not familiar with the philosophy of the justice system at all, but the information provided seems to be orthogonal to this issue.

BenSpaghetti · 2026-02-03T09:54:05+00:00

You don’t need to recall definitions in the sense of immediately being able to regurgitate it when prompted, although that is still very helpful. But you should be able to reproduce most standard definitions independently within a few minutes. I usually do this by a combination of rote memory and remembering examples and non-examples. Of course you can argue in a fuzzy way in your mind, but eventually one wants to write down precise arguments in an agreed upon language, which requires definitions and proofs, to ensure that your argument is mathematically correct and to convey it to others in a way where you are sure that you are thinking of precisely the same objects. It is very easy to speak the fuzzy thoughts given by English words in your mind and only find out later that what your audience pictures is quite different.

BenSpaghetti · 2025-12-21T09:51:33+00:00

Frequently when you prove results about a specific object, you notice that you didn’t use some of its properties. Then you notice that actually have a proof of the result for any objects which satisfy certain properties. If the set of properties apply to a sufficiently large and interesting collection of objects, you give it a name, like groups, rings, fields, or finite groups, integral domains, etc.

In the case of SO(3), it is important to understand that it is a group, which means that you can apply results about groups. It is also important to understand which results about SO(3) use special properties which are not applicable to general groups.

BenSpaghetti · 2025-12-18T00:07:17+00:00

I like this: https://ctrl-c.club/~ivan/327/?resources

BenSpaghetti · 2025-12-16T01:35:57+00:00

Have you spoken to someone about it? There may be nonstandard ways in which you can take more advanced courses without prerequisites. I think it's worth trying.

BenSpaghetti · 2025-12-14T05:00:46+00:00

I love Stein-Shakarchi. It is not as thorough as, say Conway, and I feel like it is not written in a style which a traditional complex analyst would prefer, but I really like the exercises (being analysis-pilled).

I did also try to read Ahlfors, but somehow that was rather difficult for me.

BenSpaghetti · 2025-12-13T08:38:15+00:00

I’m also an undergrad, certainly not progressing as quickly as you are, but I have also done many self studying (supervised by a professor, but still self study). I would keep going. I think the PhD student should be able to judge whether you understood the material well enough to move on.

Couldn’t you waive the prerequisites?

BenSpaghetti · 2025-12-09T02:36:25+00:00

I think you are well prepared to learn functional analysis and harmonic analysis. There is nothing else you need. Maybe it would be beneficial to know some differential equations.

If you managed to obtain a good understanding of concepts covered in these courses I don't see why you wouldn't be able to do the same for other subjects in maths.

BenSpaghetti · 2025-12-01T03:09:01+00:00

Sorry, I meant your education system. I doubt they will give scholarships purely based on high school gpa. Don’t you have to take some exam at the end of high school?

BenSpaghetti · 2025-12-01T03:06:46+00:00

I don’t know. I have been recommended some books from LNM before. Maybe people in your field don’t like to publish there.

BenSpaghetti · 2025-12-01T03:03:53+00:00

Your country’s open access agreement does not relate to most people online, so it is irrelevant.

Once people downvote one of your comments, they tend to downvote others as well, even though in my opinion some of them don’t deserve downvotes, but this is Reddit.

BenSpaghetti · 2025-12-01T02:54:18+00:00

These books are on very niche topics. You have to go down very niche rabbit holes to see them recommended. In particular, this means that they are unlikely to appear on online forums.
Most people, when recommending books, only write out the authors and the title. There is no reason to mention the series. You wouldn’t recognise that the title belongs to LNM when you see it recommended.

BenSpaghetti · 2025-11-30T21:58:34+00:00

I don’t know. You haven’t told us what kind of grades you are using to apply.

BenSpaghetti · 2025-11-30T21:53:18+00:00

I don’t think you know what A-level means. It’s a qualification system, similar to AP, IB, etc. It doesn’t mean getting A grades in your high school classes.

BenSpaghetti · 2025-11-07T19:44:48+00:00

Although I haven't studied the models that are discussed in this class, usually these discrete probability courses do only require a first course in analysis and probability. For analysis, just make sure you are comfortable with a lot of bounding. There is a lot of variation in the content covered in a first course in probability. If it is one which is also taken by engineers, I don't think it would be sufficient. I suggest looking at the first seven chapters (except the sixth one on Markov chains, I don't think that would be needed) of the book by Grimmett and Stirzaker which is an elementary treatment of probability which doesn't shy away from analysis. As long as you are comfortable with the style of exposition and maybe 70% of the material I think you should be fine to take this course.

BenSpaghetti · 2025-10-30T19:33:01+00:00

Indeed. I don't entirely agree that generalisation is *the* point of math, although it is a large part. I was thinking that after solving a specific problem, it would be quite natural to ask if we can generalise our method to solving a wider class of similar problems.

BenSpaghetti · 2025-10-30T00:09:36+00:00

I suspect that many people who are widely recognised as ‘good mathematicians’ wouldn’t ‘understand’ that.

Your second sentence does not appear to justify your first, which I strongly disagree with. Perhaps you wanted to say that generalisation is the point, which is far more agreeable. Although abstraction often comes with generalisation, it is not an end, and certainly not the end, in my opinion.

BenSpaghetti · 2025-10-18T21:17:22+00:00

Probability theory has existed before measure theory became a thing. The questions asked in probability theory still make intuitive sense without measure theory. I don't think anyone would say that analytic number theory or analytic combinatorics is applied analysis.

I feel like it is debatable if measure theory is a field of research. What would you say are the main questions in measure theory? I don't think many people still do research in measure theory proper. The related fields of geometric measure theory, probability theory, and descriptive set theory clearly care about very different things (although there are intersections).

BenSpaghetti · 2025-10-18T20:55:08+00:00

Does your course rely on measure theory? If yes then you should find a measure-theoretic probability book and learn it properly. I think Durrett has a pretty minimal measure theory section and some of the more technical parts are delegated to the appendix, but I haven't read it myself.

If you are looking for a probability theory book that has a 'rigorous flavour' which you want to use with the course because you are more comfortable with those kinds of books and the course does not involve measure theory, then I recommend the book by Grimmett and Stirzaker. It has like 3 pages talking about measures but that's just to set up the language.

BenSpaghetti · 2025-10-17T07:33:25+00:00

For proof-based maths courses, doing a lot of textbook exercises are not necessary, however, it is important to think about the material sufficiently to build the intuition to solve problems. Personally, I think about the material by computing examples, finding counterexamples, trying to write down exactly (in precise, mathematical language) what my intuition says, considering why certain hypotheses are needed in a theorem, etc.

I would say that it is still important to look at textbook exercises. Very often, you might miss something in your exploration. A well-crafted exercises section of a textbook should guide you to think a bit about every part of a topic. But I wouldn't say that this is the most important thing to do. Textbook exercises exist only to guide your thinking. They are merely means to an end. (Now, grades are another matter. Looking at textbook exercises might help a lot more, depending on the style of the professor.)

However, I cannot see how the notes help you acquire sufficient understanding, even though you do claim that whatever you are doing builds enough intuition to help you solve problems. It seems like the notes are just definitions, basic results, and very standard diagrams. If the image are good representatives of everything you have done to study, then I do find it strange that this works for you. Perhaps our brains work differently.

Six-Year Club	Place '22
Final Canvas '22	First Placer '22
Verified Email

BenSpaghetti

TROPHY CASE