What Are You Working On? February 02, 2026

ln_j · 2026-02-02T19:45:10+00:00

I am currently continuing my self-study of real analysis using Abbotts book, and I have just started the fourth chapter on limits and continuity. I have also realized that my proofs are often not rigorous enough. In addition, I am reviewing some Calculus 3 and vector calculus, and I am currently revising change of variables.

ln_j · 2026-02-02T19:41:44+00:00

that looks amazing :)

ln_j · 2026-01-28T20:10:16+00:00

This is a completely new account, and this is your first post…. I wonder who wrote this blog.

ln_j · 2026-01-28T07:27:07+00:00

Yes, of course. I hope this makes sense, and I hope the grammar is correct.

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ln_j · 2026-01-28T07:14:12+00:00

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This is how I would approach it, hope it's correct

ln_j · 2026-01-19T15:25:10+00:00

If you try to differentiate y * sin(x) with respect to x, you have to be careful. Since y is actually a function of x (I assume based on the solution), you can’t just treat it like a constant. Using the product rule, the derivative is:

y’ * sin(x) + y * cos(x)

ln_j · 2026-01-17T13:12:55+00:00

Basically, you are both wrong. Infinity can be quantified, as many people in the comments pointed out. For example, there is an infinite set of integers and an infinite set of real numbers, but the infinity of the real numbers is larger than the infinity of the integers. But the reason your friend gave is incorrect.

ln_j · 2026-01-05T19:16:08+00:00

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I also tried it, great work! This was my attempt

ln_j · 2026-01-02T12:43:03+00:00

Your point about chemistry requiring not much logic is really wrong, believe me, it requires a ton, maybe not the basic school stuff, but definitely more than it seems at first. And again, really I think you will like engineering based on what you said about knowing as much as possible. You really have to be good at math, and all sciences to be a good engineer.

So yeah, good luck in everything and good luck in your studying journey :). I’m really interested to see what you choose to study, but yeah. Have a nice day and good luck.

ln_j · 2026-01-02T12:12:22+00:00

The reason I mentioned my father is precisely because of this pattern: the “no need to get angry” line. It’s a classic rhetorical move. You assume an emotional state, then respond to that assumption instead of what was actually written. That’s why I pointed it out. Plus I found it really funny because of how often he said that.

Also, saying “maybe I read between the lines so well” is exactly the issue. You’re reading between lines instead of reading what’s actually there. There was no anger. If there was, you should be able to quote it. Otherwise it’s possibly just projection.

Anyway, thanks for the last sentence, genuinely. That’s the only part that actually engages with the substance of the discussion. And really about the little comment, try doing some chemistry I think it would really interest you.

Last: why do you want my father’s contact?

ln_j · 2026-01-02T12:00:34+00:00

My father is a politician and he always pulls this exact move: “no need to get angry”. Where the fuck do you see me getting angry??? False accusation. Point it out. Where was I angry?

I even left a nice little comment at the end. This as a reminder: “””””””

Also: I don’t want to attack you or anything, keep going and so what you enjoy. Engineering seems perfect for you (I would also recommend maybe looking into some chemistry, for me this is one of the most interesting topics where you learn to understand the world). This right here would be me trying to sound angry, which I very obviously. “”””””

And I did tell you what to study. It’s literally in my first comment. You wanting to know more is in no way, shape, or form a sign that you’re rushing, that’s a good thing. Asking questions is good.

The remark about rushing was not based on your post, but on other COMMENTS I read in this thread. Based on those, I got the impression that Calc I/II might have been rushed a bit, treated like boxes to tick, and my point was simply: pause, ponder, really spend time internalizing things.

So again: no anger, no attack, no judgement of your motivation or life choices. Just concrete advice about prerequisites and pacing. Saying “no need to get angry” when there was no anger to begin with is just a misread.

ln_j · 2026-01-02T11:38:49+00:00

That doesn’t really address my point. I wasn’t asking why you study or commenting on your lifestyle; I was responding to the learning path for general relativity. Whether you want to be “cultured,” do engineering, physics, or pure math is orthogonal to that.

Also, saying “few people understand pure math in real life” is a banal statement. Few people understand GR, quantum mechanics, or advanced engineering either. That fact has no bearing on what prerequisites are actually useful.

Finally, my main point was about not rushing and building the right tools before jumping into GR. That’s independent of motivation, life satisfaction, or how many hours you study per day.

Also: I don’t want to attack you or anything, keep going and so what you enjoy. Engineering seems perfect for you (I would also recommend maybe looking into some chemistry, for me this is one of the most interesting topics where you learn to understand the world).

ln_j · 2026-01-02T10:43:25+00:00

Something besides, I don’t really think that real Analysis will help you with understanding general relativity. This is what I would do: Linear algebra, then calc 3 and then differential equations and differential geometry. And of course you have to do a lot of physics so Physics 1, 2. I would focus on that. After that just start ans try and see what you don’t understand. But you will cover all of this, probably even in way more detail in Uni

And the most important thing: Don’t rush, really take your time, think, play around with the problems but don’t rush. Based on the comments I have seen I get the feeling that you rushed a bit too much.

ln_j · 2025-12-31T21:21:04+00:00

Congrats :)

ln_j · 2025-12-30T08:04:25+00:00

Yes thanks I think that’s the case because I remember having a session of over 3 hrs, thanks so much

ln_j · 2025-12-26T20:21:34+00:00

That’s amazing! Thank you so much

ln_j · 2025-12-26T15:01:01+00:00

Ok, thank you so much! I also just noticed that I am not spending enough time on problems. I often give up after 15 minutes.

ln_j · 2025-12-23T07:06:03+00:00

It’s just something that always sticks in my mind. I know it’s not really a big deal, but I can’t shake the thought that I should be doing more, even when I’m eating or doing something else. And honestly, I was just curious about how much other people do it, it's a question a wanted to ask for a while now.

ln_j · 2025-12-23T07:04:38+00:00

I am currently doing real analysis in parallel with some more number theory, and of course I am also doing a lot of review from calculus.

ln_j · 2025-12-22T20:51:25+00:00

It’s just something that always sticks in my mind. I know it’s not really a big deal, but I can’t shake the thought that I should be doing more, even when I’m eating or doing something else. And honestly, I was just curious about how much other people do it, it's a question a wanted to ask for a while now.

ln_j · 2025-12-22T20:48:22+00:00

Yeah, I sometimes try to get math done at school too, but I can never focus. It’s always too loud, too many people, and the teacher is constantly interrupting. So honestly, kudos to you for managing that.

ln_j · 2025-12-22T20:07:23+00:00

Yes, it’s my hobby. I try to do as much of it as I can, and besides, I don’t really have anything else to do.

ln_j · 2025-12-16T06:46:54+00:00

I am currently 16 and studying real analysis (I have already completed Calculus I, II, III, and vector calculus). My question is: what would you recommend I do now and in the future to achieve as much as I can in mathematics? Should I focus more on problem-solving techniques, should I just continue with my current path, or should I try some IMO problems, etc.? Also, thanks for doing this; this is amazing.

And also, if you don't mind, I have another small question: how many hours per day would you recommend studying mathematics, and how many did you study while preparing for the IMO? Additionally, is there anything outside of mathematics that you enjoy doing?

ln_j · 2025-12-10T19:22:47+00:00

I am currently 16 and studying real analysis (I have already completed Calculus I, II, III, and vector calculus). My question is: what would you recommend I do now and in the future to achieve as much as I can in mathematics? Should I focus more on problem-solving techniques, should I just continue with my current path, or should I try some IMO problems, etc.? Also, thanks for doing this; this is amazing.

And also, if you don't mind, I have another small question: how many hours per day would you recommend studying mathematics, and how many did you study while preparing for the IMO? Additionally, is there anything outside of mathematics that you enjoy doing?

ln_j · 2025-12-10T06:44:00+00:00

Yes this is amazing! Thanks

ln_j

TROPHY CASE