Mathematical literature - why is everything so bad?

Question

Books

In general, for a long time I could not understand what was wrong with me. After re-reading a dozen different works, the problems did not disappear - porridge remained in my head. Such that even the devil does not disentangle. Mathematical terms got mixed up, discrete mathematics became probability theory, and functional analysis became a real nightmare. And the worst thing is that almost its own mathematics was born. No, promoting science is all well and good (even despite the fact that I usually made mistakes). But. When they do not understand, everything is bad.
But not so long ago, he almost did not see the light. Everyone who wrote these fucking books has their own math too. The theremin are confused, the facts are distorted. The funny thing is that everything seems to be logical and holistic. Within one book. But you open another and "probabilistic ensembles" suddenly disappear, and instead of the mathematical expectation - the average. And in that spirit. Why, often reading English literature, in general, the brain drowned in this mess - the translation is often inaccurate, and even more so.
This is how we live. But... I study mathematics for myself, for my soul. And here all sorts of sticks are put in the wheels. After all, I would just like to stretch my brain, and suddenly you realize that you are too weak to disentangle everything at once. And you won’t be fed up with a narrow specialization - it’s mathematicians and physicists who get bogged down in their problems, as if in a fog they can’t see beyond their noses. And I would like something in common, albeit not so deep, but uniting the facts together.
Here also there was a question. Questions. Why is everything so bad? Or is there a solution? Or maybe it’s been there for a long time, I just don’t see it? But I repeat - I'm not looking for anything narrow. Ideally - a gallop through Europe, so that something remains in my head, it does not take too much time (well, I can devote a couple of weeks to a close study of one issue, but no more). Maybe someone knows something monumental. Something like Cormen, but purely mathematical.
Thank you in advance.

Answer 1

So I thought, maybe someone knows what. Maybe there is a person unknown to me who wrote a monumental work that is something comprehensive.

I got the impression that you have an attitude to mathematics as to some kind of "queen of sciences", that there is some kind of comprehensive mathematical theory, etc. From my (engineering) point of view, mathematics should be treated as a discipline that provides some models. As one person put it, all models are wrong, but some are useful under certain conditions. You don't see "straight lines", "spheres" and "cylinders" in real life, but these entities can be useful in modeling (predicting behavior, etc.) of real objects. Or an example from statistics - what difference does it make to you, 60% of patients who received the medicine recover, or 40%? It is important for you, if you are a patient yourself, whether the medicine will work for you.

For mathematics is now tearing itself apart.

I don’t understand what you mean, but if it’s about “contradictions” (the geometry of Euclid, Riemann, Lobachevsky as an example), then, in my opinion, “let thousands of flowers bloom”. Each of the "contradictory" models has a certain application to real life and some useful results. Although it may take years before the created model (Galois fields, Lobachevsky geometry) finds application.
Another point - mathematics, like other sciences, is done by people. Therefore, in my opinion, a single coherent mathematical theory of "everything" is possible when many people agree on a number of facts, concepts, categories. I don't think it will be soon.
From books, I think it might be useful to read Ouspensky's "Apology of Mathematics", although this is not quite what you are asking for.

Answer 2

Mathematical analysis, why everything is so complicated and not clear.
The question sounds like this, and not like yours. The program is designed for 4 semesters, 2-3 lessons per week: theory + practice. An acquaintance with MatMeha handed over matan 11 times. The theory of the complexity of algorithms, with proofs of 7 pages, 25 times. You just have a syndrome of high expectations, against the background of procrastination and hyperactivity. Total: they just taught badly, that's all.
PS The exact sciences and other matans are easier for downs, so at least you are not a down. This can be said for sure.

Answer 3

If you study like this, for yourself, then I advise you to look at mathematics from the other side - take some mathematical subject with a real applied effect. From him to dance into theory as much as necessary. For example, read about control theory - you will understand where and why to use difours, integrals, derivatives, mathematical modeling. Or read game theory - take a look at terver, maybe graph theory.

Answer 4

Since they began to subscribe so hastily to my completely useless question ... I'll share a semi-solution.
Khanacademy- a chic resource with a huge amount of materials. What is: all sections of mathematics, well structured, well chosen. Excellent material presented. English is very simple - I had no problems listening. What's missing: everything new. The material specifically on mathematics barely falls short of a normal university. No Lobachevsky geometries or proofs of Fermat's theorems. What's good: an attempt to teach in a playful way, good design (not outrageous), social aspect. What's bad: not a flashy design does not mean excellent, it barely falls short of good, well structured also does not mean excellent - all the same, there is some chaos, at least in the fact that the material is not very well connected even between subsections. I'm not talking about divisions. And the worst thing is that he does not evaluate current knowledge well. I've been struggling with it for a week now and often make stupid mistakes. I understand that I was wrong. But he again for his - repeats and repeats these stupid irreducible fractions. It’s lazy to open calc.exe, it’s not very good to count in the mind.
However, it may be suitable for initial systematization.