A few years ago I found the youtube channel sudgylacmoe and watched what is still their most viewed video A Swift Introduction to Geometric Algebra where he introduce in a vulgarise fashion a branch of mathematics I didn't know before, Geometric algebra more formally known as Clifford algebra(s).

Basically, geometric algebra is a generalisation of linear algebra which allow operations impossible in classic linear algebra such as multiplying vectors together and adding vectors and scalars and also generalise the objects of linear algebra to higher dimensions.

For example, you have 0 dimensional points (scalars) and 1 dimensional oriented line segment (vectors) just like in classic linear algebra, but on top of that, you have generalisations for every other dimensions: 2 dimensional oriented surfaces (bivectors), 3 dimensional oriented volumes (trivectors), etc...

One of the most interesting quirks of geometric algebra is that it makes a lot of the formalism of linear algebra as well as their applications in all sorts of sciences (physics, computer science, engineering, etc...) much simpler and more natural. For example, complex numbers, quaternions and spinors appear on their own naturally from the properties of multivector multiplication and a lot of physics equations and computer science algorithms are greatly simplified (this youtuber give the Maxwell's equation(s), special relativity and a simple computer graphics algorithm as examples in the videos linked).

The channel is full of videos and shorts about geometric algebra for those interested.

I'd like to hear lemmygrad and hexbear's math community's' opinions about it.

I want to learn about the works of soviet mathematicians.

On 1 July 2010, he rejected the prize of one million dollars, saying that he considered the decision of the board of the Clay Institute to be unfair, in that his contribution to solving the Poincaré conjecture was no greater than that of Richard S. Hamilton, the mathematician who pioneered the Ricci flow partly with the aim of attacking the conjecture.

In August 2006, Perelman was offered the Fields Medal ("Nobel in math") for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow", but he declined the award, stating: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."

More:

https://en.m.wikipedia.org/wiki/Grigori_Perelman

As the author writes:

"The philosophy of mathematics is not the most vital issue facing Marxists today, but its clarifcation can help us argue that the materialist framework is the correct one for making sense of every aspect of the world."

It is now over a year since I have sadly had to depart from my university upon obtaining my master's degree in mathematics. I have since obtained a job as a programming contractor, however classical mathematics done with pen and paper is still the love of my life. Luckily enough, I still live within two hours of my old campus, and I was able to obtain an external library card, which is my ticket to look into all the topics I missed out on for want of time (not all mathematical).

If anyone among you has a similar experience, I would like you to share your techniques, too. Be advised that my way might not be very efficient nor lend itself to people who still need to study for exams or have deadlines, because I am no longer under these pressures.

Scouting. The closer a field is to my interests, the more books I already know to be suitable or unsuitable for me to learn from. For me, the most important criterion for a maths or theoretical physics book is to have numerous exercises on many different levels of difficulty and abstraction. I also prefer the books that use familiar notations to my lectures, and those that are written in my native language. Least importantly, a little pet peeve of mine is that I don't like it when books are set in Times New Roman because I find the font hideous and I honestly can't bear to look at it for long periods of time.

Frequency. Due to my day job, I am usually unable to clear more than an hour each day to sit down and study. I tend to use this hour to either read through a chapter and fill in the blanks between the formulae and draw pictures, or to attempt to do the exercises when I am done with the required reading for them. If an exercise seems boring and not what I wanted to learn from the book, I still tend to look up the solution rather than not considering it at all.

Intensity. Because I am no longer under the pressure of cramming and deadlines, I might take longer or sometimes lack the motivation to learn a topic, but I also have the liberty to take a minute and ask questions about it for which there was no time during my student years. Unless there is an elephant in the room requiring more urgent attention, I always tend to go through three things to look for: Examples and applications, characteristics of the generic case and the singular cases, and analogies in the language of other fields.

Surroundings. I tend to learn at my desk for when I need to write or take notes, and from my bed when I don't, although I reckon that the latter is a bad habit. Although during my earlier time at uni I used to learn with classical or Latin music or even commentary, I now tend to find it too distracting and prefer silence for learning. For obvious reasons I learn alone now, but I have always found it more fun and also easier to have a study buddy.

So I found out about Marx' mathematical manuscripts, so I say "Hey, I've been studying mathematics this year at university. I understand limits and derivatives, maybe I can understand something of that gibberish." So I see the titles and the one called "On the Concept of the Derived Function", I go there and I see some notation I don't understand, he speaks about things I'm not clearly understanding, so maybe some of you could make it clear.

For example:

Why is this x sub 1 notation? Is this some other way to write derivatives? Because on the footnotes it says this:

2. In order to avoid confusion with the designation of derivatives, Marx’s notation x´, y´, ... for the new values of the variable has been replaced here and in all similar cases by x1, y1, ...

Then I saw a talk about Marx's mathematics and the infinitesimal and some of that stuff, but the one who was speaking didn't went much into the mathematical part but was more like a history talk on how the Chinese were interested in the propositions of Marx because it liberated calculus from the idealist veil with which it was conceived by Leibniz and Newton, but the one who was talking mentioned Marx learning mathematics with whatever he had around and didn't managed to read Cauchy so we was like "Yeah this is nice but it's al shit now we have proved it fully works." But well, he seems a bit biased, since he's a Usonian, so maybe Marx's writings are still relevant, I don't even know who the fuck Cauchy is, so yeah, help.

Text: https://www.marxists.org/archive/marx/works/1881/mathematical-manuscripts/ch03.html