The point is that mathematics and its methods are not learned by simply reading. Sometimes when I have faced a particularly difficult mathematical theory, I have said, well calmly simply read the main results and constructions and nothing else. Unfortunately, that is a failure, virtually always.
You can only learn mathematics by exercising them. I think many people who train in mathematics continuously (I do), will say something like this:
You need to identify your level, do not worry, do not want to show that you know more than you know, choose your level or one slightly lower, it will only take you 18 or 24 months to leave that level behind (unless you already have one Doctorate in hard sciences or bachelor's degree in mathematics).
Once you have identified your level, you need to make a list of theories or methods relevant to that level (people try to look for something applied to their work, it may serve the beginning but if you focus exclusively on content rather than methods, Will stagnate).
Now you will need a list of 4 or 5 books on these theories, I would say that depending on your ability to concentrate read 2 or 3 at the same time and if you can any more, then better. And you need to do a lot of exercises, not exercises to do, but the ones that really are like "changing levels in a video game". You need to solve problems, when you have one resolved ask yourself if you could solve a more complicated variant, every time you do that you will advance, it is the only thing that works. But it is a very demanding mental gymnastics.
Here I leave the rules explained by an assistant of Joseph-Louis de Lagrange, possibly the best mathematician of the eighteenth century on the technique of that mathematician:
When Lagrange was not able to overcome a difficulty, he put aside and took a second moment (we talked about that the best mathematician in the world was sometimes unable to solve a problem of his time to the first, so With more reason any of us).
Lagrange never left a book that had started if I had assimilated it completely (I personally do not do it with books but with chapters if I pass from 50% then I force myself to finish it if the beginning I see difficult to climb to something else).
Lagrange always tried to understand the reason why the authors of a book had followed one way and not another (solving a same problem by different methods is fantastic, because you learn to realize the conditions of when you make a better method).
Lagrange, whenever possible, sought to obtain his own method or theory on essential points in the problems he solved or the matters he worked on.
Lagrange never finished a day of work without being written what would be the next task to be solved, thanks to which he surpassed what he called "natural human sloth."
Thank you for your time, you always have to try nothing is difficult. 😊☺
Top 5 Free AI Tools to Summarize Textbooks, Notes & E-books (2026)nifornine ·
