Question on prerequisite for "higher mathematics" from a non-math student I am a student with a background in finance, recently I have seen many applications of mathematics to finance (advanced probabilities, optimization) and I find it very interesting, not only for the applications, but especially for the mathematics that there is behind. Thus, I would like to delve into these different areas of math but the question of prerequisites arises. I had very few math lessons in my university education (and it was more recipe lessons if I may say so) and what I really understood from the mathematical objects that I studied was by working on it as an autodidact, it must roughly correspond to the level of a first year in a mathematics university in France if I'm not mistaken(one-variable analysis, algebraic structure, vector space structure, linear application, linear form). Some time ago I wanted to work on measure theory by myself but I didn't succeed.
I humbly ask for your opinion because I have seen two schools on this subject: one which considers that working maths with a "backward" approach is reasonable and others not.
Thank you
 A: I would upvote this question by +100 if I could, because it shows the pursuit of mathematics from the love of mathematics and its beauty - rather from the utilitarian “if I give them the right answers, they will give me good marks, and if I get good marks, someone will give me a good job” - and all the rest of it.
If you look at the great writers such as Poincaré you will see this love.)
As to your specific question, I think it depends on your own temperament and to that extent no final answer can be given. Mathematics is an odd discipline, in that each part of it is built on some other part (and, thinking of Gödel, the whole of it is built on nothing - but let’s not deviate into philosophy).
You need to be guided by love, joy and delight. One person will be happy making calculations with real numbers - another will find delight in pursuing the question “how can we define a real number and justify our calculations?” - Dedekind cuts, Cauchy sequences, or whatever.
Your adventure into measure theory is not a failed experiment, it is an experiment with a negative result - in other words, a successful experiment. It shows you that measure theory is not for you. I had a similar adventure with languages: I found Sanskrit fascinating as being in a sense “a language older than Latin or Greek” - not only a beautiful grammar but also a script with an exotic and beautiful logic of its own. But in the end, pure fascination was not enough. Much better to try to get the rust off my Greek and hear the words that Homer sang.
Advice, then. Try again in your pursuit of “the maths behind the maths”, but try a different mathematical field. Because you are pursuing mathematics and not getting good marks in mathematics you will succeed. Moreover, as with physical exercise, it gets easier with time. Getting “mathematically fit” in one area will make you more able to take on the next area.
Read books by mathematicians, not just maths books. Make friends with a mathematician if you can, because the essence of whatever field you are studying is not always conveyed by books (especially not by modern ones).
What you really need is not a teacher but a personal trainer. But I don’t know if they exist.
