To be a mathematician you need a certain level of innate talent at math. It's not fair, but I didn't make the rules. How do you find out if you have the talent? Good question. It depends. What's your current math background (what math classes did you take in college)? If you had the standard calculus and linear algebra, I'd recommend doing the following. I thought of something that will be able to tell if you're cut out for math or not without wasting too much of your time in case you don't have what it takes or simply just don't enjoy it. Since you've already completed undergrad you need a quick "trial by fire".
>Review what you know, don't spend too long, it should be rather effortless
>Watch some videos on proofs and proof techniques, truth tables, etc, and do some basic proofs (root 2 is irrational, etc), maybe read one of those "proofs books". idk but don't spend too long on this, no longer than a few days.
>Don't do analysis first. Learn algebra, more intuitive and less frustrating. More abstract, good intro to mathematical thinking.
>Download Herstein's "Topics in Algebra" 2nd edition (NOT "Abstract Algebra", you specifically want "Topics"). His writing is very good and not overly bogged down by mathematical jargon. But the book is also rigorous and has great exercises. This is ideal for you. Also download Rudin's "Principles of Mathematical Analysis".
>Read chapter 1 of Herstein and try to understand everything/do the problems, this is crucial.
>Read chapter 1 in Rudin, and try to do as much as you can.
>Move on to chapter 2 in Herstein/Rudin, on group theory and topology respectively
>Study hard, try to do as many exercises as you can to the best of your ability. Put in several hours a day of your time reading and trying to do the exercises. Give it 3 weeks of really hard study. Don't get demoralized.
Does this kind of writing make sense to you? Do you have good intuition for it? Does it bore you? Or does it just seem like complete nonsense?
