I'm going to try to give you something totally off the wall. Don't forget that mathematicians were people. Here's three biographies of some of my favorite mathematicians:
Also, please check out some of the giants on that site and wikipedia: Gauss, Laplace, Euler. Why were they interested in what they were? What techniques did they develop? A very crucial question that very few ever ask: Would they have done much differently had they had access to a computer? (Of course).
Focusing on proofs to learn math is very perverse. A proof in a textbook is a proof that has been refined an almost ludicrous number of times. Definitions and axioms have even been optimized for the sake of elegance of said proofs. Don't get me wrong, a connoisseur appreciates what has been done. However, removed from the problem that motivated this way of thinking, mathematical techniques can often confuse more than enlighten.
In this thread I realize that I have been a bit vague. I want to develop the skills of visualization and in depth understanding of math for a reason. I want to learn how to make systems that exploit machine learning and use statistical techniques to infer patterns from data.
In the future some day I want to work in A.I. and create something beautiful with the knowledge I have gained. This is why I want to lay down the foundations to understand the beautiful advances in it I see around me.
Cool, although I'd suggest not getting to excited about AI itself. It's cool your already focusing on machine learning.
A great way to get going in that direction is to check out the state of the art as expressed by AT&T labs Netflix Prize solution. To get very far you'll want to have some background in linear algebra. However, theory isn't the way to go (although you'll probably need it eventually). Do a little digging and you'll find code for svds, the simplex method and all sorts of super important algorithms that are used all over the place.
You'll find if you ask questions like: How does x work in y algorithm? people will have a better idea of where to start. When you actually are coding and able to see numbers for a particular problem, you'll be able to wrap your mind around what's going on.
http://www-history.mcs.st-and.ac.uk/Biographies/Poincare.htm...
http://www-history.mcs.st-and.ac.uk/Biographies/Peirce_Charl...
http://www-history.mcs.st-and.ac.uk/Biographies/Smale.html
Also, please check out some of the giants on that site and wikipedia: Gauss, Laplace, Euler. Why were they interested in what they were? What techniques did they develop? A very crucial question that very few ever ask: Would they have done much differently had they had access to a computer? (Of course).
Focusing on proofs to learn math is very perverse. A proof in a textbook is a proof that has been refined an almost ludicrous number of times. Definitions and axioms have even been optimized for the sake of elegance of said proofs. Don't get me wrong, a connoisseur appreciates what has been done. However, removed from the problem that motivated this way of thinking, mathematical techniques can often confuse more than enlighten.
What would you like to learn exactly?