A Mathematics Autodidact's Aid

You might be interested in this math.SE question I asked: https://math.stackexchange.com/questions/62190/mathematical-... (https://math.stackexchange.com/questions/62190/mathematical-equivalent-of-feynmans-lectures-on-physics) (comparing to Feynman's Lectures on Physics rather than SICP.) However, I agree with zodiac: Math is a much broader field and I think very few living people have the kind knowledge you're talking about: consistent and broad knowledge in all areas. I have the same background as you and I started doing exactly this about 8 years ago. I'm just finishing my PhD in math. I'll give you some advice. First, studying math for its own sake by yourself is extremely hard. That's one reason I ended up back in academia. If you can't go back to school, still find some kind of community. Second, rather than studying generally, try to identify a goal to work towards. What are you trying to understand or figure out? Third, try to model your plan on a rigorous undergrad program, e.g., MIT. Then, in each main undergrad area (algebra, analysis, topology, geometry, etc.) try to find the "SICP" and study that. For general book recommendations, I like Fowler's A…