[andrepd]

>the thing about math books I have read is that they overemphasize rigor at the expense of intuition

I think these are not contradictory notions! Bad maths books lack rigour. Many books are like you say: rigorous but difficult to make sense of. But truly great books both explain the concepts in the simplest, most lucid and succinct way possible AND maintain the rigour necessary to do mathematics.

I like this quote from Michael Spivak: "In addition to developing the students’ intuition [...], it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions."

I couldn't agree more. Rigour is not a "masturbatory" end in itself to feel very smart, but it is not also an obstacle to understanding.

[nicoburns]

Agree, additionally I've found that the key to thw very best books is explaining how the intuition and rigour link. I have found that many books (and teachers) exaplin both seperately, but fail to adequately connect the two.