I have an incredible distaste for the axiomatic approach ,it's a very bad method,I think ,for teaching or learning about mathematics.I don't understand why I feel this way, I always thought inductive reasoning in mathematics ,the sort you find with physicist,is better than the deductive reasoning you find with the Bourbaki group. What do math people on this forum prefer ? Why ? How is it better? Any comment? P.S here's a very interesting and somewhat related quote from one of George Polya's books: ''Induction often begins with observation. A naturalist may observe bird life, a crystallographer the shapes of crystals. A mathematician, interested in the Theory of Numbers, observes the properties of the integers 1, 2, 3, 4, 5, . . . . If you wish to observe bird life with some chance of obtaining interesting results, you should be somewhat familiar with birds, interested in birds perhaps you should even like birds. Similarly, if you wish to observe the numbers, you should be interested in, and somewhat familiar with, them. You should distinguish even and odd numbers, you should know the squares 1,4,9,16,25, . . . and the primes 2,3,5,7, 11, 13, 17, 19,23, 29, . . .. Even with so modest a knowledge you may be able to observe something interesting.''