 The "Begriffsschrift" broke new ground, including a rigorous treatment of the ideas of functions and variables.Frege's goal was to show that mathematics grows out of logic, and in so doing, he devised techniques that took him far beyond the Aristotelian syllogistic and Stoic propositional logic that had come down to him in the logical tradition.A frequently noted example is that Aristotle's logic is unable to represent mathematical statements like Euclid's theorem, a fundamental statement of number theory that there are an infinite number of prime numbers.