Pythagoras, should he want to continue on for a degree in modern-day mathematics, would have to learn to abide far more counterintuitive results than numbers that cannot be written as ratios between whole numbers. From the square root of -1, to Georg Cantor's revelation of infinite domains infinitely more infinite than other infinite domains, to Kurt Godel's incompleteness theorems, mathematics has constantly displaced the borders between the conceivable and the inconceivable, and Pythagoras would be in for some long hours of awesome mind-blowing.