Pythagoras, if pursuing a degree in contemporary mathematics, would face many challenging concepts that go beyond simple ratios of whole numbers. He would encounter concepts such as the square root of negative one and the fascinating theory of infinite sets, proposed by Georg Cantor, which suggests that some infinities are larger than others.
Additionally, he would grapple with Kurt Gödel's incompleteness theorems, which highlight the limits of provability in mathematics. These advancements continuously blur the lines between what we can comprehend and what lies beyond our understanding, meaning Pythagoras would need to prepare for an intellectually demanding journey filled with astonishing revelations.