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 Gödel'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.
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.
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