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Even Arthur Conan Doyle, the creator of the world’s most famous detective, recognized the special status of mathematical proof. In A Study in Scarlet, Sherlock Holmes declares that his conclusions are “as infallible as so many propositions of Euclid.”
    On the question of whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt—mathematics was real, immutable, omnipresent, and more sublime than anything that could conceivably emerge from the feeble human mind. The Pythagoreans literally embedded the universe into mathematics. In fact, to the Pythagoreans, God was not a mathematician— mathematics was God!
    The importance of the Pythagorean philosophy lies not only in its actual, intrinsic value. By setting the stage, and to some extent theagenda, for the next generation of philosophers—Plato in particular—the Pythagoreans established a commanding position in Western thought.
    Into Plato’s Cave
    The famous British mathematician and philosopher Alfred North Whitehead (1861–1947) remarked once that “the safest generalization that can be made about the history of western philosophy is that it is all a series of footnotes to Plato.”
    Indeed, Plato (ca. 428–347 BC) was the first to have brought together topics ranging from mathematics, science, and language to religion, ethics, and art and to have treated them in a unified manner that essentially defined philosophy as a discipline. To Plato, philosophy was not some abstract subject, divorced from everyday activities, but rather the chief guide to how humans should live their lives, recognize truths, and conduct their politics. In particular, he maintained that philosophy can gain us access into a realm of truths that lies far beyond what we can either perceive directly with our senses or even deduce by simple common sense. Who was this relentless seeker of pure knowledge, absolute good, and eternal truths?
    Plato, the son of Ariston and Perictione, was born in Athens or Aegina. Figure 7 shows a Roman herm of Plato that was most likely copied from an older, fourth century BC Greek original. His family had a long line of distinction on both sides, including such figures as Solon, the celebrated lawmaker, and Codrus, the last king of Athens. Plato’s uncle Charmides and his mother’s cousin Critias were old friends of the famous philosopher Socrates (ca. 470–399 BC)—a relation that in many ways defined the formative influence to which the young Plato’s mind was exposed. Originally, Plato intended to enter into politics, but a series of violent actions by the political faction that courted him at the time convinced him otherwise. Later in life, this initial repulsion by politics may have encouraged Plato to outline what he regarded as the essential education for future guardians of the state. In one case, he even attempted (unsuccessfully) to tutor the ruler of Syracuse, Dionysius II.

    Figure 7
    Following the execution of Socrates in 399 BC, Plato embarked on extensive travel that ended only when he founded his renowned school of philosophy and science—the Academy—around 387 BC. Plato was the director (or scholarch ) of the Academy until his death, and his nephew Speusippus succeeded him in that position. Unlike academic institutions today, the Academy was a rather informal gathering of intellectuals who, under Plato’s guidance, pursued a wide variety of interests. There were no tuition fees, no prescribed curricula, and not even real faculty members. Still, there was apparently one rather unusual “entrance requirement.” According to an oration by the fourth century (AD) emperor Julian the Apostate, a burdensome inscription hung over the door to Plato’s Academy. While the text of the inscription does not appear in the oration, it can be found in another fourth century marginal note. The inscription read: “Let no one destitute of geometry enter.” Since no fewer than eight centuries separate the