There’s a pretty thought experiment that’s sometimes attributed to Democritus though it’s actually due to a later popularizer of the atomic hypothesis1 and it goes like this: Suppose we use the world’s sharpest knife to cut a block of cheese in half, leaving two small blocks where before there was one large one. If cheese…

Mathematical Enchantments

18.02.2025

Dedekind’s Subtle Knife |

“Think about the knife tip. That is where you are. Now feel with it, very gently. You’re looking for a gap so small you could never see it with your eyes, but the knife tip will find it, if you put your mind there. Feel along the air till you sense the smallest little gap…

Mathematical Enchantments

14.03.2025

How Pi Almost Wasn’t |

Since you’re reading this essay, you probably already know about the mathematical holiday called Pi Day held on March 14th of each year in honor of the mystical quantity π = 3.14.... Pi isn’t just a universal constant; it’s trans-universal in the sense that, even in an alternate universe with a different geometry than ours,…

Mathematical Enchantments

22.04.2025

Is 1 Prime, and Does It Matter? |

If you ask a person on the street whether 1 is a prime number, they’ll probably pause, try to remember what they were taught, and say “no” (or “yes” or “I don’t remember”). Or maybe they’ll cross the street in a hurry. On the other hand, if you ask a mathematician, there's a good chance…

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Mathematical Enchantments

Science

The Real Line versus the Fakes |

Dedekind’s Subtle Knife |

How Pi Almost Wasn’t |

Is 1 Prime, and Does It Matter? |

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Mathematical Enchantments