Zen Proofs
Theorems, explained intuitively. The famous results of mathematics, shown the way they actually make sense.
The Birthday Paradox: Why 23 People Are Enough for a Match
Put 23 people in a room and a shared birthday is more likely than not. The proof is a short count of 253 pairs, and it shows exactly where intuition slips.
July 20, 2026
The Monty Hall Problem: Why Switching Doors Doubles Your Chances
Three doors, one car, and a host who knows where it is. Switching doors wins twice as often as staying put, and here is the explanation that finally clicks.
July 11, 2026
Erdős and the Probabilistic Method: Proving Things Exist by Chance
Paul Erdős proved a graph must exist without ever building it, using only a coin and a counting argument. Here is the probabilistic method, his signature idea.
June 28, 2026
Euler's Identity: Why e^(iπ) + 1 = 0
Why does e^(iπ) + 1 = 0 tie five constants into one line? The proof rests on one idea: raising e to an imaginary power walks a point around the unit circle.
June 28, 2026
Euclid's Proof That There Are Infinitely Many Primes
Euclid showed, more than two thousand years ago, that no finite list can hold all the primes. The argument fits in a single paragraph and still surprises people today.
June 27, 2026
Cantor's Diagonal Argument: Why the Real Numbers Cannot Be Listed
Georg Cantor proved that no matter how cleverly you list real numbers, a simple diagonal trick always produces a number you missed. Here is the argument, step by step, without the fog.
June 26, 2026
Goodstein's Theorem: The Sequence That Explodes, Then Always Returns to Zero
Goodstein's theorem describes a sequence of whole numbers that rockets past a googol and yet, provably, always comes back down to zero. Here is why, explained with a picture instead of heavy logic.
June 25, 2026