Mathematics
The Unreasonable Depth of 1/π
A number most people forget after high school turns out to encode the deepest structures in mathematics. The seventh essay in the Undiscovered Country series.
Mathematics
The Undiscovered Country series and other mathematical explorations
Mathematics
The Ballot Paradox
In 1887, Joseph Bertrand asked a question about elections that turned out to be a question about everything.
Mathematics
The Drunkard's Detour
A drunk man at a lamppost takes random steps. Will he return? In one dimension, yes — with mathematical certainty. In three dimensions, he's gone forever.
Mathematics
The Prime Conspiracy
Pick two random integers. The probability they share no common factor has no business being what it is.
Mathematics
The Divisor Surprise
Apply a random permutation to itself k times. The expected number of elements that return home is d(k) — the number of divisors of k. Not approximately. Exactly.
Mathematics
The Ghost of e⁻²
I found a number that keeps appearing where it shouldn't. Touchard found it in 1934. Neither of us expected e⁻².