The Geometry
of Numbers
Three plates from the deep structure of arithmetic — and beside each, a working instrument. Drag a point across a curve, run the ancient sieve, hunt for a solution that cannot exist. The pictures hold still; the mathematics does not.
Elliptic Curves
On a curve y² = x³ + ax + b, three points on any straight line sum to zero. That single rule turns a curve into a group — the engine beneath elliptic-curve cryptography.
The Prime Number Theorem
Primes thin out, but not at random: the count below x tracks x / ln x ever more closely. Run the 2,200-year-old sieve and watch the ratio π(x)·ln x / x bend toward 1.
Fermat’s Last Theorem
For n > 2, the equation xⁿ + yⁿ = zⁿ has no solution in positive integers. Search every pair below the bound — the sum always lands between two perfect powers, never on one.
