Euclid (around 300 BC) wrote the most successful textbook of all time. His Elements — thirteen books laying out geometry and number theory from a handful of starting assumptions — was studied, copied and taught continuously for over 2,000 years, second only to the Bible in the number of editions printed. Abraham Lincoln kept a copy in his saddlebag to sharpen his reasoning.
Euclid's real invention wasn't any single result; it was the method. Start from a
few self-evident axioms, and build everything else by airtight logical steps. That
"definitions → axioms → theorems" structure is still exactly how mathematics is written today. From
it he gave us the
Two Euclid stories have echoed down the ages. When King Ptolemy asked for a shortcut through the Elements, Euclid reportedly replied, "There is no royal road to geometry" — no shortcuts, even for kings. And his proof that the primes never run out is a masterpiece of economy: multiply any finite list of primes together, add one, and the result is divisible by none of them — so there must always be another prime beyond your list. A two-line argument from 2,300 years ago that no one has ever improved upon.