Even in 1990 — a wealthy, public Microsoft — Gates flew economy. Company policy was coach for everyone, and colleagues recall him working an entire New York flight from a middle seat.

Bill Gates has a published mathematics paper. As a Harvard undergraduate he co-wrote “Bounds for Sorting by Prefix Reversal” (1979) on the “pancake sorting” problem with professor Christos Papadimitriou — and the bound he proved stood as the best known for roughly 30 years.

One of Bill Gates’s own coding credits is DONKEY.BAS, a crude driving game he co-wrote in 1981 (with Neil Konzen) to ship with the first IBM PC. Apple’s Macintosh team later singled it out as an embarrassment.

As teenagers around 1970, Bill Gates and Paul Allen went dumpster-diving behind a Seattle computer company — Allen boosting the smaller Gates up to the bin — and pulled out a printout of the DEC operating system’s source code to learn how it worked.