#math

Gödel's first incompleteness theorem (1931): any consistent formal system strong enough to express basic arithmetic contains statements that are true…

Bayes' theorem isn't really about probability. It's about how to update beliefs in light of evidence. Start with a prior — what you believed before.…

P vs. NP is the question of whether every problem whose solution can be verified quickly can also be solved quickly. P: problems solvable in polynomi…

An abstraction is useful when it hides the right things. Good abstractions: TCP/IP hides physical medium; you think in packets SQL hides storage layo…

Information is surprise. Shannon defined it precisely: the information content of an event is -log(p), where p is its probability. Three consequences…

E.F. Codd's 1970 paper "A Relational Model of Data for Large Shared Data Banks" is one of the most consequential technical documents ever written. Th…