A genuine break, a lasting fix. Russell's paradox is a real, exact contradiction in naïve set theory; the theory of types is a sound response, and its descendants (typed languages, proof assistants) are everywhere in computing.
The grand goal didn't fully land. Principia needed extra axioms (infinity, reducibility) that aren't pure logic, and Gödel (1931) showed no such system can be complete. Mathematics-from-logic-alone was not achieved.
Most of his life was elsewhere. Russell was a public philosopher, pacifist (jailed in WWI), educator, and essayist who won the Literature Nobel. Brilliant and contrarian — and, on some social views, a man of his era to read critically.
Most sets don't contain themselves: the set of all teacups is not a teacup. A few might: the set of all "things that are not teacups" is not a teacup, so it contains itself. Now form R = the set of all sets that do NOT contain themselves, and ask the fatal question. (The village version: a barber shaves exactly those who don't shave themselves — so who shaves the barber?)
"The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it." — Bertrand Russell
Russell's fix: stop letting sets mix levels. Individuals live at type 0. Sets of individuals at type 1. Sets of those at type 2, and so on. The rule: x ∈ y is only well-formed when type(x) = type(y) − 1 — a set may only contain things exactly one level below it. Now "R ∈ R" asks for type(R) = type(R) − 1, which nothing satisfies: the paradox can't even be written down. Pick types and check membership.
list.append(list)-style nonsense or an ill-formed recursive type: it tracks levels and refuses the ones that would let a thing swallow itself. Russell built the first one — on paper, to save arithmetic — and it became the type system running in every compiler. ⚑ The paradox didn't just get patched; it got turned into a tool.With Whitehead (1910–13): an attempt to derive all mathematics from logic. Famously, "1 + 1 = 2" is proved only well past page 360 — rigor at monumental cost.
Stratified types bar self-reference and tame the paradoxes. Direct ancestor of type theory, the Curry–Howard correspondence, and modern proof assistants.
Gate kept on. Two honesties. The logic: Russell's paradox is real and his types are a sound fix — but logicism, the dream that mathematics is just logic, did not fully succeed. Principia leaned on axioms (infinity, reducibility) that look more like mathematics than pure logic, and within twenty years [[kurt-godel]] proved that no consistent system of that strength can prove all truths or even its own consistency — so the foundation Russell rebuilt has a ceiling, like everyone's. The man: Russell lived ninety-seven enormous years mostly outside logic — a pacifist imprisoned in WWI, a campaigner against nuclear weapons into his nineties, a popular essayist and educator who won the Nobel Prize in Literature (1950) for his humane writing. He was also combative, often wrong with great confidence, and held some social views best read with a critical eye for their time. A first-rank logician who became one of the century's loudest consciences — the lineage holds the logic; the rest is his and history's to weigh.