From Plato's Theaetetus (~369 BCE) onward, the standard philosophical answer to what is knowledge was: knowledge is justified true belief. To know that p, you must believe p, p must be true, and you must have justification — and the definition seemed complete for two-and-a-half millennia. In 1963, Edmund Gettier, then a young assistant professor at Wayne State, published a three-page paper in Analysis titled Is Justified True Belief Knowledge? — two short scenarios in which someone had a justified true belief but intuitively did not have knowledge. The structure of the counterexamples was so simple and so devastating that the entire field of epistemology has been responding to Gettier for six decades since, with no settled replacement.
Gettier's two cases share a single structure. In Case 1, Smith has been told that Jones will get the job and has counted that Jones has ten coins in his pocket, so Smith forms the justified belief the man who will get the job has ten coins in his pocket — but Smith himself unwittingly gets the job and also has ten coins, so the belief is true and justified yet intuitively not knowledge, since the justification ran through the false intermediate. In Case 2, Smith has strong evidence that Jones owns a Ford and validly infers Jones owns a Ford or Brown is in Barcelona (the second disjunct arbitrary); Jones does not own a Ford but Brown happens to be in Barcelona, so the disjunction is true and justified but again not knowledge. In both cases the believer arrives at a true belief through a justified-but-false intermediate inference. The field has produced dozens of attempted fixes — causal theories (Goldman 1967), no false lemmas (Clark 1963), reliabilism (knowledge is true belief produced by a reliable process), sensitivity and safety conditions (Nozick, Sosa, framed in possible worlds), virtue epistemology (Sosa, Greco), and Williamson's knowledge-first epistemology (2000), which takes knowledge as conceptually primitive. None has produced consensus, and counterexamples to each can be constructed. What survives is that Gettier forced the field to take thought experiments and intuitions about cases seriously as data, and produced whole sub-fields — modal epistemology, virtue epistemology, knowledge-first epistemology, formal epistemology — in response to a three-page paper.
Outside academic philosophy the Gettier problem has limited direct application but substantial indirect influence. Epistemic injustice (Miranda Fricker, 2007 onward) — the harm done to people in their capacity as knowers — has reshaped social epistemology and influenced legal, medical, and educational practice. AI epistemology is the most current Gettier-adjacent conversation: large language models produce confident-sounding outputs that are often true, sometimes justified by training data, and sometimes neither, and hallucination — the model producing true outputs through unreliable processes and false outputs through processes that look the same — is structurally a Gettier problem at scale. The replication crisis is structurally analogous, with p-hacking and garden-of-forking-paths analyses producing true conclusions for the wrong reasons.