Rationalists (Descartes, Spinoza, Leibniz) thought the most important truths — math, logic, the structure of reality — could be derived by pure reason. The mind has innate concepts; experience just triggers them. Empiricists (Locke, Berkeley, Hume) thought the mind starts blank. Everything we know comes through the senses, and concepts are built up from sensory impressions.
The disagreement isn't academic. It shapes what counts as evidence, what counts as proof, what kinds of claims are even possible. A rationalist will accept a mathematical demonstration as final; an empiricist will ask what observation could falsify it. A rationalist will trust intuition; an empiricist will demand the data.
Kant tried to resolve the fight: some knowledge is *a priori* (independent of experience, like math) but applies to experience through the categories the mind imposes. Most contemporary philosophy of science is empiricist in spirit but quietly rationalist about logic and mathematics. The argument never ends because both sides catch something true — most of what you know about chairs is empirical, most of what you know about 2+2 is not.