Portrait of the French mathematician Francois Viete, 1540-1603. Viete practised law, but also worked on cryptography and mathematics and became a court official to the king in 1570. In the war against Spain he broke the Spanish secret cipher. His mathematical research was in algebra which he applied to solve geometric problems. He used letters to denote constants and variables and introduced the terms 'coefficient' and 'negative'. He published a systematic account of how to solve many trigonometric problems. He preferred to establish his identities and proofs algebraically rather than geometrically thereby setting a trend.