René Descartes

If you have ever heard someone argue that the way to get to a reliable answer is to first doubt everything you think you know, you have heard an echo of Descartes. Methodic doubt — the deliberate stripping away of inherited assumptions to see what survives scrutiny — is the practice most closely attached to his name, alongside analytic geometry, the linking of algebra and geometry that gave mathematics a new way of stating problems.

He was born in La Haye en Touraine in France in 1596, and his early training combined a strict attention to method with a willingness to draw separate fields together. Correspondence, travel and steady reading supplied the equipment; what marked his first results was not so much originality as the clarity with which they were set out. Clarity then became a working principle rather than an incidental virtue.

His middle period tightened the technique and widened its reach. Rivals and critics pressed him, and the pressure showed in the argument: publications, lectures and demonstrations turned provisional positions into settled statements. He moved between analysis and construction, theory and experiment, and even the failed attempts served as tests that sharpened what came next. Students and correspondents carried the approach beyond any single institution.

Later he turned to putting the work in order — notes, editions and reflective essays aimed at fixing the strongest form of the central ideas. He died in 1650. The surviving drafts and corrections show a process far messier than the finished prose suggests, which is part of why his writing is still used as a starting point rather than a monument, in classrooms and workshops where the method gets tried again.