Brook Taylor

Brook Taylor (1685–1731) was an English mathematician (and keen amateur musician and painter) who found a recipe for rebuilding almost any smooth curve out of nothing more than its value and its slopes at a single point. Zoom in, measure how the function is bending, and you can predict where it goes next.

The lasting imprint

That recipe is Taylor's theorem: it turns a complicated function into an endless polynomial you can chop off wherever you like, keeping only as many terms as you need. Built up around any centre point, these become the Taylor and Maclaurin series that calculators quietly use to work out sines, logs and exponentials to as many digits as you want.

Taylor published his theorem in 1715, but his writing was famously terse and cramped — he left out so much explanation that many mathematicians barely noticed how powerful it was. It took decades, and a nudge from Lagrange, before the theorem got the fame it deserved. He also feuded with the followers of Leibniz over who really invented calculus, siding firmly with fellow Englishman Newton. Brilliant, but not the man to hire if you wanted the manual explained clearly.