Jacob Bernoulli found e by asking how fast money could grow
Put one dollar in an account paying 100 percent a year. Compounded once, it doubles; compounded monthly, it reaches about 2.61; daily, about 2.71. In 1683 Jacob Bernoulli noticed the totals creep toward a ceiling rather than grow forever, and so stumbled on the constant Euler later called e.
Bernoulli was born in Basel in 1655, into a line of Protestant spice merchants on his father's side and bankers and city officials on his mother's. His father wanted a minister, and Jacob obliged by studying theology, while secretly pursuing mathematics and astronomy. From 1676 to 1682 he toured Europe, meeting the work of Hudde, Boyle and Hooke and producing a wrong theory of comets along the way. Back home he taught mechanics at Basel from 1683 and later held its mathematics chair until his death.
He and his younger brother Johann were among the first to make sense of Leibniz's cryptic 1684 paper on differential calculus, and together they helped found the calculus of variations. The partnership soured into a bitter rivalry of printed attacks and challenge problems, and by 1697 it had collapsed. In a 1690 paper Jacob reduced the isochrone, the curve down which a sliding object reaches the bottom in the same time from any starting point, to a differential equation and solved it by separating variables. He also devised the figure-eight curve now called his lemniscate in 1694. For the compound-interest limit, he pinned down only that its value lay between 2.5 and 3.
His most original book, Ars Conjectandi, came out in 1713, eight years after he died, still unfinished. It treats probability as a measurable degree of certainty, works through the expected winnings of gambling games, gave us the term Bernoulli trial, and contains the first version of the law of large numbers.
He admired the logarithmic spiral for keeping its shape as it grows and asked for one on his tombstone with the motto 'Although changed, I rise again the same'. When he died on 16 August 1705, the stonemason carved an Archimedean spiral instead.
Source: Jacob Bernoulli
