The Bernoulli Family

The Bernoullis were the most ferociously talented — and ferociously competitive — family in the history of mathematics. Over three generations this Swiss clan from Basel produced something like eight notable mathematicians. The two giants are the brothers Jacob Bernoulli (1655–1705) and Johann Bernoulli (1667–1748), who did brilliant work together and then spent years at each other's throats.

The concepts left behind

Jacob laid foundations of probability (the law of large numbers, the Bernoulli trial, the number e) and named the beautiful spiral he loved so much. Johann became a master of the new calculus and taught the young Leonhard Euler. Together they cracked the brachistochrone — the curve of fastest descent — one of the founding problems of the calculus of variations, whose shortcuts include the Beltrami identity.

\frac{\partial L}{\partial y'}\,y' - L = \text{constant}.

The Bernoullis feuded spectacularly. Jacob and Johann publicly challenged each other with problems designed to humiliate, and their letters dripped with rivalry. Johann was, if anything, worse to his own son Daniel: when Daniel won a prestigious prize that Johann had also entered, Johann was so jealous he reportedly threw him out of the house. He's even accused of trying to steal Daniel's greatest work — on fluid flow — by backdating his own book. Brilliant mathematics, terrible family reunions.