Biography - the Bernoulli family

Mathematicians are like diamonds - rare and valuable. As the greatest diamonds are the rarest of the rare, so are the greatest mathematicians. And as the world's largest diamonds have never been found near each other, so should the best mathies be well distributed. Yet fate deemed otherwise in the case of the Bernoulli family, where she chose to put at least four of the best.

The Bernoullis (or as they are sometimes called, the Bernouillis) were a family of Dutch origin, who were driven from Holland by Catholic persecutions, and finally settled at Basle in Switzerland. One of them married into an old Basle family and ended up being an extremely prosperous merchant. All his descendants became rich via trade as well, except for one Nicholas Bernoulli, who decided that it was time to apply the family genius to something else and became a doctor. Now the fun began with three of his sons --- Jacob (or James), born in 1654, Nicholas, eight years younger, and John, another five years younger. In the above family tree, they are called Jacob I, Nicholas I and John I to distinguish them from their progeny.

Here's a cross-section of the problems solved by Jacob. He was among the many who showed that the cycloidwas isochronous and verified Leibnitz's construction of the catenary (the shape of a hanging chain). He also determined the form taken by an elastic rod fixed at one end and acted on by a given force at the other, and of a sail filled with wind. He rigorously showed that the circle is the largest shape for a given perimeter. Other important work was on infinite series, analytical geometry (study of curves where co-ordinates represent each point and the remaining work is mainly algebraic) and probability (and its applications to insurance and genetics).

Nicholas Bernoulli was not as great as his brothers --- we shall speak of him only fleetingly. Having got a PhD in philosophy at 16, he went into law, earning the highest degree available in it at the age of 20. He even became a professor in it before turning to maths. He was very highly thought of and was given a state funeral by the Russian Empress Catherine.

John was a real character. More interesting than Zaphod Beeblebrox! He was taught a lot of maths by his older brother Jacob, and rewarded him with a multitude of quarrels. Their letters sparkle with swear words and strong language that would give most English teachers heart attacks. He worshipped those he agreed with and avidly hated all he didn't. To quote the author Eric Temple Bell

``after all, if rational human beings get excited about a game of cards, why should they not blow up over mathematics which is infinitely more exciting?''

He even threw his son Daniel out of his house when Daniel beat him in a maths competition! When his brother Jacob died, he took over his job. He was, however, the most successful teacher of his age, and could inspire his pupils with almost as passionate a zeal for mathematics as he felt himself.

Bar his innumerable controversies, the chief discoveries of John Bernoulli were the exponential calculus, the vigorous treatment of rigonometry as a branch of analysis, the conditions for a geodesic (the curve of shortest length between between two points on a surface. For example, on our plane surface, the geodesic is a line), the determination of trajectories, the solution of the brachistochrone (a problem he proposed), and much work in applied maths like optics, tides and ship sails.

Several members of the same family, but of a younger generation,enriched mathematics by their teaching and writings. You can see several names in the family tree, but not all of them were brilliant enough to be warranted space in this already far-from-brief account.

The bellicose John had three sons. The first, Nicholas III was born in 1695 but was drowned at St. Petersburg, where he was professor, on July 26,1726. When he was 16, he was already teaching his 11-year old brother Daniel maths. Daniel was the greatest of his generation and was a close friend of Euler .Like all the other Bernoullis, he switched to maths after starting on medicine.

At various times in his life he was professor of medicine, metaphysics,natural philosophy, anatomy, botany, maths and physics. His major workwas in mathematical physics, a subject some say he founded. Before him,there was not much maths in physics, but after his work on differentialequations, vibrating strings, the kinetic theory of gases,hydrodynamics (the Bernoulli Principle, which states that as thevelocity of a fluid increases, its pressure decreases and vice versa is due to him) and others, there was more than plenty. He also did work on calculus and probability.

The third of John's sons was John II. His work was mostly in physics, but he took over his father's job when he died. (As you may remember, his father had succeeded to the post on the death of his uncle Jacob). He also began in law before switching to maths. He had two sons, John III and Jacob II. Both turned to law before switching to maths. John III earned a doctorate in philosophy at the age of 13 and was appointed astronomer-royal, and director of mathematical studies at Berlin, while Jacob II was a professor with a very bright future before he was accidentally drowned, like his uncle Nicholas III.

You may ask what happened to all the other Bernoullis. Were they geniuses too? Let me once again quote E.T.Bell:

``No fewer than 120 of the descendants of the mathematical Bernoullis have been traced genealogically, and of this considerable posterity the majority achieved distinction --- sometimes amounting to eminence --- in the law, scholarship, science, literature, the learned professions, administration, and the arts. None were failures.''

Bell may be exagerrating here, but even if he is, my opinion is that the Bernoulli gene had some chromosome of well above average intelligence, and the fact that the gene achieved its full potential in most of the family members was due to the priority the Bernoullis placed on achievement.

For another deep article on the Mathematical Bernoullis, have a look at their Rouse-Ball biography.