22/05/2019

The remarkable Bernoulli family of mathematicians was problematic.

O matemático Johann Bernoulli – Wikimedia Commons

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

It dates back to the legend of the Phoenician princess Dido, recounted by the Roman Virgil in the epic poem "The Aeneid." Fleeing her native city of Tyre, Dido arrives in North Africa, where she needs to find shelter. Cunningly, she makes a modest request to the local king to grant her as much land as she can contain in an ox hide. The king agrees. Dido cuts the hide into very thin strips, which she uses to form a rope. With it, she encloses a large area of land, where she founds the city of Carthage, which would become Rome's greatest rival.

In mathematics, it's called the isoperimetric problem: what is the largest area we can enclose with a curve of a given length? Its solution—the area is maximum when the curve is a circle—marks the creation of a new field of research, the calculus of variations.

In 1697, Jacob Bernoulli (1654–1705) challenged his brother Johann (1667–1748) to a problem of this type. Johann solved it quickly (boasting that it only took him three minutes), but the solution was wrong. Jacob didn't miss the opportunity to publicly ridicule his brother. This ended their relationship for good.

A rare case of concentrated talent, the Bernoulli family produced eight mathematicians in the 17th and 18th centuries, three of whom were outstanding: in addition to Jacob and Johann, there was also the latter's son, Daniel (1700–1782). Many mathematicians believe that it was a single person who achieved all these works bearing the name Bernoulli (this was my belief for a long time…).

But, as a family, he had serious problems. In 1738, Daniel published a book on hydrodynamics. His father, Johann, published another book on the same subject, using Daniel's ideas but with an earlier date, claiming that his son had plagiarized him!

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