How to read this Bernoulli family tree
Read the Bernoulli family tree from the top down, one generation to a row, with each son hanging from his father. The chart draws fathers and sons only, because the subject is how mathematics passed down the family.
A portrait is a person
A silhouette stands in where no portrait is free to use.
The plate names the person
It gives the years, with a dagger before the year of death, and the post the person held.
A double ring is the centre
Johann Bernoulli is the centre, as the father of three mathematicians.
A line down is a son
Each line runs from a father to his son.
Two lines of conflict mark the rivalries of the family, between Jacob and his brother Johann and between Johann and his son Daniel. A line of closeness joins Daniel to his brother Nicolaus II, who was with him in St Petersburg and died there.5
Eight mathematicians on the Bernoulli family tree
The family came from Nicolaus Bernoulli, an important citizen of Basel, a member of the town council and a magistrate.1 He ran the spice business his own father had set up in Basel.1 He was not a mathematician, nor was his son Nicolaus, the father of Nicolaus I. The eight below them were.
| Mathematician | Generation | Son of | Best known for |
|---|---|---|---|
 Jacob Bernoulli | First | Nicolaus | Ars Conjectandi, on probability, printed in 1713. |
 Johann Bernoulli | First | Nicolaus | The calculus, the brachistochrone and the teaching of Euler. |
| NINicolaus I Bernoulli | Second | Nicolaus the painter | His letters to Euler, Leibniz and Montmort. |
 Nicolaus II Bernoulli | Second | Johann | The problem of trajectories. |
 Daniel Bernoulli | Second | Johann | Hydrodynamica and the Bernoulli principle of fluid flow. |
 Johann II Bernoulli | Second | Johann | Four prizes of the Paris Academy, on heat and light. |
 Johann III Bernoulli | Third | Johann II | Astronomy and probability, at the Berlin Academy. |
 Jacob II Bernoulli | Third | Johann II | Mathematical physics, at St Petersburg. |
Two brothers at the head of the Bernoulli family tree
Jacob Bernoulli was made to study philosophy and theology by his parents, which he resented.1 He became professor of mathematics at Basel in 1687. His younger brother Johann, sent by their father to study medicine, asked Jacob to teach him mathematics, and the two worked through the new calculus of Leibniz together.1
The partnership turned into a rivalry, and relations between the brothers broke down completely in 1697.1 Johann had gone to Groningen as professor in 1695, and in 1705 he came back to Basel and was appointed to the chair Jacob had held.2 Jacob’s Ars Conjectandi was printed in Basel in 1713, eight years after his death.1
- Jacob BernoulliProfessor at Basel from 1687.
- Johann BernoulliProfessor at Groningen, then Basel.
- Daniel BernoulliAuthor of Hydrodynamica.
Four sons and nephews
Nicolaus I was the son of the painter and studied mathematics with both of his uncles. Jacob supervised his master’s degree at Basel.3 He later held the chair at Padua that Galileo had held, from 1716, and returned to Basel in 1722 to the chair of logic.3
Johann had three sons who became mathematicians.2 Nicolaus II, the eldest, entered the University of Basel at thirteen and worked as his father’s assistant.4 Daniel learned the calculus from his father and from Nicolaus II.5 Johann II took a doctorate in law in 1727, worked on mathematics with his father and followed him in the Basel chair.6
In 1734 Daniel and his father shared the Grand Prize of the Paris Academy. Johann was furious to be ranked as the equal of his son, and Daniel was banned from his father’s house.5 His Hydrodynamica appeared in 1738.5
The grandsons at the foot of the Bernoulli family tree
The last two mathematicians on the Bernoulli family tree were the sons of Johann II. Johann III took a master’s degree in law at fourteen and was appointed to the Berlin Academy at nineteen.7 Jacob II also took a degree in law. In 1782 he applied for the chair of physics left by his uncle Daniel, and he went on to St Petersburg, where he married a granddaughter of Euler.8 He drowned in the Neva in 1789.8
Who taught whom in the Bernoulli family tree
Most of the family learned at home. The table follows each line of teaching that the MacTutor biographies record, with the two famous pupils from outside the family.
| Teacher | Pupil | What the record says |
|---|---|---|
| Jacob | Johann, his brother | Johann asked Jacob to teach him mathematics while he studied medicine. |
| Jacob | Nicolaus I, his nephew | Jacob supervised his master’s degree at Basel. |
| Johann | Nicolaus I, his nephew | Nicolaus I studied mathematics with both uncles. |
| Johann | Daniel, his son | Daniel learned the calculus from his father. |
| Nicolaus II | Daniel, his brother | Daniel learned the calculus from his elder brother too. |
| Johann | Johann II, his son | Johann II worked on mathematics with his father. |
| Johann | Leonhard Euler | One of the best pupils of Johann, who sent him to St Petersburg in 1727. |
| Johann | The Marquis de l’Hôpital | His textbook of the calculus rests on lectures by Johann. |
Questions about the Bernoulli family tree
How many mathematicians the Bernoulli family had
Eight are drawn on the chart, in three generations. Nicolaus, the father of Jacob and Johann, ran the family spice business in Basel.
Whether Euler was a Bernoulli
No. Leonhard Euler was a pupil of Johann Bernoulli, and a granddaughter of Euler married Jacob II.
How to use this chart in a class
The PNG and the PDF carry the chart and every portrait credit, and the people table lists who was alive in each period. A free account opens the chart in the full editor.
People and sources
A page of its own lists all ten people on the chart, each with a short note and the sources for it, and the eight numbered sources this article cites. It also gives the credits of the portraits and this page as a reference in the APA, MLA, Chicago and Harvard styles, ready to copy.