Great Mathematicians - Johann and Jakob Brothers

Jakob Bernoulli was born in Bale, Switzerland on December 27, 1654. In 1687, he was appointed the chair in mathematics at the university in Bale. He occupied this position until his death.

In 1691, Bernoulli write two essays which contained lectures and lessons on differential calculus. The earliest use of the term integral was found in these particular writings.

Bernoulli wrote a book on probability called Ars Conjectandi, which was published in 1713. In his book, he established the fundamental principles of the calculus of probabilities. He defined the Bernoulli numbers and explained their use. In addition, he gave some theorems on finite differences.

Jakob Bernoulli contributed to mathematics in the following ways:

• discovered the solution of the problem to find an isochronous curve
• had a general solution for isoperimetrical figures
• investigated the chief properties of the equiangular spiral
• established the fundamental principles of the calculus of probabilities

Jakob Bernoulli died in Bale on August 16, 1705. From his work on equiangular spirals, he begged that an equiangular spiral be engraved on his tombstone with the inscription eadem numbero mutata resurgo.

Johann Bernoulli was born in Bale, Switzerland on August 7, 1667. From 1695-1705, he was the chair of mathematics at Groningen. His brother, Jakob, was chair of mathematics at Bale until he died in 1705. Upon Jakob's death, Johann took up this position at Bale until 1748.

Bernoulli was extremely competitive with his brother Jakob and his own son, Daniel with regards to mathematics. One story tells of the time when Daniel won a reward from the French Academy. Johann had expected that he would receive this prize, so out of jealousy, Johann forced Daniel to move out of the house. Another story relates the time when both Johann and his brother Jakob were working on the problem of isoperimentrical curves. Johann attempted to substitute a solution discovered by Jakob for his won incorrect solution.

Bernoulli was a very successful teacher, however, and he inspired his students to have a zeal and a passion for mathematics, which he felt himself.

Bernoulli was also well acquainted with Marquis de L'Hospital, who was a very rich man. L'Hospital agreed to support Bernoulli's work only if Bernoulli allowed L'Hospital to publish his works. L'Hospital published a textbook on calculus in 1696, which contained the famous L'Hospital's rule. Bernoulli claimed that he had derived this rule and many other discoveries that L'Hospital had claimed were his after L'Hospital's death. It was not until 1955 that letters between L'Hospital and Bernoulli were discovered that explained the details of the arrangement. These letters proved that Bernoulli's claim was indeed true.

Johann Bernoulli contributed to mathematics in the following ways:

• the discovery of exponential calculus
• treatment of trigonometry as a branch of analysis
• conditions for a geodesic
• determination of orthogonal trajectories

Johann Bernoulli died in Bale on January 1, 1748.