Jacob Bernoulli
Who was Jacob Bernoulli?
Swiss mathematician (1655-1705)
Biographical data adapted from Wikipedia’s article on Jacob Bernoulli (CC BY-SA 4.0).
Biography
Jacob Bernoulli was born on January 6, 1655, in Basel, Switzerland, into a family that became famous for its contributions to mathematics in Europe. Although his family wanted him to pursue a career in theology, Bernoulli was deeply passionate about mathematics and natural philosophy. He studied theology and philosophy at the University of Basel, while independently exploring mathematics, earning a degree in philosophy in 1671 and a licentiate in theology in 1676. After finishing his studies, he traveled extensively through France, the Netherlands, England, and Germany. During these travels, he met notable scientists and thinkers of the time, including Robert Boyle and Robert Hooke, which further fueled his dedication to mathematics and scientific methods.
Once back in Basel, Bernoulli began lecturing at the University of Basel and became a professor of mathematics in 1687, a role he held for life. He married Judith Stupanus and settled in Basel, producing influential work in several areas of mathematics. He was an early supporter of Gottfried Wilhelm Leibniz's version of calculus and actively defended Leibniz's notation and methods during the argument between Leibniz and Isaac Newton. Along with his younger brother Johann, Jacob made significant contributions to what is now the calculus of variations, which deals with optimizing functionals rather than ordinary functions.
One of Bernoulli's key contributions was in probability theory. His masterwork, Ars Conjectandi, completed around 1689 but not published until 1713, established the basis for modern probability theory. In it, he formulated the first rigorous version of the law of large numbers, stating that as the number of trials increases, the observed frequency of an event will approach its theoretical probability. The work also introduced Bernoulli trials, Bernoulli distributions, and Bernoulli numbers, which have important links to number theory and analysis.
Besides probability, Bernoulli made significant contributions to infinite series, differential equations, and geometry. He discovered the constant e, the base of natural logarithms, through his work on compound interest. He examined the lemniscate of Bernoulli, a figure-eight-shaped curve he described in 1694, and conducted early studies into the elastica, the shape a flexible rod takes under compression. He also contributed to polar coordinates and extensively corresponded with Leibniz and other leading mathematicians, helping spread new analytical methods that were changing mathematics in Europe.
Jacob Bernoulli died in Basel on August 16, 1705, after battling tuberculosis. He was buried in the Basel Minster, and his gravestone famously features the spiral he studied passionately, along with the Latin inscription Eadem mutata resurgo, meaning 'I shall arise the same, though changed.' His work in mathematics, especially in probability and analysis, stayed relevant well into the 18th century and beyond.
Before Fame
Jacob Bernoulli was born into a well-known Basel family involved in business and local government. His father, Nicolaus Bernoulli, was a spice merchant and a member of the Basel city council. The family wanted Jacob to go into theology or business. However, Bernoulli secretly taught himself the new mathematics spreading through Europe and earned degrees in philosophy and theology at the University of Basel, while his real interests were elsewhere.
After finishing his studies, Bernoulli spent several years traveling through France, the Netherlands, and England during the 1670s and early 1680s, a time when European natural philosophy was rapidly changing. He learned about Descartes’s ideas and connected with scientists at the newly formed Royal Society in London. These travels exposed him to the latest European ideas and convinced him that math, not theology, was his true calling. By the time he returned to Basel and started teaching at the university, he was already working on the advanced problems in analysis and probability that would shape his career.
Key Achievements
- Derived the first rigorous statement of the law of large numbers in Ars Conjectandi, a foundational result in probability theory
- Co-founded the calculus of variations alongside his brother Johann Bernoulli
- Introduced Bernoulli numbers, Bernoulli trials, and the Bernoulli distribution, which remain central to mathematics and statistics
- Discovered the mathematical constant e while analyzing compound interest
- Described the lemniscate of Bernoulli and made significant contributions to the study of infinite series and differential equations
Did You Know?
- 01.Bernoulli requested that a logarithmic spiral be engraved on his tombstone in Basel Minster, along with the Latin phrase 'Eadem mutata resurgo' ('I shall arise the same, though changed'), reflecting his deep admiration for the curve's self-similar properties.
- 02.He and his brother Johann had a notoriously bitter rivalry, frequently clashing in public disputes over mathematical priority, a conflict that became one of the most famous family feuds in the history of science.
- 03.Bernoulli's Ars Conjectandi was left unfinished at his death and was not published until eight years later, in 1713, by his nephew Nicolaus I Bernoulli.
- 04.He discovered the mathematical constant e while studying the mathematics of compound interest, recognizing the limit that the expression (1 + 1/n)^n approaches as n grows without bound.
- 05.The lemniscate of Bernoulli, the figure-eight curve he described in 1694, was inspired by his study of an oval described by Giovanni Cassini, and it later became important in complex analysis and the theory of elliptic integrals.