# Jakob Bernoulli

#### 1654 - 1705

Jakob Bernoulli was the first of long series of Bernoulli family members, all mathematicians, whose combined contributions to mathematics and physics is unequalled in history.

• Nationality
• Swiss

• Subject
• Mathematics

• Fields
• Calculus, probability

• Distinctions
• The Bernoulli Crater on the Moon is named in honour of Jakob and his brother Johann.

• Posts
• Professor of Mathematics, University of Basel, 1687 - 1705.

• Publications
• Ars Conjectandi (Art of Conjecturing), published posthumously 1713. Deals with combinatorics (permutations and combinations), probability theory, law of large numbers

• Laws
• Law of large numbers

• Theories
• Calculus: Calculus of Variations, B. differential equation

Probability: Bernoulli numbers, trial, process, scheme, operator, sampling, distribution, random variable

Bernoulli map

Bernoulli Golden Theorem

Lemniscate of Bernoulli

Combinatorics: permutations and combinations

• Equations
• Bernoulli differential equation

Bernoulli formula

Bernoulli polynomials

Bernoulli inequality

• Experiments/Discoveries
• Bernoulli discovered the constant \$e\$, often referred to as Euler's number: \$e = {lim}↙{n→∞}(1+1/n)^n\$

Jakob planted the family tree in Basel, Switzerland. He travelled extensively, and was a contemporary of Roberts Boyle and Hooke. He took the side of the German Gottfried Leibniz against Isaac Newton in the infamous dispute over the invention of calculus. Jakob developed calculus further, together with his younger brother Johann.

The two brothers were among the earliest to develop and champion the calculus of Leibniz, published in 1684. Jakob's initial collaboration with his brother Johann turned to destructive rivalry as the latter sought to exit the shadow of elder brother.

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