Science Library - free educational site

Jakob Bernoulli

1654 - 1705

Jakob Bernouilli, 1654 - 1705, Swiss mathematician

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.

    Read Biographies from:

Choose a subject for more biographies

Some Great Scientists

Latest Item on Science Library

The most recent article is:

Air Resistance and Terminal Velocity

View this item in the topic:


and many more articles in the subject:

Subject of the Week


Physics is the science of the very small and the very large. Learn about Isaac Newton, who gave us the laws of motion and optics, and Albert Einstein, who explained the relativity of all things, as well as catch up on all the latest news about Physics, on

Gravity lens

Test your knowledge!

Question: A convex lens has a focal length of 12 cm, and has an object 8 cm from it. What is the magnification of the image?

Go to the article about: Lenses

IT Forum by Sean Bone

Quote of the day...

I have always thought that underpopulated countries in Africa are vastly underpolluted. Their air quality is probably vastly inefficiently low compared to Los Angeles or Mexico City.

ZumGuy Internet Promotions

Renewable energy media services