1. Understanding the Bernoulli Family Tree Three generations of mathematical geniuses Three largest contributors were: –Jakob –Johann (I) –Daniel Family Tree

2. Jakob Bernoulli (1654-1705) 1st studied to be a minister Went to Basel University –received degree in theology –fascinated with mathematics furthered the calculus he had learned from Leibniz worked on cantenaries –bridge structures and design Jakob was a professor at Basel until his death

3. Jakob Bernoulli (1654-1705) 1. Probability and Statistics Bernoulli distribution Bernoulli theorem 2. Differential Equations Bernoulli Equation 3. Number Theory Bernoulli numbers Bernoulli polynomial 4. Calculus Lemniscate of Bernoulli

4. Johann Bernoulli (I) (1667-1748) Followed older brother’s footsteps –often aided Jakob He studied at the University of Basel –medicine and mathematics Yearning for mathematics Became professor at University of Basel after Jakob’s death Became jealous of his brother Johann’s areas of expertise –differential calculus –refraction of light At death one of most successful mathematicians in the world

5. Daniel Bernoulli (1700-1782) His father was Johann (I) Was a quick learner –began studying at age eleven Studied at University of St. Petersburg –began in medicine –loved mathematics and physics Ended up at Basel University –professed metaphysics, medicine and natural philosophy Daniel developed hydrodynamics largely from the single principle that later became known at the Law of Conservation of Energy FOUNDER OF MATHEMATICAL PHYSICS

6. How the other Bernoullis fit in... Nicolaus (II) –integral in beginnings of probability Nicolaus (III) –fundamental in theory of Algebra Johann (II) –became chair at Basel University –studied heat and light Johann (III) –became chair at Berlin Academy at age of 19 –studied probability and theory of equations

7. Bernoulli accolades “Students of heredity have called attention to the extraordinary number of distinguished scholars who descended from the protestant populations expelled from the catholic countries in the 16th and 17th centuries” The Bernoulli family provides the “most remarkable evidences of the power of heredity or of early home influence in all the history of mathematics. No less than nine of its members attained eminence in mathematics and physics and four of them were honored by election as foreign associates of the Academie des Sciences of Paris” David Smith quoted by Nickel pg147

8. Bernoulli accolades “The Bernoulli family… in three generations produced 8 mathematicians, several of them outstanding, who in turn produced a swarm of descendants… No fewer than 120 of the descendants of the mathematical Bernoullis have been traced genealogically, and of this considerable posterity the majority achieved distinction - sometimes amounting to eminence - in law, scholarship, science, literature, the learned professions, administration, and the arts. None were failures.” Bell quoted by Nickel pg148