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Johann Bernoulli 1667 - 1748

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Spirit of the Age Development, improvement or discovery of: Logarithms Rings of Saturn Pendulum clock Barometer Air pump Sextant Compound microscope Telescope Thermometer Number theory Analytic geometry Kinematics of falling bodies Christiaan Huygens Galileo

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Born in Basel, Switzerland Father was wealthy spice and drug merchant 10 th child of his parents Younger brother of Jakob Bernoulli (Jakob was 5 th child) (12 years difference in age Father wanted sons to follow him in the family business (Jakob started in theology, Johann started in medicine) Went to University of Basel in 1683 (age 16) Was tutored in math by brother Jakob Leibnitz published his first calculus findings in 1684 Johann’s early years Also called John or Jean

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Jakob Bernoulli Was already a mathematician and physicist when Leibnitz published his article Published articles on calculus in 1690 Bernoulli equation named for him:, Held the mathematics chair at University of Basel from 1687 to 1705 Proposed the catenary problem and the isoperimetric problem Also called James or Jaques (1654-1705)

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Newton versus Leibnitz Newton discovered first: about 1655 to 1666 Didn’t publish until 1704 Leibnitz discovered about 1682-1683 Published in 1684

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Johann—professional and personal Proud CompetitiveJealous Loved a good fight Increasing rivalry between the brothers “The Bernoulli’s took their mathematics in deadly earnest. Some of their letters about mathematics bristle with strong language that is usually reserved for horse thieves.” E.T. Bell Published his first independent mathematical paper in 1691 1691—lectured in Geneva for several months 1691—traveled to Paris and met with many outstanding mathematicians including L’Hopital Finished his medical degree in 1694 (never practiced medicine) Married Dorothea Falkner in 1694 Son Nicolaus born in 1695 Took Chair of Mathematics at University of Groningen in 1695

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L’Hopital hired Johann to tutor him in the new calculus Johann and L’Hopital continued to correspond after Johann left Paris For a considerable monthly fee: “I shall ask you to give me occasionally some hours of your time to work on what I shall ask you—and also to communicate to me your discoveries, with the request not to mention them to others. …for it would not please me if they were made public.” Johann and L’Hopital Marquis Guillaume Francois de L’Hopital (1661-1704) L’Hopital published first textbook on differential calculus in 1696. Johann was barely acknowledged. “And then I am obliged to the gentlemen Bernoulli for their many bright ideas; particularly to the younger Mr. Bernoulli who is now a professor in Groningen. “

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L’Hopital’s Rule A C M D d N P O B g b f apply L’Hopital’s rule In his textbook, L’Hopital uses the same or nearly the same examples given in letters from Johann.

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The Brachistochrone Problem From “brachistos” meaning shortest and “chronikos” meaning time Proposed by Johann in June 1696 “…If two points A and B are given in a vertical plane, to assign to a mobile particle M the path AMB along which, descending under its own weight, it passes from the point A to the point B in the briefest time.” Leibnitz asked Johann to extend the contest time from January 1, 1697 to Easter to allow foreign mathematicians more time.

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The Brachistochrone Problem “so few have appeared to solve our extraordinary problem, even among those who boast that through … their golden theorems, which they imagine known to no one, have been published by others long before.” Newton solved the problem in 12 hours. “I do not love to be …teased by foreigners about mathematical things.” Sir Isaac Newton I recognize the lion by his paw. Received 5 correct answers: Johann, Jakob, Leibnitz, L’Hopital, and an unsigned entry from England…..

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The Brachistochrone Problem – Johann’s solution AF H E C G O K L M n m c D Taken from A Source Book in Mathematics, 1200-1800, p. 394. B Snell’s law Velocity of a falling body

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The Brachistochrone Problem Drawings #I, II, III—Johann; VI thru VIII—Jakob: IX and X—L’Hopital; XII and XIII- ”Anonymous” solution

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How to insult like Johann You have to really enjoy insulting someone Insult with eloquence and style “so few have appeared to solve our extraordinary problem, even among those who boast that through … their golden theorems, which they imagine known to no one, have been published by others long before.” aimed at Sir Isaac Newton, “…I would not have minded so much if (the student) had not been one of the worst students, an utter ignoramus, not known, respected, or believed by any man of learning, and his is certainly not in a position to blacken an honest man’s name, let alone a professor know throughout the learned world…” aimed at a student of the University of Groningen

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Johann’s later years 1705 Jakob died of tuberculosis. Johann was named to the mathematics chair at Basel, even though he had offers from several other universities. 1712 and 1713 Newton vs. Leibnitz (again) Johann solved a more general version of the ballistics equation and validated Leibnitz’s methods 1714 Johann published a book improving navigational methods and discussing an early understanding of kinetic energy 1720 Johann took a young Leonhard Euler as a student 1727 After the death of Newton, Johann is considered the foremost mathematician in Europe

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Johann’s accomplishments Co-discoverer of calculus of variations Provided L’Hopital with enough material for a textbook Teacher of Euler His sons Nicholas, Daniel, and Johann all became mathematicians and held mathematics chairs at European universities. Worked on and contributed to: Differential geometry Description of exponential calculus Divergence of harmonic series Principle of conservation of energy Transmission of motion Motion of the planets Navigation

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Johann died January 1, 1748 at the age of 80 years. His tombstone was inscribed with “Archimedes of his age”

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Bibliography Struik, D.J. “The Origin of L’Hopital’s rule”. Mathematics Teacher. April 1963: pp. 257-260. 2) Young, Robyn V., editor. Notable Mathematicians: From Ancient Times to the Present. New York: Gale Research, 1998. Kramer, Edna E. Biographical Dictionary of Mathematicians, Volume 1. New York: Simon & Schuster Macmillan, 1991. Article by E.A. Fellman and J.O. Fleckenstein. Katz, Victor J. A History of Mathematics: An Introduction, 2nd Edition. New York: Addison Wesley Longman, 1998. Boyer, Carl B. A History of Mathematics, 2nd Edition. New York: John Wiley & Sons, 1991. Struik, Dirk J. A Concise History of Mathematics, Fourth Revised Edition. New York: Dover Publications, Inc., 1987. Bell, E.T. Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincare. New York: Simon & Schuster, 1965. Seife, Charles. Zero: The Biography of a Dangerous Idea. New York: Penguin Books, 2000. Dunham, William. Journey through Genius: The Great Theorems of Mathematics. New York: Penguin Books, 1990. Larson, Ron, Robert Hostetler, and Bruce H. Edwards. Calculus: Early Transcendental Functions, Fourth Edition. New York: Houghton Mifflin Company, 2007. Bell, E.T. Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincare. New York: Simon & Schuster, 1937. Gillespie, Charles Coulston, Editor in Chief. Dictionary of Scientific Biography, Volume IV. New York: Charles Scribner’s Sons, 1971. Safra, Jacob E., Chairman of the Board. The New Encyclopaedia Britannica, 15th Edition, Volume 2. Chicago: Encyclopaedia Britannica, Inc., 2005. http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Bernoulli_Johann.htmlhttp://www-groups.dcs.st-and.ac.uk/~history/Printonly/Bernoulli_Johann.html Mac Tutor History of Mathematics/Biographies/Johann Bernoulli. Article by J.J. O’Connor and E.F. Robertson, September 1998. Accessed March 16, 2008. http://www-history.mcs.st-andrews.ac.uk/HistTopics/Brachistochrone.htmlhttp://www-history.mcs.st-andrews.ac.uk/HistTopics/Brachistochrone.html MacTutor History of Mathematics/History Topics/Brachistochrone. Article by J.J. O’Connor and E.F. Robertson, February 2002. Accessed March 16, 2008. Woolf, Henry Bosley, Editor in Chief. Webster’s New Collegiate Dictionary. Springfield, Massachusetts: G.&C. Merriam Co., 1979. Durant, Will and Ariel. The Age of Louis XIV, The Story of Civilization, Volume VIII. New York: Simon and Schuster, 1963. Struik, D.J., editor. A Source Book In Mathematics, 1200-1800. Cambridge, Massachusetts: Harvard University Press, 1969.

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