Johann Bernoulli
Johann Bernoulli | |
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Brachistochrone problem | |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Groningen University of Basel |
| Thesis | Dissertatio de effervescentia et fermentatione; Dissertatio Inauguralis Physico-Anatomica de Motu Musculorum (On the Mechanics of Effervescence and Fermentation and on the Mechanics of the Movement of the Muscles) (1694 (1690)[2]) |
| Doctoral advisor | Nikolaus Eglinger[1] |
| Other academic advisors | Jacob Bernoulli |
| Doctoral students | Daniel Bernoulli Leonhard Euler Johann Samuel König Pierre Louis Maupertuis |
| Other notable students | Guillaume de l'Hôpital |
| Signature | |
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| Notes | |
Brother of Jacob Bernoulli; the father of Daniel Bernoulli, Nicolaus II Bernoulli, and Johann II Bernoulli; and the uncle of Nicolaus I Bernoulli. | |
Johann Bernoulli
Biography
Early life
Johann was born in
Adult life
After graduating from Basel University, Johann Bernoulli moved to teach
In 1724, Johann Bernoulli entered a competition sponsored by the French
- What are the laws according to which a perfectly hard body, put into motion, moves another body of the same nature either at rest or in motion, and which it encounters either in a vacuum or in a plenum?
In defending a view previously espoused by Leibniz, he found himself postulating an infinite external force required to make the body elastic by overcoming the infinite internal force making the body hard. In consequence, he was disqualified for the prize, which was won by Maclaurin. However, Bernoulli's paper was subsequently accepted in 1726 when the Académie considered papers regarding elastic bodies, for which the prize was awarded to Pierre Mazière. Bernoulli received an honourable mention in both competitions.
Disputes and controversy
Although Johann and his brother Jacob Bernoulli worked together before Johann graduated from Basel University, shortly after this, the two developed a jealous and competitive relationship. Johann was jealous of Jacob's position and the two often attempted to outdo each other. After Jacob's death, Johann's jealousy shifted toward his own talented son,
The Bernoulli brothers often worked on the same problems, but not without friction. Their most bitter dispute concerned the brachistochrone curve problem, or the equation for the path followed by a particle from one point to another in the shortest amount of time, if the particle is acted upon by gravity alone. Johann presented the problem in 1696, offering a reward for its solution. Entering the challenge, Johann proposed the cycloid, the path of a point on a moving wheel, also pointing out the relation this curve bears to the path taken by a ray of light passing through layers of varied density. Jacob proposed the same solution, but Johann's derivation of the solution was incorrect, and he presented his brother Jacob's derivation as his own.[13]
Bernoulli was hired by Guillaume de l'Hôpital for tutoring in mathematics. Bernoulli and l'Hôpital signed a contract which gave l'Hôpital the right to use Bernoulli's discoveries as he pleased. L'Hôpital authored the first textbook on infinitesimal calculus, Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes in 1696, which mainly consisted of the work of Bernoulli, including what is now known as l'Hôpital's rule.[14][15][16] Subsequently, in letters to Leibniz, Varignon and others, Bernoulli complained that he had not received enough credit for his contributions, in spite of the preface of his book:
I recognize I owe much to the insights of the Messrs. Bernoulli, especially to those of the younger (John), currently a professor in Groningen. I did unceremoniously use their discoveries, as well as those of Mr. Leibniz. For this reason I consent that they claim as much credit as they please, and will content myself with what they will agree to leave me.
Works
- De motu musculorum (in Latin). Venezia: Giovanni Antonio Pinelli & Almoro Pinelli. 1721.
- Recherches physiques et géométriques sur la question comment se fait la propagation de la lumière (in French). Paris: Imprimerie Royale. 1736.
- [Opere] (in French). Vol. 1. Lausanne: Marc Michel Bousquet & C. 1742.
- Bernoulli, Johann (1786). Analyse de l'Opus Palatinum de Rheticus et du Thesaurus mathematicus de Pitiscus (in French). Parigi: sn. Retrieved 18 June 2015.
- Bernoulli, Johann (1739). Dissertatio de ancoris (in Latin). Leipzig: sn. Retrieved 20 June 2018.
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Volumes I-IV of Bernoulli's 1742 Opera Omnia -
Portrait of Bernoulli in volume I of his 1742 Opera omnia -
The front page of volume I of Opera omnia
See also
- Sophomore's dream – a pair of analytical identities by Bernoulli
- Partial fraction decomposition
Notes
- ^ English: /bɜːrˈnuːli/ bur-NOO-lee,[3] Swiss Standard German: [ˈjoːhan bɛrˈnʊli].[4]
References
- . Retrieved 14 August 2018.
- ^ Published in 1690, submitted in 1694.
- ISBN 978-1-4058-8118-0.
- ^ Mangold, Max (1990). Duden — Das Aussprachewörterbuch. 3. Auflage. Mannheim/Wien/Zürich, Dudenverlag.
- OCLC 607532308.
- ^ The Bernoulli Family, by H. Bernhard, Doubleday, Page & Company, (1938)
- ^ OCLC 185537598. Retrieved 16 July 2021.
- PMID 33943138. (here cited p. 133).
- OCLC 433236093. Retrieved 16 July 2021.
- OCLC 4062356.
- ISBN 9780198568438.
- ISBN 9783764385644.
- ISBN 0-7679-0816-3.
- OCLC 29310868.
- OCLC 20418646.
- ISBN 978-0-674-82355-6.
External links
Media related to Johann Bernoulli at Wikimedia Commons- Johann Bernoulli at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Johann Bernoulli", MacTutor History of Mathematics Archive, University of St Andrews
- Golba, Paul, "Bernoulli, Johan'"
- "Johann Bernoulli"
- ScienceWorld.
- Truesdell, C. (March 1958). "The New Bernoulli Edition". Isis. 49 (1): 54–62. S2CID 143648596. discusses the strange agreement between Bernoulli and de l'Hôpital on pages 59–62.
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