leonhard euler


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The Euler Archive: : 

The Euler Archive: Illuminating the Life and Times of Leonhard Euler http://www.EulerArchive.org Lee Stemkoski Adelphi University April 16, 2007

Leonhard Euler : 

Leonhard Euler A Leading Scholar of the 18th Century (1707 – 1783) Quantity of work (850+) Breadth of topics Depth of investigation Presentation style

Outline of Topics : 

Outline of Topics A history of publishing Euler’s works The Euler Archive: history, layout Life in Basel, St. Petersburg, Berlin Some of Euler’s major contributions Euler’s continuing influence

Publishing Euler’s works : 

Publishing Euler’s works 1830: St. Petersburg Academy “finishes” backlog of Euler’s works 1843: P.H. Fuss creates index Fuss-Jacobi correspondence 1849: Commentationes Arithmeticae 1883: F. Rudio delivers biographical talk 1896: Hagen creates updated index

The Euler Commission : 

The Euler Commission April, 1908: International Mathematical Congress discusses publication Previously discussed in 1907: - International Association of Academies - Swiss Society of Natural Sciences August, 1908: Euler Commission created 1910: Eneström creates updated index 1911: Opera Omnia publication begins

Worldwide Support : 

Worldwide Support Subscriptions Academies of Paris, Berlin, and St. Petersburg each order 40 sets Donations German Association of Mathematicians American Mathematical Society

Euler’s Opera Omnia : 

Euler’s Opera Omnia Series I: Mathematics (29/29) Series II: Mechanics, Astronomy (29/31) Series III: Physics, Miscellaneous (12/12) Series IVA: Correspondence (4/10) Series IVB: Manuscripts and Notebooks

The Euler Archive: History : 

The Euler Archive: History 2001: The Euler Society Dr. Edward Sandifer, talk at Dartmouth Two graduate students: Klyve, Stemkoski 2002: Conference presentation 2003: Euler Archive, version 1.0 Primarily a response to inaccessibility of Euler’s works (cost and location) Marianne Gerber, Deputy Consul, SHARE

The Euler Archive: Layout : 

The Euler Archive: Layout One webpage for each of Euler’s works Organization: Subject, Date, Journal Context: History, Biography, Academies, Contemporaries, Miscellaneous Features: Translations, Letters, Resources

The Life and Times ofLeonhard Euler : 

The Life and Times ofLeonhard Euler Primary Sources: Autobiography Eulogy by Nicolaus Fuss Eulogy by Marquis de Condorcet Correspondence

The Basel Period : 

The Basel Period Born: April 15, 1707 - Basel, Switzerland Parents, Religion, and Mathematics 1720: enters University of Basel 1722: prima laurea (~ Bachelor of Arts) 1723: magister (~ Master of Arts) Johann Bernoulli: no lessons, only questions Friends: Daniel and Nicolaus Bernoulli, Johann Kaspar Wettstein

Search for Employment : 

Search for Employment 1725: young Bernoulli brothers leave for the new St. Petersburg Academy; Euler offered professorship of medicine 1726: applies for professor of physics at University of Basel 1727: leaves for St. Petersburg Paris Prize Competition – essay on masting of ships wins honorable mention

The St. Petersburg years : 

The St. Petersburg years Death of Empress Catherine I Christian Goldbach and Number Theory 1733: Succeeds Daniel Bernoulli as professor of mathematics Jan. 1734: marries Katherina Gsell Nov. 1734: birth of Johann Albrecht

The St. Petersburg years:early mathematics : 

The St. Petersburg years:early mathematics 1732: Fermat numbers [E-26] 3, 5, 17, 257, 65537, 4294967297 1734: Mixed partial derivatives [E-44] 1734: Functional notation f(x) [E-45]

The Basel Problem : 

The Basel Problem In 1735: [E-41] The sum of the series 1/1 + 1/4 + 1/9 + 1/16 + 1/25 + … is exactly equal to π2 / 6.

Bridges of Königsberg : 

Bridges of Königsberg In 1735: [E-53] Can you arrange a route that crosses every bridge exactly once?

Academy Duties : 

Academy Duties Examination board member of academic gymnasium Weights and measures commission Development of hydraulic machines

Cartography : 

Cartography 1735: Euler and Delisle direct the academy’s Department of Geography 1753: Preface to Geographic Atlas 1775: on the mathematics of projections

Paris Prize Competition : 

Paris Prize Competition Euler: 18 total entries (12 wins) Sample topics: 1727: masting of ships 1738: properties of fire 1740: tides 1747: determining time from observations 1748: magnets 1748: movement of Jupiter and Saturn 1753: movement of ships without wind

Major Works during firstSt. Petersburg period : 

Major Works during firstSt. Petersburg period 1736: Mechanics [E-15][E-16] 1739: Music Theory [E-33] 1738/1740: Arithmetic [E-17][E-35]

Move to Berlin (1741) : 

Move to Berlin (1741) Political tensions in St. Petersburg Growing Family: Johann Albrecht, Karl, Katharina, Christoph, Charlotte, … Correspondence continues Russian Lodgers/Students: Razumovsky, Kotelnikov, Rumovsky

Major Works in Berlin : 

Major Works in Berlin 1744: Calculus of Variations 1745: New Principles of Gunnery 1748: Introduction to the Analysis of the Infinite 1749: Theory of Ships 1753: Theory of Lunar Motion 1755: Differential Calculus 1762: Construction of Achromatic Lenses 1765: Theory of the Motion of Solid Bodies

Introductio : 

Introductio 1748 [E-101] Variables and functions Polynomials and algebraic functions Exponents and logarithms Trigonometry Series

Polyhedral Formula : 

Polyhedral Formula 1750-1751 [E-230] V = # vertices (corners) E = # edges F = # faces Then: V – E + F = 2

Euler-Fermat Theorem : 

Euler-Fermat Theorem 1760 [E-271] Choose integer a and prime number p ap – 1 (mod p) = 1 Replace p by arbitrary number n aφ(n) (mod n) = 1 Basis of many encryption algorithms

End of Berlin period : 

End of Berlin period Fredrick the Great Maupertuis Return to St. Petersburg (1766)

Major Works from Euler’ssecond St. Petersburg period : 

Major Works from Euler’ssecond St. Petersburg period 1768: Letters to a German Princess 1768: Integral Calculus 1769: Optics 1770: Algebra 1772: Theory of Lunar Motion 1773: Complete Theory on the Construction and Maneuvering of Ships

Letters to a German Princess : 

Letters to a German Princess First published in 1768 (234 letters) General science: gravity, cosmos, tides Philosophy: the spirit, religion, morality, foundations of knowledge Physics: electricity, magnetism, telescopes, microscopes Over 40 editions by 1840

Euler’s final day : 

Euler’s final day Assistants Fuss and Lexell present Discussions about height of hot-air balloons orbit of planet Uranus Suffered a stroke in the early evening

Euler’s continuing influence : 

Euler’s continuing influence Disciples / Students J.A. Euler, Fuss, Lexell, Rumovsky, … Style of presentation Legacy of publications

Conclusion : 

Conclusion From the Eulogy written by Fuss: “What is there left … except our tender and eternal gratitude … [Euler] was worthy of admiration as much for his rare virtues as for the astonishing force of his genius.”