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.”