Leonhard Euler: Mathematical Genius in the Enlightenment
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Leonhard Euler: Mathematical Genius in the Enlightenment
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Overview
An acclaimed biography of the Enlightenment's greatest mathematician
This is the first full-scale biography of Leonhard Euler (1707–83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler’s massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler’s work in its multilayered context—personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler’s fundamental contributions to almost every area of pure and applied mathematics—especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics—to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory.
The narrative takes the reader from Euler’s childhood and education in Basel through his first period in St. Petersburg, 1727–41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton’s dynamics, and published the best-selling Letters to a German Princess—all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment.
Product Details
| ISBN-13: | 9781400866632 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 11/24/2015 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 696 |
| File size: | 33 MB |
| Note: | This product may take a few minutes to download. |
About the Author
Read an Excerpt
Leonhard Euler
Mathematical Genius in the Enlightenment
By Ronald S. Calinger
PRINCETON UNIVERSITY PRESS
Copyright © 2016 Princeton University PressAll rights reserved.
ISBN: 978-1-4008-6663-2
CHAPTER 1
The Swiss Years: 1707 to April 1727
Leonhard Euler was born on 15 April 1707 in Basel, the third largest city in the Swiss Confederation. He was the first child of Basler Evangelical-Reformed minister Paul III Euler and his wife Margaretha (née Brucker). On 17 April, the Sunday before Easter, Leonhard was baptized in Saint Martin's Church as his father had been. The church's baptismal registry for the years 1663–1762 lists for the child three godparents, who were not relatives but city officials. He was named Leonhard after one of these godparents, city privy councilor Leonhard Respinger, a close friend of the family. Exactly where in Basel Leonhard Euler was born is not known. Usually women gave birth at home, assisted by a midwife; pediatricians, gynecologists, and most pharmaceutical medicines were as yet unavailable. Many babies born in winter suffered from respiratory illnesses, and children born in summer from gastric problems, but the infant Euler was spared both. Whether his birth occurred at his parents' home or possibly that of his maternal grandparents, the residence was likely located in Saint Martin's Quarter, the picturesque center of Basel. Since this part of the city was extensively renovated later, it is doubtful that the house remains standing.
"Das alte ehrwürdige Basel" (Worthy Old Basel)
In 1727, the year Euler left, Basel was a damp and misty city at the farthest point of navigation on the Rhine; it was the wealthiest in the German-speaking Swiss areas and known for its learning and piety. The city was the capital of the Canton of Basel, one of the thirteen cantons that constituted the Swiss Confederation, having joined in 1501 mainly for reasons of self-defense. It had separated from the Holy Roman Empire, in which it had held the status of Reichsstadt (free imperial city). In Reformation Europe urban population growth usually depended upon immigration. Except during a few periods of large losses from plagues, Basel had a restrictive policy on immigration and citizenship; as a result its population had decreased from about twenty thousand in 1500 to seventeen thousand in the early 1700s. Max Weber's thesis that Protestant religions rose in parallel with capitalism and the modern sciences could look to Basel for reinforcement. Following its rejection of the Catholic faith in the 1520s, the city became a great center of northern humanism, publication, and the book trade, principally through the efforts of its intellectually inquisitive silversmiths, ribbon and fine paper makers, printers, and engravers. The printing presses developed there produced major works in the new sciences, publishing in 1566 the second edition of Nicolaus Copernicus's De revolutionibus orbium coelestium (On the revolutions of the heavenly spheres).
The year 1522 saw the beginning of the period known as the Herrschaft, when the city council came under the oversight of the two most powerful groups in the city, the artisans in the eighteen Zünfte (roughly, trade guilds organized by the merchants and manufacturers) and the Gnädige Herren ("gracious lords," consisting of the old nobility and the church establishment). Income distribution was quite uneven. The political leaders of the city, the Ratsherren, or senators, were the members of the council. The trade guilds opposed the liberum commercium, or freedom of trade across boundaries, which the Herren promoted. With city warehouses to hold finished goods — particularly silk ribbons, passementerie (trimmings), and, to a lesser degree, fine printed cottons — the merchants made Basel a hub of what was termed the putting-out system of manufacturing. Taking advantage of cheap labor in the countryside and acting essentially as middlemen, they provided rural weavers raw materials and the most advanced looms available. The weavers completed the textiles and took them to the new merchant warehouses in Basel, where the merchants bought the finished textiles at meager piecework prices. They were thus able to avoid the restrictions of the city's guilds, and this greatly increased productivity and lowered costs. At the time, silk ribbons were a far more important item in the garment industry than they are today; the fortunes of the Bändelherren, or ribbon lords, became the foundation for a private banking system in the region. As a result, Basel had transformed itself from a medieval guild city into a commercial, manufacturing, and banking center.
While its sister city of Zurich had Ulrich Zwingli as its hero and Geneva had John Calvin, early sixteenth-century Basel had the Christian humanists Oecolampadius (Johannes Heussgen) and Desiderius Erasmus. At the time scholars customarily took as pseudonyms classical versions of their original appellations or names based on admired concepts; thus Oecolampadius, of Greek origin, which means "house shine." Oecolampadius had studied at Tübingen, Stuttgart, and Heidelberg, absorbing the theories of Johannes Reuchlin, Philipp Melanchthon, and Wolfgang Capito. In 1522 he moved to Basel as vicar of Saint Martin's Church and, as a talented philologist of Greek, Hebrew, and Latin, was a proofreader for a translation of patristic literature. The next year he also became a reader of scripture at the university. Oecolampadius was among the first advocates in Europe for the movement away from Latin to the vernacular in churches and academia. In church services he preached in German, while another university faculty member in Basel, the cantankerous Paracelsus, 5 defied academic tradition by lecturing in German.
The most abrasive of the reformers transforming natural philosophy, Paracelsus also sought to overturn Aristotelian philosophy and replace it with Christian Neoplatonism and with Hermetic mysticism. Using these he worked to uncover truths in the two so-called divine books: the Bible and, metaphorically, the book of nature. For this enterprise he employed what was known as magia naturalis (natural magic) and cosmic sympathy, the latter being the influence of the stars on human life and also known as macrocosm-microcosm interpretation. In chemical science, Paracelsus proposed that his three principles — ideal forms of salt, sulfur, and mercury — were not matter but fundamental states of it, and he accepted quantification, though he adopted sidereal mathematics to indicate when to give medicines.
Paracelsus objected to mathematical abstraction as a way of understanding chemical science and based his research consistently on observation and experiment. His thought was a mixture of the mystical and the evolving modern scientific during this time when the meaning of science was shifting. He attacked the dominant Galenic and Arabic herbal medicine traditions retained from antiquity and the Middle Ages and argued for the superiority of medical chemistry, especially the use of mercury.
In the early 1500s the printer and publisher Johannes Froben asked Oecolampadius to assist Erasmus in translating the New Testament. From 1522 on, Oecolampadius — who, like Froben, protested ecclesiastical abuses in the Catholic Church — demanded in Basel a complete reformation, a total Protestant break with the church. A series of riots ensued, with mobs seeking to remove images from churches. Fearing that change of any sort might escalate to revolution in concert with the peasant revolt that was sweeping the central and southern German states and the Alpine region of imperial Austria in 1524 and 1525, the city council hesitated to act. But in 1529 it forced out the Catholic bishop and instituted a new Protestant church order.
From the time of the Reformation, Basel offered a place of refuge for well-to-do religious dissidents from northern Italian city-states, France, Alsace, Holland, the Spanish Netherlands, and neighboring Germanspeaking lands. The government in Basel did not accept the poor and the indigent; only immigrants having the kunstreiche und wohlhabende (skills and capital) to expand commerce and craft in their adopted home were welcomed as citizens, albeit for a substantial fee. Most of the new Basler Herren were widely traveled, spoke several languages, and were shrewd businessmen. Basler merchants bought, sold, and speculated in every major European market; they had contacts that by the early eighteenth century reached to Amsterdam, Bordeaux, Le Havre, London, Paris, Saint Petersburg, and Vienna. This network provided critical information about commercial conditions and opportunities.
During the seventeenth century the Euler family members were Baslers, citizens of the city-republic of Basel, the regio basiliensis (as Latinists termed it). The regions of the Swiss Confederation were highly independent; no federal Swiss state existed before the nineteenth century, and loyalties were to cities and cantons. Its geographic, economic, linguistic, and cultural connections made cosmopolitan Basel more a European city than a Swiss one.
Lineage and Early Childhood
Over time the Euler family name has had a variety of spellings, with Öwler and Äweler in the fourteenth and fifteenth centuries and Öwbler, Ewbler, and Ouwler in the sixteenth. Since at least 1287, when the first written record of an earlier form of the name Euler appeared, family members had lived on the far side of what is today known as the northern Swiss Alps, in Lindau on the Bodensee (Lake Constance) in Bavaria. But a continuous residence for them did not begin there until 1458. The family bore a double name, today often written as Euler-Schölpi. The name Euler refers not to an owl but to Äule, meaning a modest wet field or swampy meadow. In German regions, an Äuler (pronounced "oyler") was a land proprietor. This suggests that some of Euler's ancestors were landowners and tillers of the soil. Au, shorthand for Äuler, is part of the name of many small towns, such as Lindau, Dessau, and Nassau. The belief that the family name comes from the word for small pottery from Roman times (olla in Latin) transformed into the middle-high German Aul and then to Aulner and Iller is incorrect. Schölpi, which derives from the words schelb and schief, related to schielen, signifies squint-eyed, cross-eyed, or crooked. (Figuratively it can also refer to a small-time cheat or rascal.) The epithet, which became the second part of the family name and had been spelled in different ways, seems to suggest that the Eulers had a susceptibility to an eye malady.
As a Reichsstadt in the Holy Roman Empire, Lindau had for a long time enjoyed close economic, political, diplomatic, and religious ties with Basel, and the two are two hundred kilometers apart. In 1594 Hans-Georg (or Jörg) Euler, the great-great-grandfather of Leonhard, moved to Basel and became a full citizen at the age of twenty-one. The reasons for his move are unclear, but the death of his mother was possibly a factor. There were also earlier family contacts, among them the Basel shoemaker Martin Frisschmann, who died before 1582. Hans-Georg had trained to become a brush-and combmaker. As the youngest son he had to seek a new profession, because his oldest brother would succeed to his father's position in the guild, and only one place was available. In Basel Hans-Georg pursued the combmaking occupation and became a tradesman belonging to the hospitality or public house guild. He now dropped the second part of the family's double name and was to become the scion of its Basel branch. Hans-Georg married twice, fathering nine children in the first marriage and six in the second. Only four of his eleven sons would continue the family name: Remund II, Hans-Georg II, Paul I, and Johann Jakob. Hans-Georg the elder lived to be ninety. In Lindau most of his ancestors had been small landowners and vintners. Hans-Georg's oldest son, Remund II, broke with him in 1631, when the father would not surrender to him his master's position in the guild. Remund, whose father-in-law was a book dealer, may have been the first Euler in Basel to send his sons to school. Not Paul I but Hans Georg II the Younger was the great-grandfather of Leonhard Euler; Hans's son Paul II was Leonhard's grandfather.
Most male members of the first three Basler generations engaged in brush-and combmaking. None achieved distinction beyond the confines of his community, but each built a modest financial base. In the fourth generation in Basel, two of the fourteen male cousins became comb-makers, but it was now possible for five of the others, including Paul III, to study to be Basler Evangelical-Reformed ministers.
The Basler Evangelical-Reformed Church adhered to a blend of Protestant beliefs, distinct from the Calvinist, Lutheran, and Zwinglian faiths, which in the eighteenth century developed into Pietism. It was thus to be a dissident current in Protestant faiths that often conflicted with state churches. Although he was not a prominent theologian, as other founding reformers were, Oecolampadius excelled in public disputations, and he briefly assisted Zwingli. He was the first to want congregations, not an episcopal hierarchy or clergy, to constitute a secular magistracy representing their church — a position that initially distressed the Basel city council and Martin Luther, but won through the efforts of Calvin in Geneva. Oecolampadius professed the primacy of the Gospel and defended the view held by Zwingli and Luther of the metaphorical nature of the Eucharist. Rather than stress salvation through Christian faith alone, as Luther did, Oecolampadius emphasized the working of the Holy Spirit. Nor did he examine in depth the concept of predestination. He agreed with Zwingli, who was called the Cicero of his age, on esteeming humane learning but in one respect went further, rejecting Zwingli's ban on organ music in church services. Oecolampadius also stressed the education of youth; children had to receive Sunday school teaching from the Wochenkinderlehre (weekly children's instruction) booklet. By the time of Leonhard Euler, religious education would be based on the catechism of the Basler theologian Samuel Werenfels, the Nachtmahlbüchlein (Nighttime pamphlet), which included prayers and referred to those who had come before in Holy Communion and had left a rich legacy.
Paul III Euler, the father of Leonhard, bore the same name as his father. The name Paul II Euler appears in the registers of students matriculating into the University of Basel in 1654, but no record of his studies has survived. Like his forebears, Paul II was a brush-and combmaker. In 1669 he married Anna-Maria Gassner, the daughter of a pastry baker, who had emigrated from Vöcklabruck in Upper Austria near Lake Constance; the next year Paul III was born.
In 1685 Paul III moved away from the artisanal profession of his father, entering the University of Basel for general studies in the philosophical faculty preparatory to a major in Protestant theology. The university had existed since 1460. Two years earlier its founder, a lowly clerk in Basel, had been elected the humanistic Pope Pius II.
During his first semesters Paul III had to study mathematics. In October 1688 he defended, in a debate chaired by Jakob (Jacques) Bernoulli, Bernoulli's thesis "Positiones mathematicae de rationibus et proportionibus" (Mathematical positions on ratios and proportions), which contained fifteen theorems and postulates. The thesis was published in 1688 and again in the posthumous collection edited by Jakob Bernoulli's nephew Nikolaus II in 1744. It begins with algebra, rather than geometry, as basic to mathematics and stresses general methods; both were approaches Paul III was subsequently to convey to his young son. By 1769 the subject of this debate would be a section (or chapter) 3 of Leonhard Euler's Vollständige Anleitung zur Algebra (Complete elements of algebra). In addition to Jakob Bernoulli, Paul likely knew his younger brother, fellow student Johann I Bernoulli.
(Continues...)
Excerpted from Leonhard Euler by Ronald S. Calinger. Copyright © 2016 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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Table of Contents
Preface ixAcknowledgments xv
Author’s Notes xvii
Introduction 1
1. The Swiss Years: 1707 to April 1727 4
“Das alte ehrwürdige Basel” (Worthy Old Basel) 4
Lineage and Early Childhood 8
Formal Education in Basel 14
Initial Publications and the Search for a Position 27
2. “Into the Paradise of Scholars”: April 1727 to 1730 38
Founding Saint Petersburg and the Imperial Academy of Sciences 40
A Fledgling Camp Divided 53
The Entrance of Euler 65
3. Departures, and Euler in Love: 1730 to 1734 82
Courtship and Marriage 87
Groundwork Research and Massive Computations 90
4. Reaching the “Inmost Heart of Mathematics”: 1734 to 1740 113
The Basel Problem and the Mechanica 118
The Königsberg Bridges and More Foundational Work in Mathematics 130
Scientia navalis, Polemics, and the Prix de Paris 140
Pedagogy and Music Theory 150
Daniel Bernoulli and Family 160
5. Life Becomes Rather Dangerous: 1740 to August 1741 165
Another Paris Prize, a Textbook, and Book Sales 165
Health, Interregnum Dangers, and Prussian Negotiations 169
6. A Call to Berlin: August 1741 to 1744 176
“Ex Oriente Lux”: Toward a Frederician Era for the Sciences 176
The Arrival of the Grand Algebraist 185
The New Royal Prussian Academy of Sciences 189
Europe’s Mathematician, Whom Others Wished to Emulate 200
Relations with the Petersburg Academy of Sciences 211
7. “The Happiest Man in the World”: 1744 to 1746 215
Renovation, Prizes, and Leadership 215
Investigating the Fabric of the Universe 224
Contacts with the Petersburg Academy of Sciences 234
Home, Chess, and the King 237
8. The Apogee Years, I: 1746 to 1748 239
The Start of the New Royal Academy 241
The Monadic Dispute, Court Relations, and Accolades 247
Exceeding the Pillars of Hercules in the MathematicalSciences 255
Academic Clashes in Berlin, and Euler’s Correspondence with the Petersburg Academy 279
The Euler Family 282
9. The Apogee Years, II: 1748 to 1750 285
The Introductio and Another Paris Prize 287
Competitions and Disputes 292
Decrial, Tasks, and Printing Scientia navalis 298
A Sensational Retraction and Discord 303
State Projects and the “Vanity of Mathematics” 308
The König Visit and Daily Correspondence 313
Family Affairs 316
10. The Apogee Years, III: 1750 to 1753 318
Competitions in Saint Petersburg, Paris, and Berlin 320
Maupertuis’s Cosmologie and Selected Research 325
Academic Administration 329
Family Life and Philidor 333
Rivalries: Euler, d’Alembert, and Clairaut 335
The Maupertuis-König Affair: The Early Second Phase 337
Two Camps, Problems, and Inventions 344
Botany and Maps 348
The Maupertuis-König Affair: The Late Second and Early Third Phases 350
Planetary Perturbations and Mechanics 359
Music, Rameau, and Basel 360
Strife with Voltaire and the Academy Presidency 363
11. Increasing Precision and Generalization in the Mathematical Sciences: 1753 to 1756 368
The Dispute over the Principle of Least Action: The Third Phase 369
Administration and Research at the Berlin Academy 374
The Charlottenburg Estate 384
Wolff, Segner, and Mayer 385
A New Correspondent and Lessons for Students 391
Institutiones calculi differentialis and Fluid Mechanics 395
A New Telescope, the Longitude Prize, Haller, and Lagrange 399
Anleitung zur Nauturlehre and Electricity and Optimism Prizes 401
12. War and Estrangement, 1756 to July 1766 404
The Antebellum Period 404
Into the Great War and Beyond 409
Losses, Lessons, and Leadership 415
Rigid-Body Disks, Lambert, and Better Optical Instruments 427
The Presidency of the Berlin Academy 430
What Soon Happened, and Denouement 432
13. Return to Saint Petersburg: Academy Reform and Great Productivity, July 1766 to 1773 451
Restoring the Academy: First Efforts 452
The Grand Geometer: A More Splendid Oeuvre 456
A Further Research Corpus: Relentless Ingenuity 471
The Kulibin Bridge, the Great Fire, and One Fewer Distraction 485
Persistent Objectives: To Perfect, to Create, and to Order 488
14. Vigorous Autumnal Years: 1773 to 1782 495
The Euler Circle 496
Elements of Number Theory and Second Ship Theory 497
The Diderot Story and Katharina’s Death 499
The Imperial Academy: Projects and Library 502
The Russian Navy, Turgot’s Request, and a Successor 504
At the Academy: Technical Matters and a New Director 506
A Second Marriage and Rapprochement with Frederick II 509
End of Correspondence and Exit from the Academy 515
Mapmaking and Prime Numbers 517
A Notable Visit and Portrait 518
Magic Squares and Another Honor 520
15. Toward “a More Perfect State of Dreaming”: 1782 to October 1783 526
The Inauguration of Princess Dashkova 526
1783 Articles 529
Final Days 530
Major Eulogies and an Epilogue 532
Notes 537
General Bibliography of Works Consulted 571
Register of Principal Names 625
General Index 657
What People are Saying About This
"A fascinating portrait of Euler, his work and the world around him."—The Economist"Ronald Calinger's impressively detailed biography memorably portrays an extraordinarily able scientist."—Ulinka Rublack, Times Literary Supplement"A pleasure to read. . . . The book should be read by every historian of modern science."—Jeremy Gray, Isis"Will be of great value to anyone with a serious interest in the history of mathematics and the Enlightenment."—Davide Castelvecchi, Nature"Excellent."—Mark Ronan, Standpoint"Calinger successfully embeds Euler's mathematical and physics results in a rich context—cultural, political, religious, and intellectual—while providing great insight into Euler as a person."—Choice