At eighteen, Poisson caught Legendre’s attention with a paper on finite differences (he later gave Legendre’s funeral oration, saying he had only wanted to be spoken about in terms of his work). Poisson was a student, and later close friend, of both Laplace and Lagrange, and a member of the influential Société d’Arcueil that Laplace and Berthollet founded. Galois, barely twenty, sent Poisson a paper on equation theory, which Poisson thought unclear. Arago, another société d’Arcueil member, wrote Poisson’s biography, reporting his words that he was good for only two things — doing mathematics, and teaching it.

# Profession: mathematician

## Samuel König

König met his fellow-student Clairaut, as well as Maupertuis, through his studies with Johann Bernoulli (Daniel Bernoulli also taught him, as did Wolff); Clairaut became a correspondent and noted collaborator of König’s. Maupertuis introduced Voltaire and Châtelet to him, then had a famous mathematical quarrel with him, Euler putting the case against König, and Voltaire defending him in print. He travelled with his friends Voltaire and Châtelet to meet Réaumur, though Châtelet (to whom he taught algebra) later had a serious disagreement with him. Réaumur, also a friend, passed König a problem concerning the geometry of honeycombs.

## Samuel König knew…

## Pierre-Simon Laplace

A letter to d’Alembert on mathematical principles got Laplace a professorship at the École Militaire. He taught Fourier (who however thought Lagrange and Monge better teachers), and encouraged Cauchy. Lagrange was a professional rival, but both gained from the mutual flow of ideas. Laplace and Berthollet founded the influential Société d’Arcueil, whose members included Arago, Poisson, Biot, Gay-Lussac, Malus and Humboldt. With Lavoisier, he showed that respiration was a form of combustion. Biot helped prepare his work for publication, but said that Laplace often forgot his original reasoning, substituting the line “it is easy to see.”

## Pierre-Simon Laplace knew…

- Roger Joseph Boscovich
- Bernard Germain de Lacépède
- George Airy
- John Herschel
- Mary Somerville
- Marie-Anne Paulze
- Antoine Lavoisier
- Franz Xaver von Zach
- Alexander von Humboldt
- Jean-Antoine Chaptal
- Gustav Lejeune Dirichlet
- Jean-Baptiste Delambre
- Joseph Louis Gay-Lussac
- David Brewster
- Adolphe Quetelet
- John Dalton
- Alessandro Volta
- André-Marie Ampère
- Benjamin Thompson, Count Rumford
- Adrien-Marie Legendre
- René Just Haüy
- Robert Owen
- Jöns Jakob Berzelius
- Étienne-Louis Malus
- Siméon-Denis Poisson
- Marquis de Condorcet
- Joseph Louis Lagrange
- Joseph Fourier
- Jean-Baptiste Biot
- Jean le Rond d'Alembert
- Claude-Louis Berthollet
- François Arago
- Augustin Louis Cauchy

## Pierre-Louis Maupertuis

Maupertuis was taught by Bernoulli, who encouraged his development of Newton’s theories; König was a fellow-student, though a famous and bitter mathematical quarrel marked their last years. Marivaux was a friend as a young man in Paris. Maupertuis was Châtelet’s geometry tutor and lover, and also taught Buffon. Clairaut accompanied him on a year-long expedition to Lapland (they met Celsius en route), though the friendship eventually deteriorated. His great friend Euler wrote to him for two decades, and deputised for him in Berlin. Voltaire had been a good friend, but mocked his ideas and his relations with Lapp women.

## Marquis de Condorcet

D’Alembert praised the 16-year-old’s gifts, taught him and became a close friend. The youngest of Diderot’s Encyclopaedists, he was a regular at d’Holbach’s salon, and wrote a biography of another good friend, Voltaire. He encouraged Monge to submit his research to the Académie des Sciences, and Legendre to write what became a classic geometry textbook. He was one of the first mathematicians Lagrange met when he came to Paris, and helped liberalise Franklin’s views on slavery and racial equality. He posthumously edited out pious references to God in his correspondent Euler’s published letters.

## Marquis de Condorcet knew…

- Philippe Pinel
- Roger Joseph Boscovich
- Jérôme Lalande
- Antoine Lavoisier
- Horace-Bénédict de Saussure
- Félix Vicq d'Azyr
- Charles Bossut
- Thomas Paine
- Richard Price
- Thomas Jefferson
- Adrien-Marie Legendre
- Anne Robert Jacques Turgot
- Pierre-Simon Laplace
- Voltaire
- Leonhard Euler
- Joseph Louis Lagrange
- Jean le Rond d'Alembert
- Gaspard Monge
- Denis Diderot
- Baron d'Holbach
- Benjamin Franklin
- Alexis Clairaut

## Leonhard Euler

Johann Bernoulli taught Euler unofficially; his friend and fellow-student Daniel Bernoulli helped persuade Euler’s father that his great gift was for mathematics, collaborated with him, and invited him to settle in St. Petersburg, where Goldbach was among his colleagues. Condorcet and Euler had an extensive working correspondence: other correspondents included Lomosonov, Clairaut, d’Alembert, Legendre, and the unreliable Stirling. Euler deputised for Maupertuis in Berlin. When Lagrange wrote to him with a new kind of calculus, he withheld his own work to let the 19-year-old get the credit. Lexell helped him when he was virtually blind.

## Leonhard Euler knew…

- Johann Bernoulli
- Roger Joseph Boscovich
- Johann Georg Sulzer
- Caspar Friedrich Wolff
- Tobias Mayer
- Jérôme Lalande
- Daniel Bernoulli
- Christian Goldbach
- Mikhail Lomonosov
- Gerhard Friedrich Müller
- Anders Johan Lexell
- Nicolas Louis de Lacaille
- Johann Heinrich Lambert
- Samuel König
- Pierre-Louis Maupertuis
- Marquis de Condorcet
- Voltaire
- Albrecht von Haller
- Adrien-Marie Legendre
- Joseph Louis Lagrange
- Jean le Rond d'Alembert
- Alexis Clairaut
- James Stirling, mathematician

## Joseph Louis Lagrange

At 19, Lagrange wrote to Euler, proposing a new form of calculus. Poisson and he spurred each other on to refine planetary mathematics. D’Alembert supported him, Laplace was a mathematical correspondent and rival, and Lavoisier intervened to ensure that Lagrange, Italian-born, would not meet hostility in post-revolutionary Paris (Lavoisier was himself beheaded a few months later). Lagrange taught Fourier and encouraged Cauchy in his studies. A paper Germain sent led her to become (as a woman and outsider) his protégée. Lambert was a close friend, and Monge visited him when he was dying.

## Joseph Louis Lagrange knew…

- Giovanni Battista Beccaria
- Roger Joseph Boscovich
- Daniel Bernoulli
- Marie-Anne Paulze
- Antoine Lavoisier
- Johann Heinrich Lambert
- Sophie Germain
- Alessandro Volta
- Benjamin Thompson, Count Rumford
- René Just Haüy
- Étienne-Louis Malus
- Siméon-Denis Poisson
- Pierre-Simon Laplace
- Marquis de Condorcet
- Leonhard Euler
- Joseph Fourier
- Jean le Rond d'Alembert
- Gaspard Monge
- Augustin Louis Cauchy

## Joseph Fourier

Lagrange, Laplace and Monge all taught him, and may have helped his release from imprisonment on political charges. He submitted a paper on algebra to Montucla while still undecided on his career. Berthollet, Monge and Malus were fellow members of the Institut d’Egypte, with Fourier elected secretary. He taught Malus at the Ecole Polytechnique, then run by Carnot and Monge, and stimulated his protégé Champollion’s determination to decode Egyptian hieroglyphs. Delambre arranged for publication of his work on heat-conduction, and Cuvier was his fellow ‘Perpetual Secretary’ of the Académie des Sciences.

## Joseph Fourier knew…

## John Couch Adams

Unknown to Adams, Le Verrier had reached the same mathematical conclusions as him about the existence of a new planet (Neptune). Adams had already left a paper with Airy, the Astronomer Royal, asking for observations to be made to test for the predicted planet’s existence, but Airy fatally delayed his response, and when a row erupted over the truth of the discovery of Neptune, cold-shouldered Adams. Le Verrier became a good friend to Adams, despite getting all of the credit. Stokes was a professional collaborator and frequent correspondent; Babbage also corresponded with him.

## John Couch Adams knew…

## Jean-Baptiste Biot

Arago and he worked together early in their careers, Arago coming to feel that Biot had sabotaged his results (he then revenged himself by working with Biot’s protégé Fresnel on the polarisation of light). Assisting Laplace in preparing his findings for publication, Biot observed that Laplace used the stock phrase “it is easy to see” when he’d forgotten his original reasoning. Biot and Gay-Lussac were the first to ascend in a balloon for scientific purposes. He did pioneering electro-magnetic work with Savart, and asked the young Pasteur to come and demonstrate his findings about the handedness of some molecules.

## Jean-Baptiste Biot knew…

- Maria Edgeworth
- William Henry Fox Talbot
- John Herschel
- Mary Somerville
- Michel Eugène Chevreul
- Marie-Anne Paulze
- William Thomson, Lord Kelvin
- Henri-Victor Regnault
- Gustav Lejeune Dirichlet
- Joseph Louis Gay-Lussac
- David Brewster
- John Dalton
- René Just Haüy
- Joseph Banks
- Charles Babbage
- Georges Cuvier
- Jöns Jakob Berzelius
- Hans Christian Ørsted
- Étienne-Louis Malus
- Pierre-Simon Laplace
- Louis Pasteur
- Joseph Henry
- Joseph Fourier
- Christian Friedrich Schönbein
- Augustin-Jean Fresnel
- François Arago
- Augustin Louis Cauchy
- Félix Savart
- John Tyndall
- Louis Jacques Thénard
- Marc-Auguste Pictet