**Alexis Clairaut** was a French mathematician who worked to confirm the Newton-Huygens belief that the Earth was flattened at the poles.

- Alexis used Euclid's Elements while learning to read and by the age of nine he had mastered the excellent mathematics textbook of Guisnée Application de l'algèbre à la géométrie Ⓣ(Application of algebra to geometry) which provided a good introduction to the differential and integral calculus as well as analytical geometry.
- In the following year, Clairaut went on to study de L'Hôpital's books, in particular his famous text Analyse des infiniment petits pour l'intelligence des lignes courbes Ⓣ(Infinitesimal analysis for the understanding of curves).
- Few people have read their first paper to an academy at the age of 13, but this was the incredible achievement of Clairaut's in 1726 when he read his paper Quatre problèmes sur de nouvelles courbes Ⓣ(Four problems on new curves) to the Paris Academy.
- Clairaut began to undertake research on double curvature curves which he completed in 1729.
- In July 1731 Clairaut became the youngest person ever elected to the Paris Academy of Sciences.
- Maupertuis was 15 years older than Clairaut but despite this, at the age of 33, he was also a young member of the Academy.
- Clairaut became close friends of Maupertuis, Voltaire, and du Châtelet.
- Many of Clairaut's own theories were added to the book, in addition to the translation of Newton by du Châtelet.
- Together with Maupertuis, Clairaut visited Basel in 1734 to spend a few months studying with Johann Bernoulli.
- While in Basel, Clairaut became friends with Samuel König and, for many years, the two continued a useful scientific collaboration by correspondence.
- Clairaut published some important work during the period 1733 to 1743.
- The following year Clairaut studied the differential equations now known as 'Clairaut's differential equations' and gave a singular solution in addition to the general integral of the equations.
- In 1742 Clairaut published an important work on dynamics but, in the following year, he turned his attention to the topic for which he is best known.
- From 20 April 1736 to 20 August 1737 Clairaut had taken part in an expedition to Lapland, led by Maupertuis, to measure a degree of longitude.
- In addition to Maupertuis and Clairaut, the group contained other young scientists such as Lemonnier, Camus and Celsius.
- In 1743 Clairaut published Théorie de la figure de la Terre Ⓣ(Theory of the shape of the Earth) confirming the Newton-Huygens belief that the Earth was flattened at the poles.
- After his work on Théorie de la figure de la Terre Ⓣ(Theory of the shape of the Earth) Clairaut began to work on the three-body problem in 1745, in particular on the problem of the moon's orbit.
- Clairaut, more confident with Euler's support, announced to the Paris Academy on 15 November 1747 that the inverse square law was false.
- Rather remarkably, just before Clairaut made his announcement, d'Alembert deposited a paper with the Academy which showed that his calculations agreed with those of Clairaut.
- However, by the spring of 1748, Clairaut realised that the difference between the observed motion of the moon's apogee and the one predicted by the theory was due to errors coming from the approximations that were being made rather than from the inverse square law of gravitational attraction.
- Clairaut announced to the Academy on 17 May 1749 that his theory was now in agreement with the inverse square law.
- Euler still felt he did not properly understand what Clairaut had done so he tried to tempt him to write it up properly by having the St Petersburg Academy set the problem of the moon's apogee as the prize topic for 1752.
- Indeed his ploy worked and Clairaut submitted an essay which let Euler fully understand Clairaut's method.
- Clairaut published Théorie de la lune Ⓣ(Theory of the moon) in 1752 and this work, together with his lunar tables published two years later, completed his work on this particular problem.
- Clairaut decided to apply his knowledge of the three-body problem to compute the orbit of Halley's comet and so predict the exact date of its return.
- When the comet appeared, only one month before the predicted date, Clairaut was given great public acclaim.
- There was a suggestion that the comet be renamed after Clairaut, and Clairaut was called the 'new Thales'.
- Clairaut improved his results when he used a different method in his prize winning paper submitted to the St Petersburg Academy for the 1762 prize.
- A dispute arose between Clairaut and d'Alembert regarding this work on comets.
- When d'Alembert attacked Clairaut's solution of the three-body problem as being too much based on observation and not, like his own work, based on theoretical results, Clairaut strongly attacked d'Alembert in the most bitter dispute of their lives.
- It is hard to judge which of the two great mathematicians was right, but Clairaut clearly won the public argument at the time, not least because his standing was so high after the remarkable prediction of the date of the return of Halley's comet.
- We should also mention another topic to which Clairaut made important contributions, namely to the aberration of light.
- Clairaut wrote some important memoirs on the topic, studying the theory as well as conducting optical experiments.
- Clairaut worked on a wide range of problems within mathematics.
- Clairaut died at the age of 52 after a brief illness.

Born 7 May 1713, Paris, France. Died 17 May 1765, Paris, France.

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Astronomy, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive