Pierre Louis Moreau de Maupertuis (; ; 1698 – 27 July 1759) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, philosopher and

man of letters An intellectual is a person who engages in critical thinking, research, and reflection about the nature of reality, especially the nature of society and proposed solutions for its normative problems. Coming from the world of culture, either ...

. He became the director of the

Académie des Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

and the first president of the Prussian Academy of Science, at the invitation of

Frederick the Great Frederick II (; 24 January 171217 August 1786) was the monarch of Prussia from 1740 until his death in 1786. He was the last Hohenzollern monarch titled ''King in Prussia'', declaring himself ''King of Prussia'' after annexing Royal Prussia ...

. Maupertuis made an expedition to Lapland to determine the shape of the

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

. He is often credited with having discovered the

principle of least action Action principles lie at the heart of fundamental physics, from classical mechanics through quantum mechanics, particle physics, and general relativity. Action principles start with an energy function called a Lagrangian describing the physical sy ...

– a version of which is known as

Maupertuis's principle In classical mechanics, Maupertuis's principle (named after Pierre Louis Maupertuis, 1698 – 1759) states that the path followed by a physical system is the one of least length (with a suitable interpretation of ''path'' and ''length''). It is a ...

– which he expressed as an integral equation that describes the path followed by a physical system. His work in

natural history Natural history is a domain of inquiry involving organisms, including animals, fungi, and plants, in their natural environment, leaning more towards observational than experimental methods of study. A person who studies natural history is cal ...

is interesting in relation to modern science since he touched on aspects of

heredity Heredity, also called inheritance or biological inheritance, is the passing on of traits from parents to their offspring; either through asexual reproduction or sexual reproduction, the offspring cells or organisms acquire the genetic infor ...

and the struggle for life.

Biography

Maupertuis was born at

Saint-Malo Saint-Malo (, , ; Gallo language, Gallo: ; ) is a historic French port in Ille-et-Vilaine, Brittany (administrative region), Brittany. The Fortification, walled city on the English Channel coast had a long history of piracy, earning much wealth ...

, France, to a moderately wealthy family of merchant- corsairs. His father, Renė, had been involved in a number of enterprises that were central to the

monarchy A monarchy is a form of government in which a person, the monarch, reigns as head of state for the rest of their life, or until abdication. The extent of the authority of the monarch may vary from restricted and largely symbolic (constitutio ...

so that he thrived socially and politically. The son was educated in mathematics by a private tutor, Nicolas Guisnée, and upon completing his formal education his father secured him a largely honorific

cavalry Historically, cavalry (from the French word ''cavalerie'', itself derived from ''cheval'' meaning "horse") are groups of soldiers or warriors who Horses in warfare, fight mounted on horseback. Until the 20th century, cavalry were the most mob ...

commission. After three years in the cavalry, during which time he became acquainted with fashionable social and mathematical circles, he moved to

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

and began building his reputation as a mathematician and literary wit. In 1723 he was admitted to the

Stamp of Finland - 1986 - Colnect 47128 - P L-Moreau de Maupertius 1698-1759 French scientist

His early mathematical work revolved around the

vis viva ''Vis viva'' (from the Latin for "living force") is a historical term used to describe a quantity similar to kinetic energy in an early formulation of the principle of conservation of energy. Overview Proposed by Gottfried Leibniz over the period ...

controversy, for which Maupertuis developed and extended the work of

Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

(whose theories were not yet widely accepted outside England) and argued against the waning Cartesian mechanics. In the 1730s, the shape of the Earth became a flashpoint in the battle among rival systems of mechanics. Maupertuis, based on his exposition of Newton (with the help of his mentor Johan Bernoulli) predicted that the Earth should be

oblate In Christianity (specifically the Roman Catholic, Orthodox, Lutheran, Anglican and Methodist traditions), an oblate is a person associated with a Benedictine monastery or convent who is specifically dedicated to God and service. Oblates are i ...

, while his rival Jacques Cassini measured it astronomically to be prolate. In 1736 Maupertuis acted as chief of the

French Geodesic Mission The French Geodesic Mission to the Equator (), also called the French Geodesic Mission to Peru and the Spanish-French Geodesic Mission, was an 18th-century expedition to what is now Ecuador carried out for the purpose of performing an arc measu ...

sent by King

Louis XV Louis XV (15 February 1710 – 10 May 1774), known as Louis the Beloved (), was King of France from 1 September 1715 until his death in 1774. He succeeded his great-grandfather Louis XIV at the age of five. Until he reached maturity (then defi ...

to Lapland to measure the length of a degree of arc of the meridian. His results, which he published in a book detailing his procedures, essentially settled the controversy in his favour. The book included an adventure narrative of the expedition, and an account of the Käymäjärvi Inscriptions in Sweden. On his return home he became a member of almost all the scientific societies of Europe. After the Lapland expedition, Maupertuis set about generalising his earlier mathematical work, proposing the

as a metaphysical principle that underlies all the laws of mechanics. He also expanded into the biological realm, anonymously publishing a book that was part popular science, part philosophy, and part erotica: ''Vénus physique''. In that work, Maupertuis proposed a theory of generation (i.e., reproduction) in which organic matter possessed a self-organizing “intelligence” that was analogous to the contemporary chemical concept of affinities, which was widely read and commented upon favourably by

Georges-Louis Leclerc, Comte de Buffon Georges-Louis Leclerc, Comte de Buffon (; 7 September 1707 – 16 April 1788) was a French Natural history, naturalist, mathematician, and cosmology, cosmologist. He held the position of ''intendant'' (director) at the ''Jardin du Roi'', now ca ...

. He later developed his views on living things further in a more formal pseudonymous work that explored

, collecting evidence that confirmed the contributions of both sexes and treated variations as statistical phenomena. In 1740 Maupertuis went to

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

at the invitation of

Frederick II of Prussia Frederick II (; 24 January 171217 August 1786) was the monarch of Prussia from 1740 until his death in 1786. He was the last Hohenzollern monarch titled ''King in Prussia'', declaring himself '' King of Prussia'' after annexing Royal Prus ...

, and took part in the Battle of Mollwitz on a

donkey The donkey or ass is a domesticated equine. It derives from the African wild ass, ''Equus africanus'', and may be classified either as a subspecies thereof, ''Equus africanus asinus'', or as a separate species, ''Equus asinus''. It was domes ...

, where he was taken prisoner by the Austrians. On his release he returned to Berlin, and thence to

, where he was elected director of the Academy of Sciences in 1742, and in the following year was admitted into the

Académie française An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of tertiary education. The name traces back to Plato's school of philosophy, founded approximately 386 BC at Akademia, a sanctuary of Athena, the go ...

. Returning to Berlin in 1744, again at the desire of Frederick II, he was chosen president of the Royal Prussian Academy of Sciences in 1746, which he controlled with the help of

Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

until his death. His position became extremely awkward with the outbreak of the

Seven Years' War The Seven Years' War, 1756 to 1763, was a Great Power conflict fought primarily in Europe, with significant subsidiary campaigns in North America and South Asia. The protagonists were Kingdom of Great Britain, Great Britain and Kingdom of Prus ...

between his home country and his patron's, and his reputation suffered in both

and

. Finding his health declining, he retired in 1757 to the south of France with a young girl, leaving his wife and children behind and went in 1758 to

Basel Basel ( ; ), also known as Basle ( ), ; ; ; . is a city in northwestern Switzerland on the river Rhine (at the transition from the High Rhine, High to the Upper Rhine). Basel is Switzerland's List of cities in Switzerland, third-most-populo ...

, where he died a year later. Maupertuis's difficult disposition involved him in constant quarrels, of which his controversies with Samuel König and

Voltaire François-Marie Arouet (; 21 November 169430 May 1778), known by his ''Pen name, nom de plume'' Voltaire (, ; ), was a French Age of Enlightenment, Enlightenment writer, philosopher (''philosophe''), satirist, and historian. Famous for his wit ...

during the latter part of his life are examples. :"The brilliance of much of what he did was undermined by his tendency to leave work unfinished, his failure to realise his own potential. It was the insight of genius that led him to least-action principle, but a lack of intellectual energy or rigour that prevented his giving it the mathematical foundation that

Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia

Evolution

Some historians of science point to his work in biology as a significant precursor to the development of evolutionary theory, specifically the theory of

natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the Heredity, heritable traits characteristic of a population over generation ...

. Other writers contend that his remarks are cursory, vague, or incidental to that particular argument. Mayr's verdict was "He was neither an evolutionist, nor one of the founders of the theory of

uthe was one of the pioneers of

genetics Genetics is the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) It is an important branch in biology because heredity is vital to organisms' evolution. Gregor Mendel, a Moravian Augustinians, Augustinian ...

". Maupertuis espoused a theory of

pangenesis Pangenesis was Charles Darwin's hypothetical mechanism for heredity, in which he proposed that each part of the body continually emitted its own type of small organic particles called gemmules that aggregated in the gonads, contributing heritabl ...

, postulating particles from both mother and father as responsible for the characters of the child. Bowler credits him with studies on heredity, with the natural origin of human races, and with the idea that forms of life may have changed with time. Maupertuis was a strong critic of the natural theologians, pointing to phenomena incompatible with a concept of a good and wise Creator. He was also one of the first to consider animals in terms of variable populations, in opposition to the natural history tradition that emphasised description of individual specimens. The difficulty of interpreting Maupertuis can be gauged by reading the original works. Below is a translation from the ''Essai de cosmologie'', followed by the original French passage:

''Mais ne pourroit-on pas dire, que dans la combinaison fortuite des productions de la Nature, comme il n'y avoit que celles où se trouvoient certains rapports de convenance, qui pussent subsister, il n'est pas merveilleux que cette convenance se trouve dans toutes les especes qui actuellement existent? Le hasard, diroit-on, avoit produit une multitude innombrable d'Individus; un petit nombre se trouvoit construit de maniere que les parties de l'Animal pouvoient satisfaire à ses besoins; dans un autre infiniment plus grand, il n'y avoit ni convenance, ni ordre: tous ces derniers ont péri; des Animaux sans bouche ne pouvoient pas vivre, d'autres qui manquoient d'organes pour la génération ne pouvoient pas se perpétuer; les feuls qui soient restés, sont ceux où se trouvoient l'ordre & la convenance: & ces especes que nous voyons aujourd'hui, ne sont que la plus petite partie de ce qu'un destin aveugle avoit produit.''

The same text was published earlier (1748) as " Les loix du mouvement et du repos déduites d'un principe metaphysique" (translation: " Derivation of the laws of motion and equilibrium from a metaphysical principle"). King-Hele (1963) points to similar, though not identical, ideas of thirty years later by

David Hume David Hume (; born David Home; – 25 August 1776) was a Scottish philosopher, historian, economist, and essayist who was best known for his highly influential system of empiricism, philosophical scepticism and metaphysical naturalism. Beg ...

in his '' Dialogues Concerning Natural Religion'' (1777). The chief debate that Maupertuis was engaged in was one that treated the competing theories of generation (i.e.

preformationism In the history of biology, preformationism (or preformism) is a formerly popular theory that organisms develop from miniature versions of themselves. Instead of assembly from parts, preformationists believed that the form of living things exis ...

and epigenesis). His account of life involved

spontaneous generation Spontaneous generation is a superseded scientific theory that held that living creatures could arise from non-living matter and that such processes were commonplace and regular. It was hypothesized that certain forms, such as fleas, could ...

of new kinds of animals and plants, together with massive elimination of deficient forms. These ideas avoid the need for a Creator, but are not part of modern thinking on evolution. The date of these speculations, 1745, is concurrent with

Carl Linnaeus Carl Linnaeus (23 May 1707 – 10 January 1778), also known after ennoblement in 1761 as Carl von Linné,#Blunt, Blunt (2004), p. 171. was a Swedish biologist and physician who formalised binomial nomenclature, the modern system of naming o ...

's own work, and so predates any firm notion of

species A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology), ...

. Also, the work on

genealogy Genealogy () is the study of families, family history, and the tracing of their lineages. Genealogists use oral interviews, historical records, genetic analysis, and other records to obtain information about a family and to demonstrate kin ...

, coupled with the tracing of

phenotypic In genetics, the phenotype () is the set of observable characteristics or traits of an organism. The term covers the organism's morphology (physical form and structure), its developmental processes, its biochemical and physiological propert ...

characters through lineages, foreshadows later work done in genetics.

Least action principle

The

states that in all natural phenomena a quantity called 'action' tends to be minimised. Maupertuis developed such a principle over two decades. For him, action could be expressed mathematically as the product of the mass of the body involved, the distance it had travelled and the velocity at which it was travelling. In 1741, he gave a paper to the Paris Academy of Sciences, ''Loi du repos des corps'', (''Law of bodies at rest''). In it he showed that a system of bodies at rest tends to reach a position in which any change would create the smallest possible change in a quantity that he argued could be assimilated to action. In 1744, in another paper to the Paris Academy, he gave his ''Accord de plusieurs lois naturelles qui avaient paru jusqu'ici incompatibles'' (''Agreement of several natural laws that had hitherto seemed to be incompatible'') to show that the behaviour of light during refraction – when it bends on entering a new medium – was such that the total path it followed, from a point in the first medium to a point in the second, minimised a quantity which he again assimilated to action. Finally, in 1746 he gave a further paper, the ''Loix du mouvement et du repos'' (''Laws of movement and rest''), this time to the Berlin Academy of Sciences, which showed that point masses also minimise action. Point masses are bodies that can be treated for the purposes of analysis as being a certain amount of matter (a mass) concentrated at a single point. A major debate in the early part of the eighteenth century concerned the behaviour of such bodies in collisions. Cartesian and Newtonian physicists argued that in their collisions, point masses conserved both momentum and relative velocity. Leibnizians, on the other hand, argued that they also conserved what was called ''live force'' or ''vis viva''. This was unacceptable for their opponents for two reasons: the first that live force conservation did not apply to so-called ‘hard’ bodies, bodies that were totally incompressible, whereas the other two conservation principles did; the second was that live force was defined by the product of mass and square of velocity. Why did the velocity appear twice in this quantity, as squaring it suggests? The Leibnizians argued this was simple enough: there was a natural tendency in all matter towards motion, so even at rest, there is an inherent velocity in bodies; when they begin to move, there is a second velocity term corresponding to their actual motion. This was anathema to Cartesians and Newtonians. An inherent tendency towards motion was an ‘occult quality’ of the kind of favoured by mediaeval scholastics and to be resisted at all costs. Today the concept of a ‘hard’ body is rejected; and mass times the square of velocity is just twice kinetic energy so modern mechanics reserves a major role for the inheritor quantity of ‘live force’. For Maupertuis, however, it was important to retain the concept of the hard body. And the beauty of his principle of least action was that it applied just as well to hard and elastic bodies. Since he had shown that the principle also applied to systems of bodies at rest and to light, it seemed that it was truly universal. The final stage of his argument came when Maupertuis set out to interpret his principle in cosmological terms. ‘Least action’ sounds like an economy principle, roughly equivalent to the idea of economy of effort in daily life. A universal principle of economy of effort would seem to display the working of wisdom in the very construction of the universe. This seems, in Maupertuis's view, a more powerful argument for the existence of an infinitely wise creator than any other that can be advanced. He published his thinking on these matters in his ''Essai de cosmologie'' (''Essay on cosmology'') of 1750. He shows that the major arguments advanced to prove God, from the wonders of nature or the apparent regularity of the universe, are all open to objection (what wonder is there in the existence of certain particularly repulsive insects, what regularity is there in the observation that all the planets turn in nearly the same plane – exactly the same plane might have been striking but 'nearly the same plane' is far less convincing). But a universal principle of wisdom provides an undeniable proof of the shaping of the universe by a wise creator. Hence the principle of least action is not just the culmination of Maupertuis's work in several areas of physics, he sees it as his most important achievement in philosophy too, giving an incontrovertible proof of God. The flaws in his reasoning are principally that there is no obvious reason why the product of mass, velocity and distance should be particularly viewed as corresponding to action, and even less reason why its minimisation should be an 'economy' principle like a minimisation of effort. Indeed, the product of mass, velocity and distance is mathematically the equivalent of the product of the live force and time; thus the integral over distance of the product of mass and velocity is equivalent of the integral over time of the live force. Leibniz had already shown that this quantity is likely to be either minimised ''or maximised'' in natural phenomena. Minimising this quantity could conceivably demonstrate economy, but how could maximising it? (See also the corresponding principles of ''stationary'' actions by

Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaHamilton Hamilton may refer to: * Alexander Hamilton (1755/1757–1804), first U.S. Secretary of the Treasury and one of the Founding Fathers of the United States * ''Hamilton'' (musical), a 2015 Broadway musical by Lin-Manuel Miranda ** ''Hamilton'' (al ...

Relation to Kant

In '' Universal Natural History and Theory of the Heavens'',

Immanuel Kant Immanuel Kant (born Emanuel Kant; 22 April 1724 – 12 February 1804) was a German Philosophy, philosopher and one of the central Age of Enlightenment, Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works ...

quotes Maupertuis' 1745 discussion of

nebula A nebula (; or nebulas) is a distinct luminescent part of interstellar medium, which can consist of ionized, neutral, or molecular hydrogen and also cosmic dust. Nebulae are often star-forming regions, such as in the Pillars of Creation in ...

-like objects, which Maupertuis notes are actually collections of stars, including Andromeda.

Arthur Schopenhauer Arthur Schopenhauer ( ; ; 22 February 1788 – 21 September 1860) was a German philosopher. He is known for his 1818 work ''The World as Will and Representation'' (expanded in 1844), which characterizes the Phenomenon, phenomenal world as ...

suggested that

's "most important and brilliant doctrine"—contained in the ''

Critique of Pure Reason The ''Critique of Pure Reason'' (; 1781; second edition 1787) is a book by the German philosopher Immanuel Kant, in which the author seeks to determine the limits and scope of metaphysics. Also referred to as Kant's "First Critique", it was foll ...

'' (1781)—was asserted by Maupertuis:

Honours

* The crater Maupertuis on the

Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

is named after him, as is the asteroid 3281 Maupertuis.

Main works

* * * * * * * * English translation * * English translation * * * *

Notes

References

Works cited

* *

External links

*
Nineteenth century account of Maupertuis and the Principle of Least Action

Vitali Kaptug: On Comparison of the Three Meridian Arcs in Lapland
{{DEFAULTSORT:Maupertuis, Pierre Louis 1698 births 1759 deaths 18th-century French mathematicians People from Saint-Malo French physicists 18th-century French astronomers 18th-century French biologists Proto-evolutionary biologists 18th-century French philosophers French geodesists Members of the Académie Française Members of the French Academy of Sciences Members of the Prussian Academy of Sciences Fellows of the Royal Society Recipients of the Pour le Mérite (civil class) French male non-fiction writers 18th-century French male writers