Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the

watercolor portrait

#29). Biliotheque de l'Institut de France.

The True Face of Adrien-Marie Legendre

(Portrait of Legendre)

a

Fermat's Last Theorem Blog

*

Eléments de géométrie

(Paris : F. Didot, 1817)

Elements of geometry and trigonometry, from the works of A. M. Legendre. Revised and adapted to the course of mathematical instruction in the United States, by Charles Davies.

(New York: A. S. Barnes & co., 1858) : English translation of the above text

Mémoires sur la méthode des moindres quarrés, et sur l'attraction des ellipsoïdes homogènes

(1830)

Théorie des nombres

(Paris : Firmin-Didot, 1830)

Traité des fonctions elliptiques et des intégrales eulériennes

(Paris : Huzard-Courcier, 1825–1828)

Nouvelles Méthodes pour la Détermination des Orbites des Comètes

(Paris : Courcier, 1806)

Essai sur la Théorie des Nombres

(Paris : Duprat, 1798)

Exercices de Calcul Intégral V.3

(Paris : Courcier, 1816)

Correspondance mathématique avec Legendre

in C. G. J. Jacobis gesammelte Werke (Berlin: 1852) {{DEFAULTSORT:Legendre, Adrien Marie 1752 births 1833 deaths University of Paris alumni 18th-century French mathematicians 19th-century French mathematicians Number theorists Officiers of the Légion d'honneur Fellows of the American Academy of Arts and Sciences Members of the French Academy of Sciences Fellows of the Royal Society Fellows of the Royal Society of Edinburgh Scientists from Paris

Legendre polynomials
In physical science and mathematics, Legendre polynomials (named after Adrien-Marie Legendre, who discovered them in 1782) are a system of complete and orthogonal polynomials, with a vast number of mathematical properties, and numerous applicat ...

and Legendre transformation
In mathematics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involutive transformation on real-valued convex functions of one real variable. In physical problems, it is used to convert functions of ...

are named after him.
Life

Adrien-Marie Legendre was born inParis
Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

on 18 September 1752 to a wealthy family. He received his education at the Collège Mazarin in Paris, and defended his thesis in physics and mathematics in 1770. He taught at the École Militaire
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...

in Paris from 1775 to 1780 and at the École Normale
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...

from 1795. At the same time, he was associated with the Bureau des Longitudes
Bureau ( ) may refer to:
Agencies and organizations
*Government agency
*Public administration
* News bureau, an office for gathering or distributing news, generally for a given geographical location
* Bureau (European Parliament), the administrat ...

. In 1782, the Berlin Academy awarded Legendre a prize for his treatise on projectiles in resistant media. This treatise also brought him to the attention of Lagrange.
The ''Académie des sciences
The French Academy of Sciences (French: ''Académie des 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 research. It was at the ...

'' made Legendre an adjoint member in 1783 and an associate in 1785. In 1789, he was elected a Fellow of the Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

.
He assisted with the Anglo-French Survey (1784–1790)
The Anglo-French Survey (1784–1790) was the geodetic survey to measure the relative position of Royal Greenwich Observatory, Greenwich Observatory and the Paris Observatory via triangulation (surveying), triangulation. The English operations ...

to calculate the precise distance between the Paris Observatory
The Paris Observatory (french: Observatoire de Paris ), a research institution of the Paris Sciences et Lettres University, is the foremost astronomical observatory of France, and one of the largest astronomical centers in the world. Its histor ...

and the Royal Greenwich Observatory
The Royal Observatory, Greenwich (ROG; known as the Old Royal Observatory from 1957 to 1998, when the working Royal Greenwich Observatory, RGO, temporarily moved south from Greenwich to Herstmonceux) is an observatory situated on a hill in G ...

by means of trigonometry
Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. T ...

. To this end in 1787 he visited Dover and London together with Dominique, comte de Cassini
Jean-Dominique, comte de Cassini (30 June 174818 October 1845) was a French astronomer, son of César-François Cassini de Thury and great-grandson of Giovanni Domenico Cassini.
Cassini was born at the Paris Observatory. He succeeded his fath ...

and Pierre Méchain
Pierre François André Méchain (; 16 August 1744 – 20 September 1804) was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep-sky objects and comets.
Life
Pierre Méchain was born i ...

. The three also visited William Herschel
Frederick William Herschel (; german: Friedrich Wilhelm Herschel; 15 November 1738 – 25 August 1822) was a German-born British astronomer and composer. He frequently collaborated with his younger sister and fellow astronomer Caroline H ...

, the discoverer of the planet Uranus
Uranus is the seventh planet from the Sun. Its name is a reference to the Greek god of the sky, Uranus (mythology), Uranus (Caelus), who, according to Greek mythology, was the great-grandfather of Ares (Mars (mythology), Mars), grandfather ...

.
Legendre lost his private fortune in 1793 during the French Revolution. That year, he also married Marguerite-Claudine Couhin, who helped him put his affairs in order. In 1795, Legendre became one of six members of the mathematics section of the reconstituted Académie des Sciences, renamed the Institut National des Sciences et des Arts. Later, in 1803, Napoleon reorganized the Institut National, and Legendre became a member of the Geometry section. From 1799 to 1812, Legendre served as mathematics examiner for graduating artillery students at the École Militaire and from 1799 to 1815 he served as permanent mathematics examiner for the École Polytechnique
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...

. In 1824, Legendre's pension from the École Militaire was stopped because he refused to vote for the government candidate at the Institut National. His pension was partially reinstated with the change in government in 1828. In 1831, he was made an officer of the Légion d'Honneur
The National Order of the Legion of Honour (french: Ordre national de la Légion d'honneur), formerly the Royal Order of the Legion of Honour ('), is the highest French order of merit, both military and civil. Established in 1802 by Napoleon ...

.
Legendre died in Paris on 9 January 1833, after a long and painful illness, and Legendre's widow carefully preserved his belongings to memorialize him. Upon her death in 1856, she was buried next to her husband in the village of Auteuil Auteuil may refer to:
Places
* Auteuil, Oise, a commune in France
* Auteuil, Paris, a neighborhood of Paris
** Auteuil, Seine, the former commune which was on the outskirts of Paris
* Auteuil, Quebec, a former city that is now a district within ...

, where the couple had lived, and left their last country house to the village. Legendre's name is one of the 72 names inscribed on the Eiffel Tower.
Mathematical work

Abel
Abel ''Hábel''; ar, هابيل, Hābīl is a Biblical figure in the Book of Genesis within Abrahamic religions. He was the younger brother of Cain, and the younger son of Adam and Eve, the first couple in Biblical history. He was a shepher ...

's work on elliptic function
In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those in ...

s was built on Legendre's, and some of Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

' work in statistics and number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...

completed that of Legendre. He developed, and first communicated to his contemporaries before Gauss, the least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

method which has broad application in linear regression
In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is call ...

, signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniq ...

, statistics, and curve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is ...

; this was published in 1806 as an appendix to his book on the paths of comets. Today, the term "least squares method" is used as a direct translation from the French "méthode des moindres carrés".
His major work is ''Exercices de Calcul Intégral'', published in three volumes in 1811, 1817 and 1819. In the first volume he introduced the basic properties of elliptic integrals, beta function
In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral
: \Beta(z_1,z_2) = \int_0^1 t^(1 ...

s and gamma function
In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except ...

s, introducing the symbol Γ normalizing it to Γ(n+1) = n!. Further results on the beta and gamma functions along with their applications to mechanics – such as the rotation of the earth, and the attraction of ellipsoids – appeared in the second volume. In 1830, he gave a proof of Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...

for exponent ''n'' = 5, which was also proven by Lejeune Dirichlet in 1828.
In number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...

, he conjectured the quadratic reciprocity
In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard st ...

law, subsequently proved by Gauss; in connection to this, the Legendre symbol
In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo an odd prime number ''p'': its value at a (nonzero) quadratic residue mod ''p'' is 1 and at a non-quadratic residu ...

is named after him. He also did pioneering work on the distribution of primes
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

, and on the application of analysis to number theory. His 1798 conjecture of the prime number theorem
In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying ...

was rigorously proved by Hadamard
Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry and partial differential equations.
Biography
The son of a teac ...

and de la Vallée-Poussin in 1896.
Legendre did an impressive amount of work on elliptic function
In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those in ...

s, including the classification of elliptic integral
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (). Their name originates from their originally arising in ...

s, but it took Abel
Abel ''Hábel''; ar, هابيل, Hābīl is a Biblical figure in the Book of Genesis within Abrahamic religions. He was the younger brother of Cain, and the younger son of Adam and Eve, the first couple in Biblical history. He was a shepher ...

's stroke of genius to study the inverses of Jacobi Jacobi may refer to:
* People with the surname Jacobi (surname), Jacobi
Mathematics:
* Jacobi sum, a type of character sum
* Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations
* Jacobi eigenva ...

's functions and solve the problem completely.
He is known for the Legendre transformation
In mathematics, the Legendre transformation (or Legendre transform), named after Adrien-Marie Legendre, is an involutive transformation on real-valued convex functions of one real variable. In physical problems, it is used to convert functions of ...

, which is used to go from the Lagrangian
Lagrangian may refer to:
Mathematics
* Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier
** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...

to the Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...

formulation of classical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...

. In thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

it is also used to obtain the enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...

and the Helmholtz
Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, ...

and Gibbs (free) energies from the internal energy
The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...

. He is also the namesake of the Legendre polynomials
In physical science and mathematics, Legendre polynomials (named after Adrien-Marie Legendre, who discovered them in 1782) are a system of complete and orthogonal polynomials, with a vast number of mathematical properties, and numerous applicat ...

, solutions to Legendre's differential equation, which occur frequently in physics and engineering applications, ''e.g.'' electrostatics
Electrostatics is a branch of physics that studies electric charges at rest (static electricity).
Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber ...

.
Legendre is best known as the author of ''Éléments de géométrie'', which was published in 1794 and was the leading elementary text on the topic for around 100 years. This text greatly rearranged and simplified many of the propositions from Euclid's ''Elements'' to create a more effective textbook.
Honors

*Foreign Honorary Member of theAmerican Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

(1832)
*The Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

crater Legendre is named after him.
*Main-belt asteroid 26950 Legendre is named after him.
*Legendre is one of the 72 prominent French scientists who were commemorated on plaques at the first stage of the Eiffel Tower
The Eiffel Tower ( ; french: links=yes, tour Eiffel ) is a wrought-iron lattice tower on the Champ de Mars in Paris, France. It is named after the engineer Gustave Eiffel, whose company designed and built the tower.
Locally nicknamed "'' ...

when it first opened.
Publications

;Essays * 1782 ''Recherches sur la trajectoire des projectiles dans les milieux résistants'' (prize on projectiles offered by the Berlin Academy) ;Books * ''Eléments de géométrie'', textbook 1794 * ''Essai sur la Théorie des Nombres'' 1797-8 ("An VI"), 2nd ed. 1808, 3rd ed. in 2 vol. 1830 * ''Nouvelles Méthodes pour la Détermination des Orbites des Comètes'', 1805 * ''Exercices de Calcul Intégral'', book in three volumes 1811, 1817, and 1819 * ''Traité des Fonctions Elliptiques'', book in three volumes 1825, 1826, and 1830 ;Memoires in ''Histoire de l'Académie Royale des Sciences'' * 1783 ''Sur l'attraction des Sphéroïdes homogènes'' (work on Legendre polynomials) * 1784 ''Recherches sur la figure des Planètes'' p. 370 * 1785 ''Recherches d'analyse indéterminée'' p. 465 (work on number theory) * 1786 ''Mémoire sur la manière de distinguer les Maxima des Minima dans le Calcul des Variations'' p. 7 (as Legendre) * 1786 ''Mémoire sur les Intégrations par arcs d'ellipse'' p. 616 (as le Gendre) * 1786 ''Second Mémoire sur les Intégrations par arcs d'ellipse'' p. 644 * 1787 ''L'intégration de quelques équations aux différences Partielles'' (Legendre transform) ;In ''Memoires présentés par divers Savants à la l'Académie des Sciences de l'Institut de France'' * 1806 ''Nouvelle formula pour réduire en distances vraies les distances apparentes de la Lune au Soleil ou à une étoile'' (30–54) * 1807 ''Analyse des triangles tracés sur la surface d'un sphéroide'' (130–161) * Tome 10 ''Recherches sur diverses sortes d'intégrales défines'' (416–509) * 1819 ''Méthode des moindres carrés pour trouver le milieu le plus probable entre les résultats de différentes observations'' (149–154), ''Mémoire sur l'attraction des ellipsoïdes homogènes'' (155–183) * 1823 ''Recherches sur quelques objets d'Analyse indéterminée et particulièrement sur le théorème de Fermat'' (1–60) * 1828 ''Mémoire sur la détermination des fonctions Y et Z que satisfont à l'équation 4(X^n-1) = (X-1)(Y^2+-nZ^2), n étant un nombre premier 4i-+1'' (81–100) * 1833 ''Réflexions sur différentes manières de démontrer la théorie des parallèles ou le théorème sur la somme des trois angles du triangle, avec 1 planche'' (367–412)Mistaken portrait

For two centuries, until the recent discovery of the error in 2005, books, paintings and articles have incorrectly shown a profile portrait of the obscure French politicianLouis Legendre
Louis Legendre (22 May 1752 – 13 December 1797) was a French politician of the Revolution period.
Early activities
Born at Versailles, he was keeping a butcher's shop in Saint Germain, Paris, by 1789. He was an ardent supporter of the ideas ...

(1752–1797) as a portrait of the mathematician. The error arose from the fact that the sketch was labelled simply "Legendre" and appeared in a book along with contemporary mathematicians such as Lagrange. The only known portrait of Legendre, rediscovered in 2008, is found in the 1820 book ''Album de 73 portraits-charge aquarellés des membres de I'Institut'', a book of caricatures of seventy-three members of the Institut de France in Paris by the French artist Julien-Léopold Boilly
Julien-Léopold Boilly (1796–1874), also known as Jules Boilly, was a French artist noted for his album of lithographs ''Iconographie de l'Institut Royal de France'' (1820–1821) and his booklet ''Album de 73 portraits-charge aquarellés des me ...

as shown below:Boilly, Julien-Léopold. (1820). ''Album de 73 portraits-charge aquarellés des membres de I'Institut''watercolor portrait

#29). Biliotheque de l'Institut de France.

See also

*List of things named after Adrien-Marie Legendre
Adrien-Marie Legendre (1752–1833) is the eponym of all of the things listed below.
*26950 Legendre
*Associated Legendre polynomials
*Generalized_Fourier_series#Example_(Fourier–Legendre_series), Fourier–Legendre series
*Gauss–Legendre ...

* Associated Legendre polynomials
* Gauss–Legendre algorithm
* Legendre's constant
Legendre's constant is a mathematical constant occurring in a formula conjectured by Adrien-Marie Legendre to capture the asymptotic behavior of the prime-counting function \pi(x). Its value is now known to be 1.
Examination of available n ...

* Legendre's equation in number theory
* Legendre's functional relation for elliptic integrals
* Legendre's conjecture
Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between n^2 and (n+1)^2 for every positive integer n. The conjecture is one of Landau's problems (1912) on prime numbers; , the conjecture has neither be ...

* Legendre sieve
In mathematics, the Legendre sieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory. It applies the concept of the Sieve of Eratosthenes to find upper or lower bounds on the number of primes within a given set o ...

* Legendre symbol
In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo an odd prime number ''p'': its value at a (nonzero) quadratic residue mod ''p'' is 1 and at a non-quadratic residu ...

* Legendre's theorem on spherical triangles In geometry, Legendre's theorem on spherical triangles, named after Adrien-Marie Legendre, is stated as follows:
: Let ABC be a spherical triangle on the ''unit'' sphere with ''small'' sides ''a'', ''b'', ''c''. Let A'B'C' be the planar triangle wi ...

* Saccheri–Legendre theorem
In absolute geometry, the Saccheri–Legendre theorem states that the sum of the angles in a triangle is at most 180°. Absolute geometry is the geometry obtained from assuming all the axioms that lead to Euclidean geometry with the exception of th ...

* Least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

* Least-squares spectral analysis
Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the most used spectral method in science, generally ...

* Seconds pendulum
A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 0.5 Hz.
Pendulum
A pendulum is a weight suspended from a pivot so that ...

Notes

External links

* *The True Face of Adrien-Marie Legendre

(Portrait of Legendre)

a

Fermat's Last Theorem Blog

*

Eléments de géométrie

(Paris : F. Didot, 1817)

Elements of geometry and trigonometry, from the works of A. M. Legendre. Revised and adapted to the course of mathematical instruction in the United States, by Charles Davies.

(New York: A. S. Barnes & co., 1858) : English translation of the above text

Mémoires sur la méthode des moindres quarrés, et sur l'attraction des ellipsoïdes homogènes

(1830)

Théorie des nombres

(Paris : Firmin-Didot, 1830)

Traité des fonctions elliptiques et des intégrales eulériennes

(Paris : Huzard-Courcier, 1825–1828)

Nouvelles Méthodes pour la Détermination des Orbites des Comètes

(Paris : Courcier, 1806)

Essai sur la Théorie des Nombres

(Paris : Duprat, 1798)

Exercices de Calcul Intégral V.3

(Paris : Courcier, 1816)

Correspondance mathématique avec Legendre

in C. G. J. Jacobis gesammelte Werke (Berlin: 1852) {{DEFAULTSORT:Legendre, Adrien Marie 1752 births 1833 deaths University of Paris alumni 18th-century French mathematicians 19th-century French mathematicians Number theorists Officiers of the Légion d'honneur Fellows of the American Academy of Arts and Sciences Members of the French Academy of Sciences Fellows of the Royal Society Fellows of the Royal Society of Edinburgh Scientists from Paris