**Constantin Le Paige** was a Belgian mathematician who worked on the theory of algebraic form, especially algebraic curves and surfaces.

- His education was first at Spa, about 25 km south east of Liège, where he attended the François de Sclessin Foundation run by the Jesuits and the continued his education at the Middle School in Spa.
- His school education was completed at Liège where he attended the Athénée Royal de Liège, graduating on 11 September 1869.
- The professor of Higher Mathematics at the Athénée Royal de Liège was V Falisse and his mathematics course had a large impact on Le Paige.
- He entered the University of Liège to study mathematics in 1869 where he attended lectures by Falisse, who taught at the university as well as the Athénée Royal, and by Eugène-Charles Catalan.
- Le Paige undertook research for his doctorate in mathematics advised by François Folie, whose interests were mainly in descriptive geometry but also in astronomy, and he was also influenced by Catalan.
- Folie was Inspector-Director of the University of Liège from 1872 to 1884 and it was during his time in this administrative role that many of the Science and Medical buildings of the University of Liège were erected.
- During the years he studied at the university Le Paige won several prizes for his work.
- In particular he was awarded the special prize for mathematics, awarded to students who, after completing their humanities, follow science courses.
- In the academic year 1873-74 he took part in a number of academic competitions, and was given an honourable mention for the memoir he submitted on the gyroscope.
- After submitting his doctoral thesis Quelques applications de la théorie des formes algébriques à la géométrie Ⓣ(Some applications of the theory of algebraic geometry shapes), Le Paige was given an oral examination and graduated on 28 July 1875.
- After graduation, he was appointed as a lecturer at the University of Liège on 10 October 1876.
- It is a clear indication of his remarkable productivity that nine of his papers were published in 1876 and ten were published in the following year.
- Beginning in the year he was appointed to the University, he taught courses on 'Elements of the theory of determinants', which is not surprising since this was Catalan's speciality, and he also taught a 'Higher analysis' course.
- He was appointed as an extraordinary professor at the University of Liège in 1882, promoted to full professor three years later, and remained there for the whole of his career, retiring in 1922.
- He was Director of the Institute Astrophysique de Cointe-Sclession, annexed to the University of Liège, from 1897 to 1922.
- After Catalan retired in 1884, Le Paige took over teaching his probability theory course.
- Around the same time François Folie left Liège to become the director of the Royal Observatory, Uccle, Brussels, leading to a considerable increase in Le Paige's teaching and administrative duties.
- During the 1890s he began teaching courses on 'Celestial mechanics and analytical mechanics', the 'Elements of astronomy and geodesy', the 'History of mathematical and physical science', and 'Physical astronomy'.
- Another of his colleagues at the University of Liège was Joseph Neuberg who, although about twelve years older than Le Paige, had been appointed as a professor at Liège within a couple of years of Le Paige.
- Neuberg retired in 1910 and again Le Paige took over certain additional responsibilities.
- Ubric and Teresa had eleven sons, including Father Gustave Le Paige De Walque (1903-1980) who was Director of the Museo Arqueológico de la Universidad del Norte in San Pedro de Atacama.
- We mentioned above that Le Paige was administrateur-inspecteur of the University of Liège from 1905 to 1922.
- The Germans took control of Liège and made demands of the University that Le Paige was largely able to resist.
- There was a tradition of geometry at the University of Liège which created the background to Le Paige's early research.
- It was Jean-Baptiste Brasseur who learnt geometry from Dandelin at this time and he, in turn, taught course on Higher Geometry in which he outlined the theory of algebraic curves and surfaces.
- Of course, as we have indicated above, Le Paige was Folie's student and he took over teaching the course when Folie left Liège.
- Folie's approach to geometry was a purely geometrical one, but Le Paige approached the topic in a much more algebraic way, following the fashion that was beginning to take over the subject.
- He worked on the theory of algebraic forms, a topic whose study was initiated by George Boole in 1841 and then developed by Arthur Cayley, James Joseph Sylvester, Charles Hermite, Alfred Clebsch and Siegfried Aronhold.
- In particular Le Paige studied the geometry of algebraic curves and surfaces, building on this earlier work.
- Starting from the construction of a cubic surface given by a straight line, three groups of three points on a line, and six other points, Le Paige comes to the construction of a cubic surface given by three lines and seven points.
- Le Paige studied the generation of plane cubic and quartic curves, developing further Chasles's work on plane algebraic curves and Steiner's results on the intersection of two projective pencils.
- The history of mathematics was another topic which interested Le Paige.
- Here is a list of the main historical papers he wrote: Correspondance de René-François de Sluse, publiée pour la première fois et précédée d'une introduction Ⓣ(Correspondence of R-F de Sluse, published for the first time and with an introduction) (1884); Un géomètre belge du XVIIe siècle: René-François de Sluse Ⓣ(A Belgian mathematician of the seventeenth century: R-F de Sluse) (1887); Lettre de M le Paige à M G Longchamps (relative au géomètre montois J-F Lepoivre) Ⓣ(Letter from Paige to G Longchamps (on the surveyor J-FLepoivre of Mons)) (1887); Un astronome belge du XVIIe siècle: Godefroid Wendelin Ⓣ(A Belgian astronomer of the seventeenth century: Godefroid Wendelin) (1891); Notes pour servir à l'Histoire des Mathématiques dans l'ancien Pays de Liège Ⓣ(Notes for use in the history of mathematics in the region of Liege) (1890); Sur l'origine de certains signes d'opération Ⓣ(On the origin of some operation signs) (1891-1892); Sur les notations algébriques avant Descartes Ⓣ(On algebraic notation before Descartes) (1895-1896); Discours sur l'astronomie des Grecs Ⓣ(Lecture on the astronomy of the Greeks) (1895); and Discours sur l'astronomie au temps de Kepler Ⓣ(Lecture on astronomy in the time of Kepler) (1896).
- After Le Paige was appointed director of the Astrophysical Institute, he wrote a number of astronomical texts.
- For example, in the year of his appointment, 1897, he published: De l'action du Soleil sur les plaques photographiques Ⓣ(On the effect of the sun on photographic plates); Sur la photographie de l'atmosphère (suite à une note de M De Heen) Ⓣ(In the photograph of the atmosphere (following a note from De Heen)); Sur la photographie du Soleil Ⓣ(On photography of the Sun); and Discours sur l'astronomie moderne Ⓣ(Lecture on modern astronomy).
- Let us note some of his students who went on to outstanding academic careers: Jacques Deruyts, François Deruyts, Marcel Dehalu, and Henry Janne.
- Le Paige received many honours.
- He was elected a corresponding member of the Royal Belgium Academy of Sciences on 15 December 1885, becoming a full member on to the 15 December 1890.
- He was elected to the Royal Society of Sciences of Liège in 1878, becoming its Secretary General in 1886.
- He was elected to the Royal Society of Bohemia in 1881, and in the same year became a foreign corresponding member of the Accademia Pontificia dei Nuovi Lincei in Rome.
- He was elected to the Royal Academy of Sciences of Lisbon in 1883 and, in the same year, to the Leopoldino-Carolina Naturae Curiosorum Academia in Halle.
- Finally, we note Le Paige's love of collecting old books.
- The "Divisie Chronijk" of 1517 is celebrated for its wood-cuts by Lucas van Leyden, and a "Livre d'Heures" of 1513 is printed on parchment and illustrated with coloured wood engravings.
- The sale contains also rare books on art and science, music books, geographical works, etc.

Born 9 March 1852, Liège, Belgium. Died 26 January 1929, Liège, Belgium.

View full biography at MacTutor

Algebra, Astronomy, Geometry, Origin Belgium

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