Julius Plücker (16 June 1801 – 22 May 1868) was a German mathematician and physicist.

School period

Gallery of Julius Plücker

Königlichen Gymnasium, Düsseldorf, Germany

In 1816 Plücker attended the Königlichen Gymnasium in Düsseldorf to prepare for university studies and graduated in 1819.

College/University

Gallery of Julius Plücker

University of Paris, Paris, France

After Plücker went to France in March 1823, he attended courses on geometry at the University of Paris.

Gallery of Julius Plücker

University of Heidelberg, Heidelberg, Baden-Württemberg, Germany

Plücker attended the University of Heidelberg which he entered in the summer semester of 1819. He spent three semesters at Heidelberg where he attended the lectures of Georg Friedrich Creuzer, the professor of philology and ancient history.

Gallery of Julius Plücker

University of Bonn, Bonn, North Rhine-Westphalia, Germany

Plücker attended the University of Bonn beginning his studies there in the winter semester of 1820. Here he was taught physics and chemistry by Karl Wilhelm Gottlob Kastner who lectured at Bonn from 1818 to 1821.

Gallery of Julius Plücker

Philipps University of Marburg, Marburg, Hesse, Germany

Plücker completed his doctoral dissertation Generalem analyeseos applicationem ad ea quae geometriae altioris et mechanicae basis et fundamenta sunt e serie Tayloria deducit while he was in Paris which he submitted to the University of Marburg. His thesis advisor at Marburg was Christian Ludwig Gerling who had studied under Carl Friedrich Gauss. He sent the thesis from Paris to Marburg in July 1823 and was awarded his doctorate "in absentia" on 30 August 1823.

Career

Gallery of Julius Plücker

Julius Plücker, 16 June 1801 – 22 May 1868.

Achievements

Alten Friedhof, Bonn, Germany

A memorial bust of Julius Plücker (16 June 1801 – 22 May 1868), a German mathematician and physicist.

Membership

Royal Society of London

Royal Society of London, 6-9 Carlton House Terrace, St. James's, London SW1Y 5AG, England, United Kingdom

Plücker was a member of the Royal Society of London which awarded him the Copley Medal in 1866.

Awards

Copley Medal

1866

Plücker was the recipient of the Copley Medal from the Royal Society.

University of Heidelberg, Heidelberg, Baden-Württemberg, Germany

Plücker attended the University of Heidelberg which he entered in the summer semester of 1819. He spent three semesters at Heidelberg where he attended the lectures of Georg Friedrich Creuzer, the professor of philology and ancient history.

University of Bonn, Bonn, North Rhine-Westphalia, Germany

Plücker attended the University of Bonn beginning his studies there in the winter semester of 1820. Here he was taught physics and chemistry by Karl Wilhelm Gottlob Kastner who lectured at Bonn from 1818 to 1821.

Philipps University of Marburg, Marburg, Hesse, Germany

Plücker completed his doctoral dissertation Generalem analyeseos applicationem ad ea quae geometriae altioris et mechanicae basis et fundamenta sunt e serie Tayloria deducit while he was in Paris which he submitted to the University of Marburg. His thesis advisor at Marburg was Christian Ludwig Gerling who had studied under Carl Friedrich Gauss. He sent the thesis from Paris to Marburg in July 1823 and was awarded his doctorate "in absentia" on 30 August 1823.

Julius Plücker was a prominent German mathematician and physicist. He is noted for making fundamental contributions to analytic and projective geometry as well as experimental physics. His most famous contribution to the field of physics was his discovery of the electron. Also, he was one of the first among scientists who investigated cathode rays.

Background

Ethnicity:
Julius's background was a mixture of French and German and throughout his life, it is evident that he found both attractive.

Julius Plücker was born on June 18, 1801, at Elberfeld (now part of Wuppertal), Duchy of Berg. Plücker's family was descended from merchants who had originally lived in Aachen but had settled in Elberfeld during the Reformation in the 16th Century. His father, Johann Peter Plücker, was a businessman in Elberfeld although he later retired to Dusseldorf. Julius's mother was Johanna Maria Lüttringhausen, a daughter of Johannes Lüttringhausen. Peter and Johanna Plücker had both been born in Elberfeld and they married in that town on 21 September 1797. They had three children: Julius Plücker, the subject of this biography, Moritz Rudolf Plücker and Emil Plücker (died 1871).

Education

Julius Plücker first attended the Normal School in Elberfeld run by Johann Friederich Wilberg who had undertaken research on the effects of different styles of teaching on the characters of the pupils. Plücker studied there from 1806 to 1815 and his ability was recognized by Wilberg who approached Plücker's father persuading him that his son's talents merited further scholarly training. Wilberg recognized that geometry was an excellent teaching tool to develop self-creative thinking and independence in his students. His friend, the mathematician William Adolph Diesterweg encouraged him in the technical aspect of this idea.

In 1816 Plücker, following Wilberg's advice, moved to the Königlichen Gymnasium in Düsseldorf to prepare for university studies. After graduating with a diploma in 1819 he followed the typical path for German university students of the time, studying at a number of different universities. He first attended the University of Heidelberg which he entered in the summer semester of 1819. He spent three semesters at Heidelberg where he attended the lectures of Georg Friedrich Creuzer, the professor of philology and ancient history.

Next he moved to the University of Bonn beginning his studies there in the winter semester of 1820. Here he was taught physics and chemistry by Karl Wilhelm Gottlob Kastner who lectured at Bonn from 1818 to 1821. He was also taught mathematics and physics by Karl Dietrich von Münchow, the professor of astronomy, mathematics, and physics, and mathematics by Wilhelm Adolf Diesterweg who had been appointed professor of mathematics in 1819.

His next move was to go to France in March 1823 where he attended courses on geometry at the University of Paris. He attended lectures by, among others, Jean-Baptiste Biot, Augustin-Louis Cauchy, Sylvestre Lacroix and Siméon Poisson. He completed his doctoral dissertation Generalem analyeseos applicationem ad ea quae geometriae altioris et mechanicae basis et fundamenta sunt e serie Tayloria deducit while he was in Paris which he submitted to the University of Marburg. His thesis advisor at Marburg was Christian Ludwig Gerling who had studied under Carl Friedrich Gauss. He sent the thesis from Paris to Marburg in July 1823 and was awarded his doctorate "in absentia" on 30 August 1823.

In 1825 Plücker became Privatdozent at the University of Bonn, where in 1828 he was promoted to extraordinary professor. In 1833 he served in Berlin simultaneously as extraordinary professor at the university and as teacher at the Friedrich Wilhelm Gymnasium. In 1834 he became ordinary professor at the University of Halle. He then served as a full professor of mathematics (1836–1847) and physics (1847–1868) at Bonn, where he succeeded Karl von Münchow.

When Plücker began his work in mathematics, the only German mathematician of international repute was Gauss. In 1826, however, Crelle founded, in Berlin, his Journal für die reine und angewandte Mathematik; and the work of Plücker, Steiner, and others soon became well known. Their field of research was not the differential geometry of Monge and Gauss, but rather the analytic and projective geometry of Poncelet and Gergonne. But differences between the synthetic school in geometry, of which Steiner was the head in Berlin, and Plücker’s analytical school - together with a conflict of personality between the two men - resulted in Plücker”s being resident at Berlin for only a year.

In 1828 Plücker published his first book, volume I of Analytisch-geometrische Entwicklungen, which was followed in 1831 by volume II. In each volume he discussed the plane analytic geometry of the line, circle, and conic sections; and many facts and theorems - either discovered or known by Plücker - were demonstrated in a more elegant manner. The point coordinates used in both volumes are nonhomogeneous affine; in volume II the homogeneous line coordinates in a plane, formerly known as Plücker’s coordinates, are used and conic sections are treated as envelopes of lines. The characteristic features of Plücker’s analytic geometry were already present in this work, namely, the elegant operations with algebraic symbols occurring in the equations of conic sections and their pencils. His understanding of the so-called reading in the formulas enabled him to achieve geometric results while avoiding processes of elimination, and his algebraic elegance was surpassed in some matters only by Hesse. Plücker’s careful treatment, in the first book, of conic sections that osculate with one another in different degrees is still noteworthy.

In 1829 Plücker introduced the so-called triangular coordinates as three values that are proportional to the distances of a point from three given lines. Simultaneously, Mobius introduced his barycentric coordinates, another type of homogeneous point coordinates. In his Analytisch-geometrische Entwickhmgen, however, Plücker used only nonhomogeneous point coordinates. At the end of volume II he presented a detailed explanation of the principle of reciprocity, now called the principle of duality. Plücker, who stood in the middle of the Poncelet-Gergonne controversy, was inclined to support Poncelet’s position: Plücker introduced duality by means of a correlation polarity and not in the more modern sense (as in Gergonne) of a general principle. Thus Plücker’s work may be regarded as a transitional stage preceding the pure projective geometry founded by Staudt.

After 1832 Plücker took an interest in a general treatment of plane curves of a higher degree than the second. Although his next book, System der analytischen Geometrie, insbesondere eine ausführliche Theorie clear Kurven. Ordnung enthaltend (1835), discussed general (or projective) point and line coordinates for treating conic sections, the greater part of the book covered plane cubic curves.

Plücker devoted the greater part of Theorie der algebraischen Kurven (1839) to the properties of algebraic curves in the neighborhood of their infinite points. He considered not only the asymptotic lines, but also asymptotic conic sections and other curves osculating the given cubic in a certain degree. For the asymptotic lines he corrected some false results given by Euler in Introduction in anatysin infinitorum (1748).

Although the increasing predominance of projective and birational geometry abated interest in these particulars about the behavior of curves at infinity, the second part of Theorie der algebraischen Kurven was of more permanent value. It contained a new treatment of singular points in the plane, a subject previously discussed in Cramer’s work (1750) on the theory of curves. Plücker’s work also resolved several doubts concerning the relation between the order and class of curves in the work of Poncelet and Gergonne.

In the last chapter of Geometrie der algebraischen Kurven Plücker dealt with plane quartic curves and developed a full classification of their possible singular points. A nonsingular quartic curve that possesses twenty-eight double tangents is the central fact in his theory of these curves.

In 1829, independent of Bobillier, Plücker extended the notion of polars (previously known only for conic sections) to all plane algebraic curves. He also studied the problem of focal points of algebraic curves, the osculation of two surfaces, and wave surface, and thus became concerned with algebraic and analytic space geometry. This field was also discussed in System der Geometrie des Raumes in neuer analytischer Behandltmgsweise (1846), in which he treated in an elegant manner the known facts of analytic geometry. His own contributions in this work, however, were not as significant as those in his earlier books.

After 1846 Plücker abandoned his mathematical researches and conducted physical experiments until 1864, when he returned to his work in geometry. His mathematical accomplishments during this second period were published in Neue Geometrie des Raumes gegriindet auf die Betrachtung der Geraden als Raum-element, which appeared in 1868. Plücker’s death prevented him from completing the second part of this work, but Felix Klein, who had served as Plücker’s physical assistant from 1866 to 1868, undertook the task. Plücker had indicated his plans to Klein in numerous conversations. These conversations served also as a source for Plücker’s ideas in Neue Geometrie, in which he attempted to base space geometry upon the self-dual straight line as element, rather than upon the point or in dual manner upon the plane as element. He thus created the field of line geometry, which until the twentieth century was the subject of numerous researches.

Plücker’s algebraic line geometry was distinct, however, from the differential line geometry created by Hamilton. Plücker introduced the notions (still used today) of complexes; congruences; and ruled surfaces for subsets of lines of three, two, or one dimension. He also classified linear complexes and congruences and initiated the study of quadratic complexes, which were defined by quadratic relations among Plücker’s coordinates. (Complex surfaces are surfaces of fourth order and class and are generated by the totality of lines belonging to a quadratic complex that intersects a given line.) These complexes were the subject of numerous researches in later years, beginning with Klein’s doctoral thesis in 1868. In Neue Geometric Plücker again adopted a metrical point of view, which effected extended calculations and studies of special cases. His interest in geometric shapes and details during this period is evident in the many models he had manufactured.

In assessing Plücker’s later geometric work it must be remembered that during the years in which he was conducting physical research he did not keep up with the mathematical literature. He was not aware, for example, of Grassmann’s Die Wissenschaft der exten-siren Grösslehre oder die Ausdehnungslehre (1844), which was unintelligible to almost all contemporary mathematicians.

Plücker’s guide in physics was Faraday, with whom he corresponded. His papers of 1839 on wave surface and of 1847 on the reflection of light at quadric surfaces concerned both theoretical physics and mathematics, though often counted among his forty-one mathematical papers. Plücker also wrote fifty-nine papers on pure physics, published primarily in Annalen der Physic and Chemie and Philosophical Transactions of the Royal Society.

He investigated the magnetic properties of gases and crystals and later studied the phenomena of electrical discharge in evacuated gases. He and his collaborators described these phenomena as precisely as the technical means of his time permitted. He also made use of an electromagnetic motor constructed by Fessel and later collaborated with Geissler at Bonn in constructing a standard thermometer. Plücker further drew upon the chemical experience of his pupil J. W. Hittorf in his study of the spectra of gaseous substances, and his examination of the different spectra of these substances indicates that he realized their future significance for chemical analysis.

Although Plücker was educated primarily in Germany, throughout his life he drew much on French and English science. He was essentially a geometer but dedicated many years of his life to physical science. While Plücker was a professor of mathematics and physics at the University of Bonn, he is said to have always been willing to remind other physicists that he was competent in both fields. It is particularly noteworthy that Plücker chose to investigate experimental rather than theoretical physics; Clebsch, in his celebrated obituary on Plücker, identified several relations between Plücker’s mathematical and his physical preoccupations. In geometry, he wished to describe the different shapes of cubic curves and other figures, and in physics, he endeavored to describe the various physical phenomena more qualitatively. But in both cases, he was far from pursuing science in a modern axiomatic, deductive style.

Membership

Plücker was a member of the Royal Society of London which awarded him the Copley Medal in 1866.

Royal Society of London
,
United Kingdom

Personality

Quotes from others about the person

“"... Plucker never attained great manual dexterity as an experimenter. He had always, however, very clear conceptions as to what was wanted, and possessed in a high degree the power of putting others in possession of his ideas and rendering them enthusiastic in carrying them into practice." - Johann Hittorf.”

Connections

On September 4, 1837, Julius Plücker married Maria Louise Antonie Friederike Altstätten (1813-1880) at Haus Altstätten, Neugasse, Bonn. They had one son Albert Plücker (1838-1901) born in Bonn on 1 August 1838.