**Julius Plücker** was a German mathematician who made important contributions to analytic geometry and physics.

- This meant that Julius's background was a mixture of French and German and throughout his life it is evident that he found both attractive.
- We note that almost all sources give Julius's date of birth as 16 June 1801 but the date on his gravestone is 16 July 1801 and we have adopted this date.
- Julius Plücker first attended the Normal School in Elberfeld run by Johann Friederich Wilberg (1766-1846) who had undertaken research on the affects of different styles of teaching on the characters of the pupils.
- In 1816 Plücker, following Wilberg's advice, moved to the Königlichen Gymnasium in Düsseldorf to prepare for university studies.
- It was while he was studying in Paris that Plücker learned the importance of analytical mechanics as developed by Laplace and Lagrange as well as that of geometric mechanics as developed by Poinsot.
- This interplay between geometry and mechanics would form the topic of Plücker's research throughout his career from this time onwards.
- Plücker gave all his courses in German but sometimes gave the occasional lecture in French.
- This dual role made Plücker think about how to bring his teaching and his research closer together.
- For most Germans a position in Berlin would be the ultimate goal and one would have expected Plücker to spent the rest of his career there.
- Steiner was the leader of the German school of synthetic geometry, while Plücker followed the analytical approach.
- Plücker quickly decided that he would have to find a position away from Berlin as soon as possible.
- At Halle, Plücker gave lecture courses on: Analysis and Algebra; Geometry, Mathematical Physics; and Physics.
- As we have indicated, Plücker was a geometer yet he firmly believed in the importance of the applications of mathematics to the physical sciences.
- It occurred to Plücker that if gases could be contained in an enclosure, the discharge effect should be observable for a length of time.
- When Plücker generated the discharge, an eerie, mysterious, and beautiful greenish glow appeared.
- Plücker, the complete scientist, recognised that this fluorescence within the tube responded to an electromagnet on the wall of the tube; he discerned that these expressions of light were rays or beams of some electrical property.
- Geissler and Plücker had propelled Faraday's Effect into a visual manifestation.
- Although Plücker continued to hold the chair of physics at Bonn until his death, in 1865 his research interests returned to mathematics and Felix Klein served as his assistant 1866-1868.
- Let us now look briefly at the highly significant contributions which Plücker made to mathematics.
- 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.
- This work also contains the celebrated 'Plücker equations' relating the order and class of a curve.
- In 1868 Plücker published the first part of Neue Geometrie des Raumes, gegründet auf die Betrachtung der geraden Linie als Raumelement Ⓣ(New geometry of space, based on the consideration of the straight line as a space element) (1868) but died before the second part was complete.
- Klein was, at this time, his assistant and had discussed the ideas that Plücker intended to develop in this second part.
- Klein therefore carried out the plan as envisaged by Plücker publishing the second volume in 1869.
- Plücker developed this idea over several years and the final result is contained in the posthumous memoir, edited in 1868-69 by Klein and Clebsch, entitled "New Geometry of the Space based on the Consideration of a Line as a Space Element".
- Strangely enough, in the period when four-dimensional manifolds appeared in relativity theory and became fashionable, nobody compared the Minkowski fourfold and the Plücker fourfold which appeared 50 years earlier.
- Plücker is buried in the Alter Friedhof (Old Cemetery) in Bonn.

Born 16 July 1801, Elberfeld (now Wuppertal), Duchy of Berg (now Germany). Died 22 May 1868, Bonn, Germany.

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Astronomy, Origin Germany

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