**Enno Heeren Dirksen**'s parents were Dirk Heeren Dirksen and Elisabeth Berends. Dirk had been born in Bedekaspel in 1737 but moved to Eilsum were he was an agricultural worker. He met Elisabeth in Eilsum. She had been born in Visquard in 1752 and, when she met Dirk, was working as a maid in Uiterstewehr. Dirk and Elisabeth were married in 1784 and only one of their children, Enno Heeren the subject of this biography, survived beyond childhood. Frisia, the area where Enno was born, was divided into Friesland, East Friesland and North Friesland in 1815. We have already mentioned the villages of Bedekaspel, Eilsum, Uiterstewehr and Visquard, all in East Friesland (or Ostfriesland) within a 15 km radius of Emden, the main city in the district and a seaport on the river Ems.

It is possible that Enno lived for a while in Hamswehrum, about 7 km south west of Eilsum (and still within 15 km of Emden), as he was growing up since he had relations there and a number of older biographies incorrectly gave Hamswehrum as his place of birth. Between 1803 and 1807 Dirksen received private lessons in mathematics, physics, astronomy and navigation from Cornelius Voorn who was a teacher at the Emden Navigation School. At this stage Voorn hoped that Dirksen would succeed him as teacher at the Navigation School. After completing this course of private lessons, Dirksen became a teacher in Hatzum, about 10 km south east of Emden. He taught there until 1815 when he moved to Hinte, 6 km north of Emden, where again he taught in the local school. Soon after he began teaching in Hinte, Jabbo Oltmanns, a mathematician who worked in Emden, suggested that Dirksen should study mathematics at Göttingen University to improve his mathematical skills. On 22 April 1817, he followed Oltmanns' suggestion and matriculated at Göttingen. He spent three years there being taught by Gauss as well as by B F Thibaut, J T Mayer and G F Sartorius. Bernhard Friedrich Thibaut (1775-1832) was the professor of mathematics at Göttingen and renowned as an exceptional teacher. Johann Tobias Mayer (1752-1830), the son of Tobias Mayer, was a physicist who had written well-known mathematics and physics textbooks. Georg Friedrich Sartorius (1765-1828) was the professor of economics and history.

Dirksen studied for his doctorate advised by Mayer and Thibaut, although he also assisted Gauss in calculating the orbits of comets and asteroids. He was awarded his doctorate on 5 February 1820 for his thesis *Historiae progressuum instrumentorum mensurae angulorum accuratiori interserventium inde a Tob. Meyeri temporibus ad umbratione non de artificio multiplicationis* Ⓣ. In this work he considered the improvements which had been made to the reflecting circle after it was invented by Tobias Mayer. In October 1819 Dirksen had requested support from the ministry in Hanover so that he could spend a year in Berlin working at the Academy of Architecture with Johann Albert Eytelwein. This was approved and he went to Berlin early in 1820 but quickly changed his plans and began working for the astronomer Johann Elert Bode (1747-1826), the director of the Berlin Observatory who is famed for 'Bode's law' giving distances of the planets from the sun. Dirksen assisted Bode both in making observations and in doing mathematical computation and he habilitated at Berlin University on 6 May 1820 as an expert in astronomy in the Mathematics Department. His inaugural lecture was entitled *Über eine zweckmässige Methode, die Opposition eines Planeten mit der Sonne zu berechnen* Ⓣ. It discussed a method of calculating the opposition of a planet with the sun.

On 26 August 1820 the Prussian Ministry appointed Dirksen as an extraordinary professor in Berlin University and four years later, on 18 June 1824, he was appointed as a full Professor of Mathematics. Two months later Jabbo Oltmanns, a friend who he had known when in Emden, was appointed as Professor of Applied Mathematics in Berlin University. Dirksen was elected to the Berlin Academy of Sciences on 9 June 1825 and over the next twenty plus years he served both the University and the Academy. He married Pauline von Wingene (1809-1858) in 1838; they had one son who died as a baby. He retired from teaching at the University in the winter semester of 1848-49 and, already seriously ill, went with his wife to Paris. After his death in Paris he was buried in the Montmartre cemetery.

We cannot rate Dirksen highly as a research mathematician but his role in the development of Berlin University as a world-class mathematical centre is substantial. One of the most notable contributions he made was in his role as a thesis advisor. Among around twenty students whom he advised, the most famous are Carl Jacobi (doctorate in 1825), Adolph Göpel (doctorate in 1835), and Eduard Heine (doctorate in 1842). We must, however, also mention some of his publications. *Analytische Darstellung der Variations-Rechnung, mit Anwendung derselben auf die Bestimmung des Grössten und Kleinsten* Ⓣ (1823) is one of the earliest comprehensive accounts of the calculus of variations. This work was highly praised in reviews at the time and recommended as necessary reading by anyone wishing to delve deeply into the calculus of variations. He also published *Über die Anwendung der Analysis auf die Rectification der Curven, die Quadratur der Flächen und die Cubatur der Körper* Ⓣ (1835) and *Über die Darstellbarkeit der Wurzeln einer allgemeinen algebraischen Gleichung mittelst expliceter algebraischer Ausdrücke von den Coëfficienten* Ⓣ (1836). His final work was the first part of *Organon der gesamten transcendenten Analysis* Ⓣ (1845) in which he tried to unify many different problems in transcendental number theory. Extensive notes and drafts of further parts of this work were among the manuscripts he left at the time of his death.

Finally we note that his somewhat old-fashioned approach to mathematics at a time when new techniques were rapidly being developed led to arguments between Dirksen and various colleagues. Perhaps the colleague with whom he argued most frequently was Martin Ohm. However, it is clear that Martin Ohm fell out with all his colleagues both because of his views on teaching and the fact that he thought so highly of himself.

**Article by:** *J J O'Connor* and *E F Robertson*

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