**Martin Bartels** was a German mathematician best known as the teacher of Gauss and Lobachevsky.

- Heinrich Bartels was a pewterer, making plates and vessels for household use from pewter, an alloy of tin with lead or copper.
- The Bartels lived in Brunswick, which today is the city of Braunschweig in Germany, and their home was on the Wendengraben (today Wilhelmstrasse) beside a canal of the same name.
- Martin Bartels showed a considerable interest in mathematics as a young boy but, in 1783, at the age of fourteen, he was employed as an elementary school teacher in the Katherinen-Volksschule which was close to his home.
- There he was an assistant to the teacher Büttner and soon Bartels began to teach a young boy who, like him, lived on the Wendengraben.
- Bartels did more for Gauss than to induct him into the mysteries of algebra.
- In particular Bartels informed Eberhard August Wilhelm Zimmermann (1743-1815) who had been professor of mathematics, physics and natural history at the Collegium Carolinum in Brunswick since 1766.
- This was extremely valuable for the young Gauss, but this remarkable meeting of minds between Gauss and his young teacher Bartels led to Bartels becoming determined to pursue his study of mathematics.
- Bartels' association with the Collegium Carolinum was formal from 23 August 1788 when he became a visitor there.
- However, mathematics was not the only subject that Bartels studied, for in the winter semester of 1793-4 he studied Experimental Physics, Astronomy, Meteorology and Geology.
- In 1800, Bartels was appointed to teach mathematics in Reichenau, a Swiss town close to the city of Chur.
- However, in 1801 Bartels had moved to Aarau in the north of Switzerland where he taught at the cantonal school.
- Bartels took up his post at professor of mathematics at Kazan in 1808 and, during the following twelve years, he lectured on the History of Mathematics, Higher Arithmetic, Differential and Integral Calculus, Analytical Geometry and Trigonometry, Spherical Trigonometry, Analytical Mechanics and Astronomy.
- In 1808 Nikolai Ivanovich Lobachevsky had the good fortune to study with Bartels at Kazan University not long after he took up his post there.
- Not only did Bartels assist Lobachevsky with his studies, but he also looked after his young student, supporting him when he got into trouble with the authorities (which happened quite often!) When Lobachevsky was due to graduate it was Bartels who spent three days lobbying the other professors to award him a Master's degree.
- Bartels won the argument and Lobachevsky was awarded a Master's Degree.
- After graduating in 1811, Lobachevsky remained in Kazan to study with Bartels who guided his reading of Gauss's "Disquisitiones Arithmeticae" Ⓣ(Investigations in arithmetic) and Laplace's "Mécanique Céleste" Ⓣ(Celestial Mechanics).
- In 1814 it was mainly due to Bartels that Lobachevsky was appointed as an assistant professor.
- We should note that Lobachevsky took Bartels' course on the History of Mathematics which, following Montucla, considered in detail Euclid's Elements and his theory of parallel lines.
- In 1821 Bartels moved to the university in Dorpat (now Tartu in Estonia).
- Bartels founded the Centre for Differential Geometry at Dorpat, and remained there until his death in 1836.
- Bartels made most of his contributions to mathematical research after being appointed to the University of Kazan.
- Some we only know of because his students included the results in their own work acknowledging that Bartels had given them in his lecture courses.
- One such result is the famous Frenet-Serret formulas that were discovered first by Bartels.
- To each point of a space curve Bartels associated a trihedron, which later became called the Frenet trihedron, and Bartels obtained the formulas now known as the Frenet-Serret formulas.
- We only know of this since they were published in a prize work by his student Carl Eduard Senff in Principal theorems of the theory of curves and surfaces in 1831, with due acknowledgement to Bartels.
- Bartels corresponded with Gauss from the time that he was working in Switzerland.
- After Gauss became famous, a joke went round that Bartels was the best mathematician in Germany because Gauss was the best mathematician in the world.
- A couple of years after Bartels moved to Dorpat, he became a Privy Councillor in 1823.

Born 12 August 1769, Brunswick, Brunswick-Lüneburg, Germany. Died 20 December 1836, Dorpat, now Tartu, Estonia.

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Origin Germany

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