He earned his doctorate in 1811 at Friedrich-Alexander-University, Erlangen-Nuremberg where his advisor was Karl Christian von Langsdorf. In 1817, he was appointed professor of mathematics and physics in the gymnasium at Thorn. In 1821 he moved to Berlin, and in 1839 became a full professor in the University of Berlin. He delivered courses of lectures at the academy of architecture from 1824 to 1831, and at the schools of artillery and engineering from 1833 to 1852; and he also taught in the military school from 1826 to 1849.
Ohm was the first to fully develop the theory of the exponential ab when both a and b are complex numbers in 1823. He is also often credited with introducing the name "golden section" (goldener Schnitt).
Ohm's students included Friedrich August, Friedrich Bachmann, Elwin Bruno Christoffel, Paul Bachmann, Joseph Brutkowski, Heinrich Eduard Heine, Rudolf Lipschitz, Leo Pochhammer, Friedrich Prym, Wilhelm Wagner, Hermann Waldaestel, Wilhelm Wernicke, Elena Gerz, Valentien Gerz, and Johanna Gerz.
- Cajori, Florian (1991). A History of Mathematics (5e ed.). pp. 329–330. ISBN 0-8218-2102-4.
- Ripley, George; Dana, Charles A., eds. (1879). "Ohm. II. Martin". The American Cyclopædia.
- Underwood Dudley (1999). Die Macht der Zahl: Was die Numerologie uns weismachen will. Springer. p. 245. ISBN 3-7643-5978-1.
- "Martin Ohm". Mathematics Genealogy Project.