Georg Simon Ohm — The Physicist Who Made Electricity Calculable

A Wasted Opportunity at Erlangen

In 1805, at age 15, Ohm entered the University of Erlangen. Instead of applying himself, he spent his first three semesters dancing, ice skating, and playing billiards. His father, furious at the waste of opportunity, pulled him out and sent him to Switzerland.

Teaching and Self-Study in Switzerland

In September 1806, Ohm accepted a position as a mathematics teacher at a school in Gottstadt bei Nidau, Switzerland. When his former professor Langsdorf moved to Heidelberg University in 1809, Ohm hoped to follow and restart his studies there. Langsdorf advised against it, instead recommending that Ohm study independently through the works of Euler, Laplace, and Lacroix.

Reluctantly, Ohm followed this advice. He left his teaching post in March 1809 to become a private tutor in Neuchâtel, where he spent two years tutoring while continuing his private mathematical studies.

The Doctorate

In April 1811, Ohm returned to the University of Erlangen. His years of independent study had prepared him well — he earned his doctorate on 25 October 1811 and immediately joined the faculty as a lecturer in mathematics. The position paid poorly and offered little prospect for advancement.

Poverty and Dead-End Teaching Posts

Ohm's early career was a cycle of financial hardship and unsatisfying positions. After three semesters at Erlangen, he resigned because he could not survive on his lecturer's salary. In January 1813, the Bavarian government offered him a post teaching mathematics and physics at a poor-quality school in Bamberg. Deeply unhappy, he began writing an elementary textbook on geometry to prove his abilities.

When the Bamberg school closed in February 1816, the government transferred him to another overcrowded school to help with mathematics teaching — another dead end.

The Geometry Book That Changed His Fortune

Ohm sent his completed geometry manuscript to King Wilhelm III of Prussia. The King was impressed enough to offer Ohm a position at the Jesuit Gymnasium of Cologne on 11 September 1817. This school had a strong reputation for science education and, crucially, a well-equipped physics laboratory.

For the first time in his career, Ohm had the instruments and space to conduct real experiments.

Discovering Fourier and Ørsted

During his years in Cologne, Ohm read voraciously. He worked through the leading French mathematicians — Lagrange, Legendre, Laplace, Biot, and Poisson — and then discovered the work of Joseph Fourier, whose Théorie Analytique de la Chaleur (1822) presented a complete mathematical theory of heat conduction. Fourier's approach — describing the flow of heat through materials using precise equations — became the template for Ohm's own thinking about electricity.

In 1820, Ohm learned of Hans Christian Ørsted's discovery that electric current creates a magnetic field. This breakthrough opened the door between electricity and magnetism, and inspired Ohm to begin his own electrical experiments in the Cologne laboratory.

First Experiments with a Voltaic Pile (1825)

In 1825, Ohm published his first paper on electricity, examining how the electromagnetic force produced by a wire decreased as the wire's length increased. His experimental setup was ingenious: he measured the deflection of a compass needle placed near a current-carrying wire, using this as a proxy for current strength. Ammeters had not yet been invented.

His power source was a voltaic pile — an early battery invented by Alessandro Volta. The results were frustratingly inconsistent. The problem, not obvious to researchers at the time, was that voltaic piles produce unstable voltage that drops under load.

The Thermocouple Breakthrough (1826)

Ohm's colleague Johann Christian Poggendorff suggested he try a thermocouple, a device based on Thomas Johann Seebeck's 1821 discovery that holding two different metals at different temperatures produces a stable voltage.

Ohm constructed a bismuth-copper thermocouple, immersing one junction in boiling water at 100°C and burying the other in ice at 0°C. This gave him a power source that delivered constant, reproducible voltage for over 30 minutes — a dramatic improvement over the voltaic pile.

In two papers published in 1826, Ohm gave a mathematical description of electrical conduction modelled directly on Fourier's study of heat conduction. These papers represented the first steps toward a comprehensive theory.

The Law — V = IR

Ohm's experiments revealed a fundamental relationship: for a given conductor, the current flowing through it is directly proportional to the voltage applied across it and inversely proportional to the conductor's resistance.

Where V is voltage (potential difference) in volts, I is current in amperes, and R is resistance in ohms (Ω). The equation can be rearranged to I = V/R or R = V/I — twelve total formulas when combined with the power equation P = VI.

The Book — Die galvanische Kette, mathematisch bearbeitet (1827)

In 1827, Ohm published his complete theory in a 245-page book titled Die galvanische Kette, mathematisch bearbeitet (The Galvanic Circuit Investigated Mathematically). The book opens with the mathematical background necessary to follow the argument — a section that was essential because most German physicists of the era worked in a non-mathematical, qualitative tradition.

Ohm presented his theory as one of "contiguous action" — the idea that electricity propagates between adjacent particles in a conductor, much as heat conducts through matter. He used the term "contiguous particles" to describe this mechanism, opposing the rival concept of "action at a distance."

This work marked the early beginning of circuit theory as a formal discipline, although circuit theory would not become a major field until the end of the 19th century.

Ohm was confident the book would earn him the university appointment he had pursued his entire career. He was wrong.

The Hostile Reception

The reception of Die galvanische Kette was devastating. German academic culture in the 1820s was dominated by the philosophical idealism of Georg Wilhelm Friedrich Hegel, which held that scientific truths could be deduced through pure reasoning and that experimental methods were inferior to philosophical argument. Ohm's mathematical, experiment-driven approach clashed directly with this philosophy.

"A Physicist Who Professed Such Heresies"

"A physicist who professed such heresies was unworthy to teach science."

— Johannes Schultz, German Minister of Education, persuaded by Georg Friedrich Pohl

Georg Friedrich Pohl, an influential physics professor in Berlin and adherent of Hegel's school, attacked the book viciously. Pohl rejected the very premise that experiments could yield scientific conclusions. He called Ohm's results "an unmistakable failure" and persuaded Johannes Schultz, the German Minister of Education, that Ohm was unworthy to teach. Other critics called the work "a web of naked fancies."

Resignation, Poverty, and Grief

Devastated by the feeling that his own superiors at the Gymnasium were offended by his publication, Ohm declared it impossible for him to retain his position. He resigned from Cologne and moved to Berlin, where he lived in his brother Martin's house. For the next several years, he scraped by tutoring privately and holding temporary positions at minor Berlin schools — what one biographer described as years of "mortification and grief."

In 1833, Ohm finally received a professorship at the Polytechnic School of Nuremberg — an improvement, but still far below the university position he believed his work deserved.

The Copley Medal and International Acclaim

While German academics dismissed Ohm's work, British and French scientists — who were more comfortable with quantitative, mathematical approaches to physics — began to recognise its importance through the 1830s.

The turning point came through Charles Wheatstone, the prominent British physicist and inventor, who drew the attention of the Royal Society of London to Ohm's work. In 1841, the Royal Society awarded Ohm its highest honour: the Copley Medal, for his "researches into the laws of electric currents."

In 1843, Wheatstone introduced the "Wheatstone bridge" circuit by explicitly crediting it to "the principles established by Ohm in his theory of the voltaic circuit" — a public endorsement that carried enormous weight.

Honours Flow at Last

He was also elected to the Accademia delle Scienze di Torino and made an honorary citizen of Nuremberg.

"Their support gave him courage which had previously been softened by mortification and grief."

— Georg Simon Ohm, dedicating his 1849 book to the Royal Society

The Lifelong Dream — A University Professorship

In 1849, Ohm was appointed curator of the Bavarian Academy's physics cabinet in Munich, and became professor of experimental physics at the University of Munich. In 1852, he received the full chair of physics at Ludwig-Maximilians-Universität München. He was 63 years old. The appointment he had pursued for over 30 years had finally arrived.

Decomposing Sound into Pure Tones

Ohm's scientific interests extended well beyond electrical circuits. In 1843, he published a major paper on acoustics in the Annalen der Physik und Chemie titled "Über die Definition des Tones" ("On the Definition of a Tone").

The Dispute with Seebeck

The claim sparked a bitter dispute with the physicist August Seebeck, who argued that Ohm's assumptions about how the ear processes sound were not entirely correct. Seebeck's criticisms had merit — the reality of auditory perception is more complex than Ohm's model — but the core insight that complex sounds can be analysed as superpositions of pure tones was correct and became foundational to modern acoustics and signal processing. Fourier analysis of sound waves is used today in every audio codec, every music equaliser, and every speech recognition system.

The Scooped Discovery and Unfinished Work

In 1849, Ohm published the first volume of Beiträge zur Molecular-Physik (Contributions to Molecular Physics), with plans for three or four volumes exploring the internal dynamics of matter through mathematical principles. However, he abandoned the project when he discovered that a Swedish scientist was about to publish the same original discovery he had recorded.

"The episode has given a fresh and deep sense for my mind to the saying 'Man proposes, and God disposes.' The project that gave the first impetus to my inquiry has been dissipated into mist, and a new one, undesigned by me, has been accomplished in its place."

— Georg Simon Ohm

Ohm was working on a textbook on optics — Grundzüge der Physik als Compendium zu seinen Vorlesungen — when he died. It was published posthumously in 1853–1854, incomplete.

The Ohm Unit (Ω)

In 1881, 27 years after Ohm's death, the International Electrical Congress in Paris officially named the unit of electrical resistance the "ohm" (symbol: Ω) in his honour. One ohm is the resistance between two points of a conductor when a constant potential difference of 1 volt produces a current of 1 ampere.

Before the ohm was standardised, several competing units of resistance existed across different countries, driven by the rapid growth of telegraphy. In 1884, Germany adopted a "legal ohm" as a national standard. The ohm remains one of the most commonly used SI derived units in electrical engineering and physics worldwide.

Henry Cavendish — The Unknown Prior Discoverer

"The first verifier of Ohm's Law."

— James Clerk Maxwell, describing Cavendish

Because Ohm discovered the relationship independently and published it first, the law rightly bears his name.

Impact on Electrical Engineering and Modern Technology

Ohm's Law was the first mathematical relationship established in the science of electricity. Without it, the subsequent development of electrical engineering would have been impossible.

The telephone, electric lighting, the transistor, the computer, and every electronic device ever built depends on the relationship V = IR.

Commemorations

Ohm's legacy is honoured across Germany and internationally. The Technical University of Nuremberg (Georg-Simon-Ohm-Hochschule), the Erlangen Academy, and the Cologne Vocational College all bear his name. His bust stands in the Ruhmeshalle (Hall of Fame) in Munich. A statue of Ohm is displayed in Munich, and a memorial by sculptor Wilhelm von Rümann stands at the Technical University of Munich.

A 1994 German postage stamp commemorated his discovery as part of a series honouring famous German scientific achievements. The large symbol Ω on the plinth of his Munich statue serves as a permanent reminder that the unit of electrical resistance carries his name worldwide.