James Clerk Maxwell FRS FRSE (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who developed the classical theory of electromagnetic radiation. This theory was the first to explain electricity, magnetism, and light as different forms of the same phenomenon. Maxwell’s equations for electromagnetism helped join electricity, magnetism, and light into one theory, which was the second major unification in physics, following the earlier unification by Isaac Newton. Maxwell also played a key role in creating statistical mechanics.

Maxwell graduated from Trinity College, Cambridge, in 1854, where he excelled in mathematics and won the Smith’s Prize. He briefly stayed at Cambridge, publishing early mathematical work and studying optics, especially the principles of color mixing and color blindness. Later, he became the Chair of Natural Philosophy at Marischal College in Aberdeen, where he studied Saturn’s rings and correctly suggested they were made of many small particles. This work earned him the Adams Prize in 1859. During this time, he married Katherine Mary Dewar, who helped him with laboratory work. From 1860 to 1865, he taught at King’s College London, where he developed his theory of electromagnetic fields. His 1865 paper, A Dynamical Theory of the Electromagnetic Field, showed that electric and magnetic fields travel as waves at the speed of light, proving that light is a wave in the same medium that causes electric and magnetic effects. His work led to the prediction of radio waves.

Maxwell was the first to create the Maxwell–Boltzmann distribution, a method for describing gas behavior based on the kinetic theory of gases. He worked on this topic throughout his career. In 1861, he produced the first lasting color photograph and demonstrated that any color can be made by mixing red, green, and blue, the basis for color television. He also studied the strength of rod-and-joint structures, like those in bridges. He developed modern dimensional analysis and helped create the CGS system of measurement. He was the first to understand chaos and the first to highlight the butterfly effect. His 1863 paper, On Governors, laid the groundwork for control theory and cybernetics and was the earliest mathematical study of control systems. In 1867, he proposed the thought experiment known as Maxwell’s demon, which questions how information affects entropy in thermodynamics. In his 1867 paper, On the Dynamical Theory of Gases, he introduced the Maxwell model for describing the behavior of a viscoelastic material and created the Maxwell-Cattaneo equation for explaining heat transfer.

In 1871, Maxwell returned to Cambridge as the first Cavendish Professor of Physics, overseeing the building of the Cavendish Laboratory. Because of his work, he is considered a founder of modern electrical engineering. His discoveries helped begin the era of modern physics, laying the foundation for fields like relativity (a term he introduced into physics) and quantum mechanics.

Life

James Clerk Maxwell was born on June 13, 1831, at 14 India Street, Edinburgh. His father was John Clerk Maxwell of Middlebie, a lawyer, and his mother was Frances Cay, the daughter of Robert Hodshon Cay and the sister of John Cay. His birthplace now has a museum run by the James Clerk Maxwell Foundation. His father was from the Clerk family of Penicuik, who held the baronetcy of Clerk of Penicuik. His father’s brother was the 6th baronet. His father was originally named "John Clerk" but later added "Maxwell" to his name after inheriting the Middlebie estate, a property owned by the Maxwell family in Dumfriesshire. James was a first cousin of Jemima Blackburn, an artist, and William Dyce Cay, a civil engineer. Cay and Maxwell were close friends, and Cay helped Maxwell during his wedding.

Maxwell’s parents married when they were in their thirties. His mother was almost 40 when he was born. They had one child before him, a daughter named Elizabeth, who died as an infant.

When Maxwell was young, his family moved to Glenlair, in Kirkcudbrightshire, a large estate his parents built. From an early age, Maxwell showed a strong curiosity. By age 3, he asked questions like, "What’s the go o’ that?" about anything that moved, shone, or made noise. His mother wrote about his natural interest in learning.

His mother, Frances, taught him at first because, in the Victorian era, women often handled a child’s education. At age 8, Maxwell could recite long parts of John Milton’s poetry and the entire 119th psalm (176 verses). He knew the Bible well and could find the chapter and verse for almost any quote from the Psalms. His mother later became very sick with abdominal cancer and died in December 1839 when he was 8. After that, his father and his father’s sister-in-law, Jane, helped educate him. His formal schooling started with a tutor, but the tutor was harsh and was fired in 1841. His father took him to see a demonstration about electricity and magnetism by Robert Davidson in 1842, which deeply interested him.

In 1841, at age 10, Maxwell went to Edinburgh Academy, a respected school. He stayed with his aunt Isabella during school terms. His older cousin, Jemima, encouraged his love for drawing. Maxwell, who had grown up in the countryside, struggled to fit in at school. He was placed in a class with older students and was teased for his accent and homemade clothes, earning the nickname "Daftie." He never seemed upset by the name. His loneliness ended when he met Lewis Campbell and Peter Guthrie Tait, who later became famous scholars and remained his lifelong friends.

Maxwell was fascinated by geometry early on, discovering shapes like regular polyhedra before learning about them in school. Though he won a prize for a Bible biography in his second year, his academic work was not noticed until he was 13, when he won a math medal and prizes for English and poetry.

Maxwell’s interests went beyond school, and he focused more on learning than exams. At age 14, he wrote his first scientific paper about using a piece of twine to draw mathematical curves, including ellipses and shapes with multiple foci. The paper, titled "On the Description of Oval Curves and Those Having a Plurality of Foci," was presented to the Royal Society of Edinburgh by James Forbes, a professor, because Maxwell was too young to present it himself. While not entirely original—René Descartes had studied similar shapes before—Maxwell simplified their construction.

Maxwell left Edinburgh Academy in 1847 at age 16 and began studying at the University of Edinburgh. He could have gone to the University of Cambridge but chose to finish his studies in Edinburgh. His teachers included Sir William Hamilton, who taught logic and metaphysics; Philip Kelland, who taught math; and James Forbes, who taught natural philosophy (the study of nature and science). Maxwell found his classes easy and spent much of his free time studying privately. At home in Glenlair, he experimented with homemade tools to study light and stress in materials. Through these experiments, he discovered photoelasticity, a method to see how stress affects physical structures.

At age 18, Maxwell contributed two papers to the Transactions of the Royal Society of Edinburgh. One, "On the Equilibrium of Elastic Solids," laid the groundwork for later discoveries about light refraction in liquids. The other, "Rolling Curves," was again presented by his tutor, Kelland, because Maxwell was too young to speak at the meeting.

In October 1850, Maxwell moved to the University of Cambridge. He first attended Peterhouse but later transferred to Trinity College, where he believed it would be easier to earn a fellowship. At Trinity, he joined the Cambridge Apostles, an exclusive group of scholars who debated ideas. His understanding of science and his Christian faith grew during this time.

During his third year, Maxwell visited the home of the Rev. C. B. Tayler, a family friend. The Taylers’ love for God and their care for him during an illness deeply impressed him.

After returning to Cambridge, Maxwell wrote a letter to the Taylers, expressing his gratitude. In November 1851, he studied under William Hopkins, a teacher known for helping students become top mathematicians.

In 1854, Maxwell graduated from Trinity College with a degree in mathematics. He ranked second in his class, finishing behind only one other student.

Scientific legacy

In a survey of the 100 most well-known physicists by Physics World, James Clerk Maxwell was ranked third greatest physicist of all time, behind Isaac Newton and Albert Einstein. A similar survey by PhysicsWeb also placed him third.

Many scientists believe Maxwell was the most influential 19th-century scientist for 20th-century physics. His contributions are often compared in importance to those of Newton and Einstein. On the 100th anniversary of Maxwell’s birth, Einstein called his work “the most profound and the most fruitful that physics has experienced since Newton.” When Einstein visited the University of Cambridge in 1922, he was told he stood on Newton’s shoulders. Einstein replied, “No. I stand on the shoulders of Maxwell.” Tom Siegfried described Maxwell as “one of those rare geniuses who understood the physical world better than others around him.”

Maxwell studied electricity and magnetism as early as 1855. His paper, On Faraday’s Lines of Force, explained how electricity and magnetism are connected. He created a set of 20 equations that summarized all known knowledge about these forces. This work was published in 1861 as On Physical Lines of Force.

In 1862, while teaching at King’s College, Maxwell calculated that electromagnetic waves travel at nearly the speed of light. He believed this was not a coincidence, stating, “We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”

Maxwell later showed that his equations predicted electromagnetic waves moving through empty space at a speed that could be measured through simple experiments. Using data from his time, he calculated the speed as 310,740,000 meters per second. In his 1865 paper, A Dynamical Theory of the Electromagnetic Field, he wrote, “The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.”

Maxwell’s famous 20 equations, now written as four partial differential equations called Maxwell’s Laws, first appeared in his textbook A Treatise on Electricity and Magnetism in 1873. Oliver Heaviside simplified Maxwell’s theory into these four equations. His work helped unify electricity, magnetism, and light into one theory.

As Barrett and Grimes (1995) noted, Maxwell’s connection between light and electromagnetism is considered one of the greatest achievements in 19th-century physics.

Maxwell also introduced the idea of an electromagnetic field, building on Faraday’s concept of force lines. At the time, he believed light required a medium called the luminiferous aether to travel through. However, experiments like the Michelson–Morley experiment later showed the aether did not exist. This challenge inspired Einstein to develop the theory of special relativity, which eliminated the need for the aether.

Einstein acknowledged Maxwell’s work, stating:

He also noted:

Like many scientists of his time, Maxwell was interested in psychology. He studied color vision, following the work of Isaac Newton and Thomas Young. Between 1855 and 1872, he published research on color perception, color blindness, and color theory. He was awarded the Rumford Medal for his work on On the Theory of Colour Vision.

Newton showed that white light, like sunlight, is made of different colors that can be recombined. He also found that mixing yellow and red paint could look like orange light, even though it was physically different. This created a puzzle: two different lights could look the same. Thomas Young proposed that the eye uses three types of color receptors, a theory called trichromatic color vision. Maxwell used math to prove Young’s idea, showing that three different lights could create the same color. He invented color matching experiments and developed the field of colorimetry.

Maxwell applied his color theory to photography. He proposed that three black-and-white photos taken through red, green, and blue filters could be combined to recreate full-color images. In 1861, he demonstrated this at a Royal Institution lecture. Thomas Sutton took photos of a tartan ribbon using red, green, blue, and yellow filters. However, the photos were not perfect because the photographic materials used were not sensitive to red and green light. Researchers later noted that better materials could improve the results.

Publications

• Maxwell, James Clerk (1873), A treatise on electricity and magnetism, Volume I, Oxford: Clarendon Press
• Maxwell, James Clerk (1873), A treatise on electricity and magnetism, Volume II, Oxford: Clarendon Press
• Maxwell, James Clerk (1876), Matter and Motion, London and New York: Society for Promoting Christian Knowledge and Pott, Young & Co.
• Maxwell, James Clerk (1881), An Elementary treatise on electricity, Oxford: Clarendon Press
• Maxwell, James Clerk (1890), The scientific papers of James Clerk Maxwell, Volume I, Dover Publication
• Maxwell, James Clerk (1890), The scientific papers of James Clerk Maxwell, Volume II, Cambridge, University Press
• Maxwell, James Clerk (1908), Theory of heat, Longmans Green Co.
• Three articles by Maxwell appeared in the Ninth Edition (1878) of Encyclopædia Britannica: Atom, Attraction, and Ether; and three articles appeared in the Eleventh Edition (1911): Capillary Action, Diagram, and Faraday, Michael.