# Ann Varela: James Maxwell- Mathematician from Edinburgh to Cambridge and Back

An Interview with Ann Varela: James Maxwell- Mathematician from Edinburgh to Cambridge and Back

1) Ann, James Maxwell was a fascinating mathematician, with fascinating ideas and was widely regarded during his lifetime. Let’s start with his early life- when was he born and what were his early years like?

Maxwell was born “James Clerk” in 1831 in Edinburgh, Scotland, to parents who were in their late thirties. While still a toddler, the Clerk family moved to an inherited estate at Glenlair from the Maxwell side of the family tree. It was then that his father, a lawyer, assumed the additional family name of Maxwell.

As an only child, he was close to his parents and even educated by his mother for the first eight years of his life. The death of his mother made it necessary to engage a tutor for young Maxwell’s continued learning. Maxwell’s father hired a teenaged tutor who proved to be too harsh and abrasive toward the younger Maxwell. By the age of ten, it was now time for Maxwell to receive a formal education from Edinburgh Academy. This did not go well. Maxwell was used to a more free and spontaneous learning environment. The confines of school and enduring mocking peers made the transition to a formal education a difficult one until he made the acquaintance of Lewis Campbell and Peter Guthrie Tait who would become his life-long friends.

Maxwell excelled in mathematics, English, and poetry at the academy and won prizes in all of those subjects. At the age of thirteen, geometry was his current passion. Apparently, Maxwell did not overly concern himself with earning high marks in school, yet managed to write a scientific paper at the age of fourteen. The topic of the paper was drawing mathematical curves with a piece of string. His manuscript “Oval Curves” was presented to the Royal Society of Edinburgh. Although his work was not original (Descartes also studied these same ellipses), Maxwell did manage to streamline the construction of multifocal ellipses.

Maxwell was adept at memorization and was inquisitive about his surroundings. He was inquisitive and pondered the workings of his environment to exhaustion. Not long after his publication, Maxwell was admitted to the University of Edinburgh. In 1854, he graduated from Trinity College in England with a mathematics degree, which led him to receive a fellowship to Cambridge where he became a tutor. Not long after that, he became a professor at Marischal College in Aberdeen, Scotland. Unfortunately, Maxwell’s teaching career at Marischal College only lasted four years due to restructuring of the faculty. Nevertheless, he obtained a professorship at King’s College, London and remained there for six years. In fact, he implemented important research at King’s College pertaining to his kinetic theory of gases and research demonstrating color photography.

2) Now, Maxwell seemed to be able to integrate various fields- such as electricity, magnetism and light- and believed they were all part of the same phenomenon. Can you explain this to me?

In the mid 1800’s, William Thomson, Maxwell’s mentor, established a common mathematical foundation fundamental to various areas of physics including heat, mechanical motion, fluid motion, electricity, and magnetism. This foundation made it possible to expand upon work done previously by other notable scientists. The unification of foundations in math and physics enabled Maxwell to associate electromagnetism with light and later with radio waves. Maxwell was able to calculate the speed of propagation of an electromagnetic field and found it to be similar to the speed of light. This provided the foundation for Einstein’s research on relativity. In fact, Einstein once said, “The special theory of relativity owes its origins to Maxwell’s equations of the electromagnetic field.”

3) Apparently Maxwell was thought of as second only to Isaac Newton in terms of physics- what were his contributions?

Maxwell was motivated to study the rings of Saturn because it was the topic of the Adam’s Prize in 1857. Maxwell spent two years performing mathematical computations to prove that Saturn’s rings are composed of numerous small particles, each individually circumnavigating Saturn. His work predicted that a regular solid ring could not be stable. He claimed that a liquid ring would produce a wave-like motion, which would ultimately separate into globules. It was not until Voyager’s images of Saturn’s rings in the 1980’s that finally proved Maxwell’s prediction to be true. See Figure 1. A famous quotation from Sir George Biddell Airy states, “It is one of the most remarkable applications of mathematics to physics that I have ever seen.”

Figure 1

https://www.famousscientists.org/fs/wp-content/uploads/2014/07/maxwell-saturn-rings.jpg

4) Electric and magnetic fields- what do they have to do with math?

One of Maxwell’s greatest accomplishments was to express all of the present-day (up to 1855) knowledge of electricity and magnetism into a connected set of differential equations with twenty equations in twenty variables. Differential equations relate a function with its derivatives. Commonly, in applications, a function represents physical quantities, while derivatives represent their rates of change, and the equation describes an association between these attributes.

Four of Maxwell’s equations dealt specifically with field theory. Maxwell was able to calculate the speed of electromagnetic waves and found their speed was similar to the speed of light. It was his conclusion that light was an alternative form of an electromagnetic wave. He thought this suggested that other forms of electromagnetic waves could exist. Maxwell’s claim was substantiated in 1887 when Heinrich Hertz produced the first synthetic radio waves.

5) Quantum mechanics- what does this mean and why is it relevant?

Maxwell’s research and discoveries helped to introduce the age of contemporary physics, making it possible for the field of quantum mechanics to be established. Quantum mechanics uses mathematics to describe motion and interaction of subatomic particles. It endeavors to describe and explain the properties of molecules and atoms. Quantum mechanics explores how the particles interact with one another and with electromagnetic radiation.

Maxwell was able to apply quantum mechanics (although it was not formally known as quantum mechanics at this time) to his theories of electromagnetic fields in 1865. He demonstrated that electric and magnetic fields travel through space as waves. Those waves were moving at the speed of light. He related the fields of light and magnetism via quantum mechanics by experimentation. It was not until 1927, that the field of quantum physics materialized. It was later found that the subatomic particles that Maxwell was studying actually were not exclusively particle or wave, but instead contained certain properties of each.

6) Apparently, he was the first to show a color photograph. Is this correct?

Maxwell lectured to the Royal Society of Edinburgh on his *Experiments of Colour *in 1855. However, it was while he taught at King’s College, that Maxwell first demonstrated colored photography. Maxwell’s experiments involved using a color wheel and filtering light through three different colored filters. His technique later became known as the color separation method. A photograph of tartan ribbon is shown in Figure 2.

Figure 2

http://www.odec.ca/projects/2007/hugg7a2/Images/tartan_ribbon_diagram.png

7) In some survey, Maxwell was thought to be the third greatest physicist of all time, surpassed, only by Sir Isaac Newton and Einstein. Thus, he should be held in high regard. What do you see as his major accomplishments?

Maxwell’s theories branched off into other important theories in the twentieth century. One example is Einstein’s theory of relativity developing from the electromagnetic theory and its related field equations.

Quantum theory was another major revolution of the twentieth century. Quantum theory applies to chemistry, superconducting magnets, light-emitting diodes, lasers, transistors, and semiconductors. Without this knowledge we would not have the necessary technology to construct medical imaging machines. Infra-red telescopes used in space exploration also use electromagnetic radiation.

Maxwells’s research made it possible for present-day advancements in the communications field. Applications of electromagnetic radiation exist in radio, television, radar, microwaves and thermal imaging.

In engineering, Maxwell defined most of the electrical units operational today. He led the way with developing calculations that modeled stresses in framed arches and suspension bridges.

Maxwell had an aptitude for envisioning phenomena and then deriving equations to show the relationships pertaining to such peculiarities. One such example involves a “curl” that exists in the electromagnetic field. He coined the term “curl” to designate the vector operator. See Figure 3.

Figure 3

8) His later years were spent at Kings College in London. What were his accomplishments there?

At just 29 years of age, Maxwell performed experiments for his kinetic theory of gases and research demonstrating color photography. His work with color photography earned him the Royal Society’s Rumford Medal in 1860. One year later, he was elected to the Royal Society. Although the kinetic theory of gases was studied previously by Daniel Bernoulli, Maxwell’s ideas were revolutionary. He theorized that temperatures and heat involved only molecular movement, not certainty of flow direction. His theory modified Bernoulli’s theory in the following way: molecules of higher temperatures have only a high probability of moving toward those at lower temperatures. Maxwell also determined that there are 8 billion collisions of air molecules per second at room temperature.

One noteworthy accomplishment of Maxwell’s during his time at King’s College includes developing a system of defining physical quantities (now known as dimensional analysis). Dimensional analysis looks for connections between molecules (in this case) and their different physical quantities. Identification of molecular dimensions like length, mass, time, and electric charge can be compared with units of measure. Then, comparisons can be noted. Another of Maxwell’s topics of study was electromagnetic induction. This area consists of miniscule spinning cells of magnetic flux. Each point on a surface is linked with a direction, called the surface normal. The magnetic flux through a point is then the section of the magnetic field along this direction. See Figure 4.

Figure 4

Maxwell was also fortunate to attend lectures at the Royal Institution. This is how he became acquainted with Michael Faraday, who greatly inspired Maxwell and may explain why Maxwell’s research was sometimes an extension of Faraday’s work.

9) What have we neglected to mention about this astoundingly famous and brilliant mathematician?

Maxwell was notorious for his sense of humor. Apparently, his conversations were laced with comic anecdotes. He even poked fun at himself instead of retaliating against those who poked fun at him. It seems he was a bit of a jokester at Marischal College, but had to tame his tongue, as others did not share his sense of jocularity.

Maxwell was also a poet and his sense of humor is magnificently demonstrated in his poem entitled, *“A Problem in Dynamics.”*