The first 8 years of his life had been wonderfully happy. He was born in Edinburgh¹ but brought up at Glenlair, his father’s estate in the gently rolling Vale of Urr in the Galloway region of south-west Scotland². His parents, John and Frances Clerk Maxwell, had married late and their first child, Elizabeth, had died in infancy. Frances was almost 40 when James was born. She and John adored their son and watched over his development with indulgent devotion. As soon as he could walk and talk a little it became plain that he was a remarkable boy. Like all children he was curious about everything around him, but his curiosity was of a different order and reached into places rarely explored. For example, it was not enough for him to discover how to ring the house bells; he had to find out which of the bell-pulls around the house rang which bell in the kitchen and where all the wires ran. And he could turn everyday objects to surprising uses. One day his nurse Maggy gave him a tin plate to play with. Perhaps he first tried banging it with a spoon or rolling it across the floor but soon he was excitedly calling his mother and father to come and see how he had brought the sun into the house by reflecting its image off the plate on to a wall.

As he grew, he played rough-and-tumble games with the local children, climbed trees, explored the fields and woods and watched the animals and birds with rapt attention. He enjoyed the morning chore of fetching water from the river by cart. Nothing that went on in the house escaped his attention. Nobody could do anything without having young James appear, demanding a full explanation and insisting on having a go himself. He knitted, made baskets, took a hand in the baking and helped his father design and plan improvements to the estate. Like all boys he could be a little monkey at times. One evening, just after dark, he blew out the candle as Maggy was approaching with the tea tray and lay down in the doorway.

He quickly learnt to read and, under his mother’s guidance, began to understand the wider world. He enjoyed history and geography and, especially, literature. Before long he was reading everything within reach. Milton and Shakespeare were particular favourites. What is more, he seemed to remember most of what he had read.

For entertainment, the family would often read novels or poetry aloud or act out a play. And religion was an important part of the domestic routine: every day the household, including servants, met for prayers and every Sunday they went to Parton church, five miles to the west. His father’s background was Presbyterian, his mother’s Episcopalian, but both took a tolerant view of doctrinal matters. The Clerk Maxwells played their full part in the social life of the area; there were fairs and dances and visits exchanged with other leading families. There were also visits to and from relations in Edinburgh and Penicuik, the estate of James’ uncle.

Life at Glenlair was harmonious, stimulating and gently bustling. It was also full of jokes and banter. There was no pomposity whatever—no person, institution or topic was above some gentle debunking. The spirit of these times stayed with James all his life. We shall see this demonstrated time and again but, even so, let us cheat a little by taking a glimpse now at a poem he wrote when he was 26, teasing his friend William Thomson, who was consultant to the Atlantic Telegraph Company, when its cable-laying ran into difficulties.

James’ parents were fairly new arrivals in the Happy Valley, as the Vale of Urr was known to its residents. John Clerk Maxwell was an advocate who had lived most of his life in Edinburgh. He had an adequate private income and it did not matter much to him that his practice never flourished. John’s heart lay elsewhere —in his hobby, which was what we would now call technology. He had built up a wide range of friends in industry, agriculture and universities and enjoyed keeping abreast of new ideas. His life ticked away pleasantly but ineffectively until events took a turn when he was in his late 30s. A long-standing acquaintance with the sister of a friend blossomed into romance and she agreed to marry him. Frances Cay was a spirited and resolute woman who supplied the get-up-and-go he had so far lacked. Both their lives were transformed and Glenlair was the focus. John had inherited the estate some years before and had toyed with the idea of going to live there and applying his ideas on farming. Now the day-dreams changed into hard and purposeful activity—they resolved on setting up home at Glenlair.

Previous owners of the estate had been absentee landlords and there was no suitable dwelling there. But to John this was an advantage: the prospect of designing and building his own family house was irresistible. The house he designed was a modest one for a country gentleman of that time—he planned to extend it later. Impatient to start their new life, he and Frances moved to Glenlair soon after building started and lived in one of the estate cottages until the house was habitable. They launched themselves wholeheartedly into country life, then endured the anguish when their first child died. When Frances became pregnant for the second time they decided to go to Edinburgh for the birth, to be near relations and hospital if needed. Soon after James was born they returned home and family life began.

Glenlair had belonged to John’s family for only three generations. It was the 1500 acre residue of a much larger estate called Middlebie, which had been the seat of the fierce Maxwell clan. John’s family name was Clerk: by the normal reckoning he was not really a Maxwell at all; neither was James. The Clerks had acquired the Middlebie estate by marriage in addition to their own baronetcy of Penicuik, 10 miles south of Edinburgh. They arranged that Penicuik would be passed on to the senior heir and Middlebie to the second, and that whoever inherited Middlebie would add Maxwell to the family name. When John’s grandfather lost a fortune in mining investments most of Middlebie had to be sold, leaving only Glenlair. So it came about that James’ father was John Clerk Maxwell of Glenlair while his uncle was Sir George Clerk of Penicuik.

John and Frances came from exceptionally talented families—previous generations of Clerks and Cays had distinguished themselves in many fields⁴. To do justice to this point would take us too far from our story, but two examples from the Clerk line will give an idea.

James’ great-great-grandfather, Sir John Clerk, was the kind of man whose easy brilliance at everything he did makes most of us despair of our own efforts. As well as being a Baron of the Exchequer of Scotland and a Commissioner of the Union he wrote good music that is still performed today. He was a Fellow of the Royal Society and an influential authority in archaeology, architecture, history, astronomy, geology and medicine.

One of Sir John’s sons, another John Clerk, was a spectacularly successful businessman as well as a gifted artist and geologist. He worked with his friend James Hutton and illustrated a volume of Hutton’s seminal work, Theory of the Earth. But his masterpiece was an essay on naval tactics. It is extraordinary that a landlubber —he never went to sea—should even think of writing such a book, but what is more remarkable is that it became the standard work on the subject. Nelson used several sentences straight from the essay in his orders for the battle of Trafalgar.

There was little evidence in John and Frances’ homely house at Glenlair of their illustrious antecedents. No grand family silver, no portrait gallery. Their one prized heirloom was a battered set of bagpipes which James’ grandfather, a captain in the British East India Company’s Navy, had used to keep afloat when he was shipwrecked. The lack of formal trappings made it a wonderful home for their son. James had a much closer relationship with his parents than was usual among the gentry; his mother became his tutor and his father often took him along when dealing with estate business. This still left him plenty of time to run around with the local children. He learnt their Galloway speech and acquired a local accent that he would never entirely lose. No child could have been happier, but sadness was to come.

Frances became ill and abdominal cancer was diagnosed. She decided to have an operation without anaesthetic. The chances of success were slim but she wanted to live longer if possible for the sake of her husband and son and so chose to undergo this excruciating treatment. But the operation was not successful and Frances died soon afterwards. She was 47 years old.

Frances had been the hub of the family; without her the house at Glenlair must have been a desolate place for a while. Heavy of heart, John and James were glad, at least, that her suffering was over. The loss brought them even closer together and the father enjoyed his son’s lively companionship. There was, however, the problem of schooling. The plan had been for James to be educated at home until he was 13, when he would go straight to university. But John was too busy with the estate and with various county boards and committees to teach the boy himself. There was no suitable school within daily travelling distance and he dreaded the loneliness that would follow if he sent James away.

He decided to engage a private tutor and chose a 16 year-old boy from the neighbourhood. The lad had done well in exams at school but delayed going to university so he could take the post. No-one then or since has been able to fathom how John Clerk Maxwell came to make such an ill-judged choice. Knowing he had an exceptionally gifted son, how could he entrust his education to a youth with little knowledge and no experience of life beyond school? Whatever the reasons, the results were disastrous.

The tutor used the methods by which he had himself been taught: rote learning encouraged by physical chastisement. The lessons became a moral and physical ordeal. James wanted to please his father but saw no sense in the mechanical recitation of words and numbers divorced from any meaning. No amount of ear pulling and cuffing about the head could persuade him to learn in that fashion. His local friends had no doubt suffered similar treatment at school, so perhaps he thought it was simply something that had to be endured. But eventually, after more than a year of torment, he rebelled.

Beside a duck pond near the house was a large washtub that James used to use as an improvised boat. In the middle of a lesson, his tolerance exhausted, he ran out, pushed the tub into the water, jumped in and paddled himself to the deepest part of the pond. Ignoring the tutor’s urgings, he refused to come in. Although reproved by his father for this act of rebellion, James had made his point.

His Aunt Jane, Frances’ younger sister, who lived in Edinburgh, was quick to understand what had been going on and persuaded John that it was high time that 10 year-old James had proper schooling. John’s widowed sister, James’ Aunt Isabella, who also lived in Edinburgh, agreed. The Edinburgh Academy⁵, one of the best schools in Scotland, was only a short walk from her house; James could stay with her during term time and return to Glenlair for the holidays. Much as he hated the thought of parting from his son, John could see that Jane and Isabella were right and agreed to the plan.

Unfortunately, the first year class was full, so James had to enrol in the second. There he would be joining a class of 60 older boys who had already spent more than a year in the school, long enough to have absorbed its conventions and developed their own schoolboy culture. They were mostly from smart Edinburgh families and spoke with refined accents. Clearly, life was not going to be easy for the newcomer. What made things even harder was that his father had designed and made special clothes for him. From a logical standpoint, they were excellent: warm, hard-wearing and comfortable, with a loose tunic and square-toed shoes. But John seemed oblivious to the human factor: to the boys in James’ new class, in their conventional tight jackets and slim shoes, the newcomer looked like a ridiculous peasant from a foreign land.

So it was that James arrived for his first day at the city school, a country boy with a strange accent and wearing peculiar clothes. As we have seen, he was tough enough to ride out his rough reception and parry the taunts. A hard time lay ahead, but in the end the attitude of his classmates was to turn from ridicule to acceptance, and finally to admiration.

His mind was a-whirr with impressions, thoughts and part-formed ideas. For a long while these found no expression at school. He was, as a classmate later put it, like a locomotive under full steam but with the wheels not gripping the track. More than a year went by before he made a real friend. But he showed himself to be strong and brave and these qualities commanded respect. He sought no quarrels and bore no grudges: for all his odd ways it became plain to everyone that he was good-natured and generous.

Two things held him back in class at first. One was the numbing effect of the repetitive exercises in Greek and Latin, harking back to the time with his tutor. The other was a hesitancy of speech, the words coming in spates between long pauses. This defect remained with him to some extent all his life and may also have stemmed from his time under the tutor. He eventually managed to overcome the worst of the problem by projecting a mental image of answers to the master’s anticipated questions on to the classroom windows, so he could simply read them out when needed.

At Aunt Isabella’s house¹ there were no such problems. Life there was congenial and stimulating. The library was even better stocked than that at Glenlair and he was soon reading Swift and Dryden.

He loved to draw and had the example of his cousin Jemima, who had often brought her sketchbook to Glenlair and was now a rising young artist. Landseer had said that ‘in portraying animals he had nothing to teach her’ and she was soon to have pictures exhibited in the Royal Academy². Jemima was also learning woodcutting and let James borrow her tools. His artistic efforts displayed more gusto than skill but had a rugged charm that made them his own.

Sometimes he and Jemima combined their talents by producing ‘wheels of life’ for parlour entertainment. A series of pictures, like an animated cartoon film, was set on a spinning wheel or cylinder so that one saw the images in rapid succession and got the impression of movement. James designed and made the machines and sketched sequences of pictures, which Jemima would then draw—a favourite sequence showed a rider doing acrobatic tricks on the back of a galloping horse.

His father came to Edinburgh whenever he could. When he was in town on a Saturday the two would walk up the rocky hill, Arthur’s Seat, or visit other local attractions. Every new experience fed James’ probing and retentive mind. One of these Saturday treats was to see an exhibition of ‘electromagnetic machines’. The sight of these primitive devices—nothing like the generators and motors we know today—started in the boy’s mind a process of thought that would ultimately transform the way physicists think about the world, a change that Einstein called ‘the most profound and useful that physics has experienced since the time of Newton’.

When they were apart, father and son wrote to one another frequently. James’ letters were full of childish jokes in which his father clearly took delight. He signed them with anagrams of his name, such as Jas Alex McMerkwell, and addressed some of them to Mr John Clerk Maxwell, Postyknowswhere, Kirkpatrick Durham, Dumfries. One letter, just after his 13th birthday, gives a tiny hint of things to come. After fulsome accounts of a minstrel show and a trip to the beach, he asks about events and people at Glenlair and finally mentions ‘I have made a tetrahedron and a dodecahedron and two more hedrons that I don’t know the right names for’. He had not yet learnt any geometry in school but had somehow found out about what mathematicians call the regular polyhedra: solid figures whose faces are all identical polygons and whose vertex angles are all equal. There are only five of them: the most familiar is the cube, which has six faces; the others have four, eight, 12 and 20. James quickly worked out how to make them out of pasteboard and went on to make other symmetrical solids derived from the basic ones.

We do not know what triggered his thoughts on this topic: he may have read something but it is unlikely to have been a mathematical account. Whatever the stimulus, James’ response showed an intuitive grasp of symmetry and a flair for exploring different forms of it, qualities that later shone through his scientific work.

At first, the method of teaching in James’ class was not very different from that of his old tutor. The boys spent long hours reciting Greek verbs and doing routine arithmetical exercises, and the class master, Mr Carmichael, was free with the tawse —a fearsome leather strap cut into strips at the end. But gradually the rote-based drudgery gave way to more appealing work and James began to take interest and be noticed. From somewhere near the bottom of the class in his first year, he rose to 19th overall in the second and won the prize for scripture biography.

He came to see that Greek and Latin were worth learning and his position in class improved. As the boys had to sit in places corresponding to their rank in the class, he now found himself in more sympathetic company. His knowledge of the Bible, which probably exceeded that of the masters, helped him to win the scripture biography prize in his second year, but it was in the third year that things really started to happen. Mathematics lessons began and ‘Dafty’ astonished his classmates by the ease and speed with which he mastered geometry. His confidence boosted, he became less reticent in the other lessons; he began to shine in English and was soon in the top group in all subjects.

By a stroke of luck, Lewis Campbell’s family moved to a house almost next door to Aunt Isabella’s. Lewis was the star of James’ class, a very clever boy who was well liked and usually came top. He and James had just begun to strike up a friendship before the move. Now they walked home together, often continuing the conversation by an open front door until voices from inside complained of the draught. The world opened up for James. For the first time he could share his teeming ideas with someone of his own age. Geometry was their first common ground but soon the topics ranged over the full sweep of their experiences and thoughts. It became a lifelong friendship. When Maxwell died at the age of 48, Campbell wrote a moving biography.

James’ friendship with Lewis Campbell put an end to his social isolation in school. Soon he found himself among a group of boys with lively minds who enjoyed his whimsical chatter and his unending flow of thought-provoking ideas. Among them was another who was to become a lifelong friend, Peter Guthrie Tait³.

P. G. Tait became one of Scotland’s finest physicists. As we shall see, the careers of Maxwell and Tait ran closely in parallel: more than once they found themselves competing for the same post. But friendship far outstripped rivalry and they continued the practice, begun as schoolboys, of bouncing ideas off one another. At school the two of them were always challenging each other with ‘props’, mathematical propositions or problems⁴. One was to find the shape of a mirror that would show a person his image the right way round. When both were senior professors, their letters, or more often postcards, were still written in a kind of schoolboy argot, more polished than that of 25 years earlier but just as exuberant.

We now come to James’ first publication. He was 14. It was about the kinds of curves that can be drawn on a piece of paper using pins, string and a pencil. Everyone knows that if you (1) stick in a pin, (2) tie one end of a piece of string to it and the other end to a pencil and (3) draw a curve by moving the pencil with the string taut, then the curve will be a circle. Groundsmen use the same method to mark out the circles in the middle of football pitches. People who have studied a little geometry will know that the construction can be modified in an interesting way. If you use two pins instead of one, tie one end of the string to each, push the pencil against the string and move the pencil while keeping the string taut, you get an oval-shaped curve called an ellipse. Each pin is at one of the two focal points of the ellipse (just as the sun is at one focal point of the earth’s elliptical orbit). If you put the pins close together the ellipse will be almost like a circle; the further you put them apart, the flatter the oval shape becomes.

For most people this would be the end of the matter. Not so for James. He untied one end of the string from its pin and tied it to the pencil instead. Then he looped the string around the free pin, pushed the pencil against it to make it taut, and drew another curve. It was a pleasing but lop-sided oval, like the outline of an egg. This was just the beginning. He reasoned that the simple ellipse could be defined as the locus of a movable point from which the sum of the distances to the two focal points (pins) was constant (the length of the string). As an equation: where p is the distance to one focal point, q is the distance to the other and s is the length of the string. When drawing his new oval he had doubled the string between the pencil and one of the two focal points, so the equation was:

It was not unusual for James to produce geometrical propositions. He was doing it all the time. But his father decided to show this set to James Forbes, a friend who was professor of natural philosophy at Edinburgh University. He and his mathematical colleague Philip Kelland were struck by the boy’s ingenuity.

They combed the mathematical archives to see if anything at all similar had been done before. Sure enough, it had—by no less a person than René Descartes, the famous seventeenth century French mathematician and philosopher. Descartes had discovered the same set of bi-focal ovals but James’ results were more general and his construction method simpler. What is more, his equation for bi-focal curves turned out to have a practical application in optics.

Here was James’ debut on the scientific stage. Forbes read the paper⁵ to the Royal Society of Edinburgh because James was deemed too young to do it himself. It generated a lot of interest. Among those interested was D. R. Hay, a printer and an artist whose attempts to create pleasing shapes by mathematical means were well known in Edinburgh. It was his quest for ‘the perfect oval’ that had prompted James to experiment with pins and string. It transpired that Hay had also tried pins and string and had eventually had some success using three pins. But he used just a simple loop. This gave an oval made up from three part-ellipses joined together, neat but not very beautiful. The question ‘Why didn’t I think of that?’ comes to all of us at some time but rarely as emphatically as it must have struck Mr Hay when he saw James’ solution.

Level-headed as he was, James enjoyed the celebrity. His father was pleased as Punch. But the ovals paper marked the start of James’ scientific career in another, far more significant, way. It introduced him to the work of René Descartes, one of the great creators of mathematics. As it happens, he soon found a small mistake in the great man’s calculations, but the overwhelming feeling he had was one of fellowship. He went on in later years to read the work of all the pioneers in each area of science to which he turned his hand.