Celebrating Mary Somerville

When the Royal Bank of Scotland (RBS) issues its new ten-pound note towards the end of 2017, the 19th century’s “Queen of Science” will surely inspire new generations in her homeland. But the legacy of self-taught mathematician Mary Fairfax Somerville reaches way beyond Scotland: she was a brilliant translator of science for the public and a passionate advocate for women’s education.

The RBS’s new polymer note shows Mary as a young woman; but she was 50 years old by the time she shot to fame in 1831, after the publication of her cutting-edge Mechanism of the Heavens. Academics were astounded: it was said that no more than five men in Britain were capable of writing such a demanding book, based as it was on the work of leading French mathematician Pierre-Simon Laplace. It was a phenomenal achievement for a woman who taught herself science and mathematics at a time when most universities did not admit females. Mechanism of the Heavens was not just a momentary curiosity; it was used as a textbook in Cambridge’s advanced mathematical astronomy classes for the next century.

This latest accolade stems from RBS’s decision to issue its first polymer banknotes. For the new banknote, Somerville was selected in an online competition. She garnered many votes from students at Somerville College. Oxford’s first women’s college (it became coeducational in 1994) was named after her in 1879, just a few years too late for her to enjoy the honour. She died in 1872, just shy of 92.

Mary Fairfax (who later married physician William Somerville) was born in Jedburgh, close to the border with England, but raised in Burntisland just across the picturesque Firth of Forth north of Edinburgh. The old whitewashed house where she grew up still stands, in what is now Somerville Square. A plaque above the doorway acknowledges its famous former resident but the house is rather run-down today. There is no sign of the spacious garden where Mary’s mother grew fruit and vegetables to feed the family – her father’s naval pay was poor, despite his eventual rise to the position of vice admiral. But the common where the family’s cow grazed still exists, as does the nearby church they attended – and of course there is the beach, whose shoreline is depicted in the design of the new banknote. It is a symbolic choice. Educational wisdom at the time held that because women weren’t as strong as men, and had smaller brains, academic study would damage girls’ health or even send them mad. Consequently, while her brothers were sent to school, Mary was relegated to home duties; her only diversion was roaming the beach with the seabirds for companions.

Not surprisingly, she grew up, as she later put it, a “wild creature”. Even in her teens she was virtually illiterate and innumerate, despite “an utterly wretched” year at a boarding school when she was 10. But Burntisland’s rocks, birds, plants and stars inspired a wondrous curiosity about the natural world. She was determined to understand the way nature worked.

As for mathematics, her interest was kindled by tamer pursuits. In the mid-1790s, when she was 15, an older girl showed her a women’s magazine containing sewing patterns. Mary’s eye was taken not by the exquisite needlework but by a collection of x’s and y’s arranged in strange, alluring patterns. It was a solution to one of the magazine’s mathematical puzzles, whose popularity testified to the intellectual hunger among many women. Her friend knew only that “they call it algebra”; but those magical symbols fired Mary with an indomitable desire to speak this secret language.

It took her many years, and she did it mostly alone. When Britain’s scientists and mathematicians were finally exposed to her erudition, they were stunned. Her introduction to London’s scientific society had followed her 1812 marriage to Dr Somerville, who was supportive of his wife’s intellectual attainments. Through him she met leading scientists on both sides of the Channel, including Laplace. Some years later Lord Henry Brougham, co-founder of the liberal Edinburgh Review, invited her to write on Laplace’s work. When she finished her Mechanism of the Heavens, however, Brougham thought it too academic for the self-improvement book for technical professionals he had envisaged. Eventually the innovative publisher John Murray took a chance on it, catapulting Mary to fame.

Understanding Laplace’s work required knowledge of the user-friendly form of calculus that German mathematician Gottfried Leibniz had developed, and which is now universally taught in high schools. British mathematicians were still teaching Isaac Newton’s more opaque symbolism but, because she was self-taught, Mary had bypassed this and taught herself Leibniz’s “continental” calculus, along with the Latin required to read Newton’s Principia and the French to read Laplace’s monumental follow-up work, Mécanique Céleste (Celestial Mechanics).

Laplace’s update of Principia had made him deservedly famous, but his celebrity hinged on his resolution of a conundrum: was the solar system stable?

The controversy had begun a century earlier. Newton’s theory of gravity had suggested it was not. Early opponents of Newton’s theory, such as Leibniz, had favoured the ancient idea of “the ether”, unseen cosmic vortices carrying the planets in their wake. It was also assumed that God had set these ethereal whirlpools in perpetual motion to create a perfectly stable Solar System. The planetary motions certainly seemed stable, but Newton followed the logical consequences of his gravitational theory. His famous inverse-square law gave rise to an elliptical orbit taking account of the mutual gravity between the Sun and a planet. But each planet’s orbit would be distorted by the additional gravity of nearby bodies, so Newton predicted that, far into the future, the accumulated distortions of all the orbits would lead to chaos.

Laplace and Joseph-Louis Lagrange undertook the herculean task of applying Newton’s law of gravity to all the planets, moons and other known bodies in the Solar System. They eventually found the resulting distortions in the various orbits do increase and decrease over the millennia, but within such narrow limits the whole system remains stable. (Today chaos theory tells us the Solar System is inherently unstable but models suggest we’re unlikely to see any disastrous planetary collisions within the Sun’s lifetime.)

The use of Newton’s law alone to show the long-term stability of the Solar System was a great victory for the theory of gravity, and generated enormous excitement among mathematical physicists. Mary’s Mechanism of the Heavens made that excitement accessible to a broader audience of physicists and university students, because she explained the mathematical reasoning underlying the relevant conclusions in Laplace’s monumental Mécanique Celeste. (Mechanism was an explicated account of the first two books of the five-volume Mécanique.)

Her next book, On the Connexion of the Physical Sciences, was published in 1834. It was popular rather than academic, and soon became a bestseller also translated into Italian and German. It captured the spirit of the times – the sense that scientists were connecting the dots to reveal a unified cosmic scheme. For instance, the connection between electricity and magnetism was big news. That these seemingly separate phenomena were two sides of the same coin had only recently been demonstrated by Michael Faraday: in 1831, 10 years after Denmark’s Hans Oersted discovered electricity can induce magnetism, Faraday found the converse, generating electricity simply by moving a magnet through a coil of wire.

Connexion had benefited from Mary’s friendships with many of the leading scientists of the day: as well as Laplace and Faraday, she also knew Thomas Young, who proposed the wave theory of light, Charles Babbage, the computer pioneer, and his collaborator Ada Lovelace (profiled in Cosmos 60, p78) who she tutored and mentored. Mary could not believe such people took notice of her – she always saw herself as a backwoods Scottish girl with no formal education. Through this circle she learned first-hand about the latest developments in physics, although she was no stranger to scientific experimentation. In 1826 she had her first paper published in Philosophical Transactions of the Royal Society. (She and German-born British astronomer Caroline Herschel were the first women published in the prestigious journal.)

Mary’s paper described her experiments on the possible connection between magnetism and light. No one knew then that light itself was electromagnetic but experimenters were beginning to wonder if light and magnetism could affect each other. Her conclusions, though praised for their originality, were ultimately proven incorrect – as is often the way in science.

The first definitive evidence of a connection between light and magnetism was found by Faraday 20 years later, in 1846. James Clerk Maxwell would complete the puzzle with his electromagnetic theory of light in 1864 (see Cosmos 66, p60).

In Connexion, she also conjectured that observed distortions in the orbit of Uranus – discovered by her friend William Herschel (Caroline’s brother) – might be due to the effects of a body as yet unseen. Neptune was duly discovered in 1846, as a result of independent calculations using Newton’s theory by Englishman John Couch Adams and Frenchman Urbain Le Verrier. Adams later said his search for the planet had been inspired by the passage in Mary’s book.

Perhaps there is no better testament to Somerville’s writing than the opinion of one of the men she defeated in RBS’s public poll: James Clerk Maxwell, the ultimate 19th-century unifier who theorised the connection between electricity, magnetism and light. He said her second book put “into definite, intelligible and communicable form the guiding ideas that are already working in the minds of men of science … but which they cannot yet shape into a definite statement”.

Mary’s next book, Physical Geography, published in 1848, was both successful and controversial, because it included discussion of the new science of geology. The use of rocks and fossils to understand the Earth’s history put its age far beyond the biblical estimation of 6,000 years or so. Mary later recalled that this aroused more controversy than Darwin’s theory of evolution.

Her fourth book, On Molecular and Microscopic Sciences, published in 1869, was by her own account “a great mistake”: by then 88 years old, she no longer moved in scientific circles, and the book lacked the cutting edge freshness of her earlier works.

Everyone seemed to love and admire Mary Somerville. She was showered with honours, including a government pension awarded to important writers and scientists. Even the Royal Society, which did not admit female members at the time, erected her bust in its Great Hall, and the Royal Astronomical Society made her an honorary member (along with Caroline Herschel, in 1835).

After her death, her story lay dormant for a century, until scholars went searching for historical female role models to show girls that it was culture, not biology, that limited women’s participation in science. Mary Somerville’s triumph against such great odds makes her story particularly resonant.

At 91, while studying the new mathematical topic of quaternions, she revealed one of the secrets of her success: whenever she encountered a difficulty, she remained calm but determined, because “if I do not succeed today, I will attack [the problem] again on the morrow.” She helped pioneer the way for women in science, but her approach to life remains timeless.