Numbers are male, said Pythagoras, and the idea persists

Commentary

By Margaret Wertheim

The New York Times
October 3, 2006

When I was a physics major in the late 1970's, my very few fellow female students and I had high hopes that women would soon stand equal with men in science. But progress has proved slower than many of us imagined. A report last month by the National Academy of Sciences documents widespread bias against women in science and engineering and recommends a sweeping overhaul of our institutions.

While there may indeed be subtle biological differences contributing to the scarcity of women in the top ranks of science, interviews make clear that many female scientists continue to experience both overt and covert discrimination.

The academy's report is welcome, yet there is reason to believe that when it comes to the mathematically intensive sciences like physics and astronomy, it is not just bureaucracies that stand in the way.

Female physicists, astronomers and mathematicians are up against more than 2,000 years of convention that has long portrayed these fields as inherently male. Though women are no longer barred from university laboratories and scientific societies, the idea that they are innately less suited to mathematical science is deeply ingrained in our cultural genes.

The problem goes back to the ancient Greeks, particularly to Pythagoras (left), the philosophical giant who dreamed the dream that became modern physics. Pythagoras almost certainly learned his famous theorem about right-angled triangles from the Babylonians, but we owe to him a far greater idea: “All is number,” he declared, becoming the first person to say that the physical world could be described by the language of mathematics.

Pythagoras also gave us the idea of the “music of the spheres,” a set of mathematical relationships that would describe the structure of the universe itself. His vision would eventually give rise to the scientific revolution led by Copernicus, Kepler, Galileo and Newton. The search for a theory of everything today is the latest version of the ancient Pythagorean quest for divine “cosmic harmonies.”

Though many cultures have developed sophisticated mathematical traditions, including the Chinese, the Arabs, the Indians and the Mayans, the West is the one that came to see the material world as an embodiment of mathematical laws. And from the beginning, the search for such laws was viewed as an innately male activity.

The Pythagorean society of the fifth century B.C. was a cradle of mathematical research, but Pythagoreanism was also a religion, and like many Greek cults its beliefs were dualistic. For Pythagoreans, reality consisted of two parts: on one side were the mind and spirit and the transcendent realm of the gods; on the other side were the body and matter and the mundane realm of the earth. Like many Greek thinkers, the Pythagoreans associated the mind/spirit side of reality with maleness and the body/matter side with femaleness.

Pythagoras introduced numbers into this mix and put them on the male side of the ledger. In the Pythagorean system, thinking about numbers, or doing mathematics, was an inherently masculine task. Mathematics was associated with the gods, and with transcendence from the material world; women, by their nature, were supposedly rooted in this latter, baser realm.

At the end of the Middle Ages, Pythagorean interest in a mathematical approach to science began to gain ground, and it is here that we begin to see the seeds of modern physics.

”The creation of number was the creation of things,” Thierry of Chartres wrote in the 12th century, when the first universities were formed and academic learning was formalized. The universities were founded to educate the clergy, and since women could not be priests they could not attend. Many university departments did not admit women at all until the early 20^th century, and physics departments were often among the last to accept students and professors who were women.

The Pythagorean association of mathematics with transcendence was easily imported into a Christian context, giving rise to the idea of the Judeo-Christian god as a mathematical creator. When Stephen Hawking links a theory of everything to the mind of god today, he is reiterating an essentially Pythagorean view. But this godly-mathematical connection also sat easily with the Catholic tradition of a male-only priesthood. Thus, from the start, women were excluded from this academic field and its associated sciences.

When the early scientific societies formed in the 17th and 18th centuries, most continued this misogynistic trend. Henry Oldenburg, an original secretary of the Royal Society in Britain, wrote that the organization¹s mission was to “raise a Masculine Philosophy.” Not until 1945 did this bastion of science admit a woman as a full member.

Female physicists have continued to confront deep-seated prejudices. Emmy Noether (photo left), who discovered that all physical conservation laws were associated with mathematical symmetries, was a contemporary to Einstein and helped work out some of the math of general relativity. She did so without a formal academic position and mostly without pay.

Lise Meitner (top photo), who developed the theory of nuclear fission, was not included when the Nobel Prize was given for this work in 1944. The Harvard University physics department did not give tenure to a woman until 1992.

This week, the Swedish Academy announces the Nobel Prizes in science. It will be remarkable if any women are on the list. Marie Curie won a Nobel in physics in 1903; the only woman to follow her was Maria Goeppert Mayer in 1963, when she shared the award for her theory about the structure of atomic nuclei. In mathematics women have fared even worse. The Fields Medal, the mathematical equivalent of a Nobel, has never gone to a woman.

Many women who have gone into science since the 1970¹s continue to be stunned at how slow change has been. Gail G. Hanson, distinguished professor of physics at the University of California, Riverside, and the only woman to have won the W. K. H. Panofsky Prize in experimental particle physics, said by phone: “At this point there seems to be an acceptance of women in science at relatively junior levels. But once we get to more senior levels, a kind of antagonism sets in.”

As a postdoctoral fellow at the Stanford Linear Accelerator Center, Dr. Hanson discovered quark jets, the work for which she would later be awarded the Panofsky Prize. Yet throughout her research career, she said, she has continued to be treated like a junior colleague, not like a leading researcher.

Dr. Hanson is the subject of a chapter in a new book tracing the lives and work of 40 outstanding female physicists of the past century. Called “Out of the Shadows” and edited by Nina Byers and Gary Williams, physicists at the University of California, Los Angeles, the book recounts the barriers many of these women faced -- and continue to face today. A number of younger female physicists contacted for this article agreed that bias remained real, but they did not want to be quoted on the record.

With sadness and anger evident in her voice, Dr. Hanson said: “I thought these kinds of things only happened in the 1950's. It's appalling that women still confront these hurdles.”

She added: “And when you get the prizes, you¹re often treated even worse. Men can tolerate a woman in physics as long as she is in a subordinate position, but many cannot tolerate a woman above them.”

The National Academy's report states that we still have a long way to go. Compared with their male colleagues of similar experience, female scientists and engineers are underpaid, undervalued and underrepresented in the top tiers of science. Given the long history of antipathy toward women of a mathematical bent, it was perhaps naïve to think we could change our institutions in a generation. It is not just bureaucratic will that needs to shift; it is the cultural zeitgeist.

Margaret Wertheim is the author of “Pythagoras' Trousers,” a cultural history of physics and women.

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