NOTE: Galleys are finally finished! And now I am off to New York City for a few days to take in Book Expo America and also see Lisa Randall at the New York Academy of Sciences, chatting with Alan Alda about pop-up particle physics. So here's another tasty blast from the past with a math-y tie-in in honor of the forthcoming The Calculus Diaries: a lightning tour of a couple of notable women of mathematics. It's also timely because it mentions x-ray analysis of the Archimedes palimpset and Floyd Landis and his steroid scandal, both of which have been in the news again recently. Enjoy! Original posting will be back very soon, we promise.
It's official: Floyd Landis is a testosterone-pumping fiend, if the results of his "B" test are to be believed. He stands to become the first winner of the Tour de France to be stripped of his title because of doping allegations -- not quite the footnote to athletic history he was hoping to achieve. Landis still denies it vociferously, though, and vows to prove his innocence. We would like to believe him, we really would. But our skepticism is mounting. Not only were there traces of synthetic testosterone in his blood, but the tests revealed a whopping 11 to 1 ratio of testosterone to epitestosterone. For comparison purposes, the maximum allowed ratio by the World Anti-Doping Agency is a trifling 4 to 1. It's not looking too good for Floyd.
Second, we cannot believe we completely missed Friday's live Webcast -- courtesy of the San Francisco Exploratorium (which still has our vote for coolest science museum ever) -- of the last bit of deciphering via synchrotron radiation of that classic text by Archimedes, which we mentioned in passing in a prior post. There is little excuse for our lapse. Wired.com tried to tell us. Yet somehow, the news eluded us until it was too late. How embarrassing. But if Landis can still make excuses, so can we. I hereby blame Bloglines, which occasionally suffers unconscionable delays in posting feed updates.
Still, missing a Webcast by a few measly hours isn't nearly so bad as not hearing about a world-class female mathematician for over 100 years. Last week, in response to the question of hip scientific names to drop for aspiring geeks, someone mentioned one Sonya Kovalevsky, a Russian woman who was a protege of the Swedish mathematician Gosta Mittag-Leffler, founder of the journal Acta Mathematica. Once again, we were caught napping. I'd never heard of Kovalevsky, and since I'm a firm believer in the importance of ferreting out long-forgotten women in science and math throughout history (my own little way of disseminating "herstory," if you will), I Googled her over the weekend. She was, indeed, a fascinating, admirable woman, whose story certainly doesn't deserve to be gathering dust in the faded archives of scientific history.
It wasn't hard to uncover the bare basics of Sonya's life; we got all kinds of hits, with everyone pretty much relating the same laundry list of accomplishments: first woman member of the Russian Academy of Sciences (although still unable to attend actual meetings); first modern European woman to attain a full professorship; established the first significant result in the general theory of partial differential equations; and winner of the prestigious Prix Bordin. She was also a gifted writer (of both novels and magazine articles), and often quoted thusly: "Many who have never had occasion to learn what mathematics is confuse it with arithmetic, and consider it a dry and arid science. In reality, however, it is the science which demands the utmost imagination.... It seems to me that the poet must see what others do not see, must look deeper than others look. And the mathematician must do the same thing."
(Lengthy side note: The question of how to refer to women scientists is a thorny one -- by first name? last name? married name? But after spending so much time with Ms. Kovalevsky this weekend, we feel like we know her well enough to be on a first-name basis. Besides, it's exhausting to have to keep spell-checking "Kovalevsky." Plus, she is sometimes referenced as Sofia Kovaleskaya, because no self-respecting 19th century person of Russian descent would have any fewer than three forms of their name, including nicknames. It's all very confusing. So henceforth, she shall be Sonya.)
I wasn't surprised to learn that Sonya was a product of Russia's privileged class, the daughter of a military officer and landowner; her mother was the granddaughter of a Russian astronomer. Education was such a taboo for women, even in the mid-19th century, that only those women who moved in rarefied aristocratic circles were exposed to intellectual pursuits . "All my life I have been unable to decide for which I had the greater inclination, mathematics or literature," Sonya wrote in her autobiography, recognizing that because of her educational opportunities, she'd had a choice. Not that those opportunities were especially stellar: like most early women in math and science, she was doggedly persistent about vaulting over the many obstacles "Society" sought to erect in her path.
Sonya's interest in math was sparked by an eccentric uncle, who taught her chess and discussed all kinds of abstract concepts with her: "squaring the circle, asymptotes, and other things that were unintelligible to me and yet seemed mysterious and at the same time deeply attractive." When her room was redecorated at age 11, there wasn't enough wallpaper to complete the project, so one wall was temporarily papered with her father's old calculus lecture notes from college. Initially the symbols were little more than hieroglyphics to her, but after reflecting on them night after night, she began making connections between the symbols and the concepts she discussed with her uncle. Another 19th century mathematician, Mary Somerville, had a similar breakthrough around the same age: she stumbled upon algebraic symbols while perusing a puzzle in a magazine, also igniting a lifelong thirst to know more. And like Somerville, Sonya's father eventually grew dismayed at his daughter's "unfeminine" interests and tried to put a stop to them. ("We shall have young Mary in a straitjacket one of these days," Somerville's father supposedly lamented.)
Somerville continued to study by candlelight, and when her father confiscated her candles, she memorized texts during the day and worked out problems in her head at night. The family of French mathematician Sophie Germain -- inventor of "Germain primes," i.e., double a Germain prime and add 1 to get another prime number -- used a similar tactic to dissuade their equally precocious daughter from studying geometry, algebra and calculus... to no avail. Sonya also studied under the covers at night, borrowing an algebra textbook from one of her tutors.
Then a neighbor, who taught science, gave the family a copy of a basic physics book he'd written. Sonya turned to the section on optics, and discovered trigonometry. Even though she'd never encountered it before, she managed to make sense of the derivations for small angles by substituting "a chord for the mysterious sine." In short, she independently rediscovered the same method by which the whole concept of a sine had been developed historically. Impressed, the neighbor convinced Sonya's father to let her study analytic geometry and calculus privately in St. Petersburg. She mastered both subjects in a single winter. Her astonished tutor noted that it was almost as if she'd known the concepts in advance.
Someone with such a formidable innate aptitude couldn't be satisfied for long with simple calculus, but Sonya's opportunities for further study were severely limited because of her gender. She entered into a marriage of convenience with a young paleontologist named Vladimir Kovalevsky, and the couple moved to Heidelberg, Germany. She still couldn't formally enroll in a university, but she managed to get permission to "unofficially" attend lectures by some of the foremost scientists in Europe. In that respect, she fared a bit better initially than Germain, who was forced at one point to impersonate a male student who had passed away in order to study with Joseph LaGrange (via correspondence) at L'Ecole Polytechnique in Paris. But in both cases, the women performed so spectacularly that they won the admiration and mentorship of prominent men: LaGrange and later Carl Friedrich Gauss, in German's case, and Karl Weierstrass (and, later, Mittag-Leffler) in Sonya's case.
Weierstrass wasn't a familiar name to me, but at the time he was the most renowned German mathematician, a professor at the University of Berlin. Sonya came to him bearing glowing recommendations from her Heidelberg professors, yet even then, he was skeptical, and far from enthusiastic about taking her on. To discourage the young woman, he gave her a set of problems he'd prepared for his most advanced students, assuming she'd never make sense of them. Instead, she solved them in record time; not only that, her solutions were clear and original, demonstrating a grasp of the material lacking in most of his male students (Mittag-Leffler being one notable exception). So he agreed to teach her privately, and came to consider her among the most brilliant and promising of all his students.
Sonya didn't disappoint her mentor. By the age of 25, she had produced three original papers, each of which was deemed worthy of a PhD degree: one on the shape of Saturn's rings, another on elliptical integrals, and a third on partial differential equations. Not that Berlin would ever award a woman a PhD, especially one that had never been officially matriculated. Anywhere. (And how could she possibly matriculate when they wouldn't allow it? Yes. Exactly.) To his credit, Weierstrass fought for her, eventually convincing the University of Gottingen to award her a PhD in mathematics, summa cum laude.
I would like to tell you this story has a happy ending, or at least that Sonya's intellectual struggles ended with her PhD. Alas, such is not quite the case. She and Vladimir returned to Russia, where she found she could only get a job teaching basic arithmetic at a girl's elementary school. The irony wasn't lost on her: "I was, unfortunately, weak in the multiplication tables," she acidly observed in her memoirs. Instead, she began reviewing theater performances and writing articles about science and technology for a local newspaper (huzzah! a fellow science writer!), as well as starting a novel. And her platonic marriage mysteriously turned non-platonic: she gave birth to a daughter during this period, too. That didn't make the marriage a happy one. Eventually she left Vladimir and moved first to France, and then Stockholm, when the university there offered her a probationary position, thanks to the urging of Mittag-Leffler. By then, she was a widow: Vladimir had committed suicide, distraught and depressed over his many failed business ventures, among other things.
Sonya, in contrast, proved so popular with her students that she was given a five-year professorship at Stockholm, and also became an editor of Acta Mathematica. In 1888, she reached the pinnacle of her career when she won the French Academy of Sciences' prestigious Prix Bordin for her treatise, On the Problem of the Rotation of a Solid Body About a Fixed Point. They might have excluded her from the competition on the basis of gender -- the French Academy was far from welcoming, as Sophie Germain could attest -- but the papers were all submitted anonymously and the judges weren't aware they'd selected a woman until it was, as it were, "too late." Still, so impressed were they by her work that they actually doubled the prize. It seems too cruel a twist of fate that, only three years later, she succumbed to pneumonia following an influenza epidemic.
By now we hope you're convinced that Sonya deserves wider repute. Apparently the novelist Thomas Pynchon thinks so, too. His much-heralded forthcoming new book, Against the Day, is rumored to feature cameo appearances not just by Nikola Tesla, Bela Lugosi, and Groucho Marx, but also to "trace the life and loves of Sofia Kovalevskaya," per Wikipedia (which we know is never wrong). True, Sonya (or Sofia, if you prefer) died in 1891, and the book's events purportedly take place between the 1893 Chicago World's Fair and the aftermath of World War I, but novelists have been known to take liberties with chronology, and for Pynchon, time has always been a somewhat fluid quantity. Maybe she's featured post-humously.
Still, bare facts can only tell us so much; the nuances of Sonya's life and work, the complex layers of the living, breathing woman, eluded me in my weekend research. That's probably because the definitive biography of Sonya Kovalevsky remains to be written. Fortunately, the same cannot be said of Ada Lovelace (tempestuous daughter of the poet Lord Byron), brought into vivid focus in Benjamin Woolley's The Bride of Science, or of the incomparable Emilie du Chatelet, who is celebrated in David Bodanis' new book, Passionate Minds. We have already pre-ordered the US version of this book on Amazon, and encourage our readers to do the same, since if nothing else, it proves to be a torridly rollicking good read. It also boasts the longest subtitle I've ever seen for a science book: "The Great Love Affair of the Enlightenment, Featuring the Scientist Emilie du Chatelet, the Poet Voltaire, Sword Fights, Book Burnings, Assorted Kings, Seditious Verse, and the Birth of the Modern World." Whew! Throw in a shipwreck on a deserted island, and you've got a potboiling bestseller on your hands. From our perspective (and no doubt for Bodanis as well), that's a very good thing.
Emilie (may we call her Emilie?) was another precocious child of aristocrats, this time in 18th century France. Her parents feared she would never make a good marriage, because no great lord would want a woman who "flaunts her mind and frightens away the suitors her other excesses have not driven off." I shall have to wait for Bodanis' book to be enlightened on what these other excesses might have been, but it's a matter of historical record that she had no shortage of admirers and lovers, including the duc de Richelieu and -- yes -- Voltaire.
Despite her parents' fears, her father's wealth and position ensured a "marriage of convenience" at the age of 19 to the older marquis du Chatelet. She dressed up like a man in 1733 and gate-crashed the Cafe Gradot, where all the happening intellectuals hung out. People like Voltaire. Soon the two were shacking up in her husband's country estate, living and working in separate studies. She completed a translation of Isaac Newton's Principia there, duplicating his experiments by hanging pipes, rods and wooden balls from the rafters.
She and Voltaire remained friends even after they split (Bodanis claims Voltaire couldn't deal his lover's superior intellect). Alas, her unconventionality, while admirable, couldn't save her from that most conventional of fates: dying in childbirth. An ill-advised liaison with a young poet resulted in Emilie's pregnancy at age 41, which everyone -- including Emilie herself -- knew was pretty much a death sentence in that day and age. Voltaire supported her during her last days, writing that "she wasn't angry, just sad to have to leave before she was ready." She died in August 1749, a few days after giving birth. (The child didn't survive either.)
It's a compelling story, and easy to see what drew Bodanis to write a book about this remarkable woman. So we were peeved (Jen-Luc Piquant was frankly outraged) to read snarky comments in the UK reviews criticizing the book for supposedly short-shrifting on the science, taking this as evidence that Emilie wasn't really all that important a figure in science history. What is this overweening need some people have to belittle the accomplishments of women scientists throughout history? Such critics completely miss the point: what makes Emilie du Chatelet and her sisters "great" is the very fact that they were able to pursue their love of math and science in defiance of social norms, public ridicule, bureaucratic red tape designed specifically to exclude them, and lord knows what else. (This is not, incidentally, meant to be read in any way as casting aspersions on their scientific achievements.)
That's not even counting the day-to-day, constant barrage of criticism, doubt and skepticism that would inevitably cause even the toughest spirit -- regardless of gender -- to question one's aptitude or worth, something that continues to plague aspiring women scientists today. The unspoken cultural prejudice about the "female mind" and its ability (or inability) to excel at math and science is so deeply ingrained that women themselves often unwittingly buy into it. Mary Somerville is a prime example of this, eventually coming to believe that women just weren't as gifted as men when it came to scientific creativity. She certainly doubted her own abilities: "I have perseverance and intelligence, but no genius," she once wrote.
Admittedly, Somerville is primarily known for popularizing scientific treatises by LaPlace and Newton, not for original research. Nonetheless, these achievements earned her election to the Royal Astronomical Society, among other honors, and when she died, London obituaries hailed her as the "queen of science." Most significantly, she never had any real educational opportunities, unlike her male counterparts. The same is true of most of the pioneering women in math and science, many of whom did make significant original contributions to research -- and often got short-shrifted when it came to recognition of those achievements. Sophie Germain never felt she received the recognition and respect she deserved. And would the French Academy have awarded Sonya Kovalevsky such a prestigious prize had it known from the outset that she was a woman? (For that matter, Jocelyn Bell was excluded from consideration for the Nobel Prize for her role in the discovery of quasars.) We will never know what these formidable women in history might have accomplished, had they been encouraged in their early years of study, had their innate talent been supported and fostered, rather than stymied and blocked at every turn.
In short, I must agree with Bodanis: "Emilie du Chatelet deserves to be brought back to life, in all her stumbling excitement and fears." The same could be said of Sonya Kovalevsky, Mary Somerville, Sophie Germain, the chemist Agnes Pockels, Hypatia, and any number of forgotten women who blazed their own bravely idiosyncratic path in a world of men to which they were rarely welcomed -- only to disappear into a fog of obscurity once the all-too-brief flame of life was extinguished. Too many admirable women in science and math have been unjustly forgotten because we have been sleepwalking through our own "herstory." Let us make sure we remember -- and honor -- their names, and pass their stories on to the next generation, thereby inspiring both girls and boys to emulate their passion and courage.