The fates of Hypatia and Emmy Noether, a cautionary tale; Beating the Odds and Defending the Caveman
Of the women mathematical geniuses, Hypatia (AD 350/370 – 415) was the first and Emmy Noether (1882 – 1935) the greatest. Hypatia was a Greek scholar from Alexandria. She became entangled in local politics and did not fare well. She was brutally killed by a mob led by Peter the Reader, the first assistant of Bishop Cyril, an important saint.
Fast forwarding 1,500 years, Emmy Noether got entangled in academic politics. The world had not become a gentler, kinder place, as the first World War occurred and the second was looming. However the focus was not on murdering her, but rather on murdering her academic career.
The two succeeding subpages close on more optimistic, and humorous, notes. One is about about an extraordinarily resourceful woman entrepreneur, the first black millionaire in the U.S., Madam J. Walker. The other is Bridges own extension to the one-man comedy show that treats the differences between men and women, Rob Becker´s "Defending the Caveman." The extension is made on the third and last subpage of this section, one segment in German, the other in English: "Diamond Jill. . . + die Frau als Heimtier."
I. Hypatia (AD 350/370 – 415)1
Hypatia was the daughter of Theon, the last mathematician known to be associated with the Museum of Alexandria. Her studies were at first with her father. Later she continued them in Athens and Italy. A respected historical source is the Suda, a Byzantine encyclopedia written in the 10th century. According to it, ca. 400 AD she became the leader of the Platonist school in Alexandria, teaching the philosophy of Plato and Aristotle. Her fame was such that students from prominent families journeyed to Alexandria to study with her. A number of them later achieved high-level positions in government and some of her Christian students, high-level ones in the Church.
Therefore not at all surprising is that she is thought to have been well respected by the emerging Christian community. (Her religion is unknown.) In fact, some later Christian authors cited her as a symbol of virtue. She was an influential figure in Alexandrian political circles, but most important as a mathematician and scientist.
Besides being one of the foremost teachers of her day, she is also credited with:
- A commentary on the 13-volume Arithmetica by Diophantus
- A commentary on Apollonius´s Conics
- Editing Ptolemy's Almagest
- Editing her father's commentary on Euclid's Elements
- The Astronomical Canon. (Possibly a new edition of Ptolemy's Handy Tables.)
- Charting of celestial bodies
- Inventing the hydrometer (It is used to determine the relative density and gravity of liquids.)
Politics is a murderous business, and Hypatia is one of its countless victims. She supported the moderate Orestes, who was in conflict with the fundamentalist, ultra conservative Bishop Cyril. Some influential Christians felt Orestes was resisting the bishop in part because of her influence. Apparently the bishop, the renowned Saint Cyril of Alexandria, decided indirectly to attack Orestes by eliminating the support of Hypatia, who was a thorn in his side.
Her chariot was waylaid on her route home by a Christian mob during Lent (in March) AD 415. The mob was led by a man identified as Peter the Reader by Nitrain monks. As the Bishop´s first assistant and righthand man, Peter would hardly have acted independently. The article continues:
“The Christian monks stripped her naked and dragged her through the streets to the newly Christianized Caesareum church, where she was brutally killed. Some reports suggest she was flayed with ostraca (pot shards) and set ablaze while still alive.” (Wikipedia, 2010)
As far as the details of her demise are concerned, the scholarly majority comes down in favor of the version related by Socrates Scholasticus (5th century):
“Some of them therefore, hurried away by a fierce and bigoted zeal, whose ringleader was a reader named Peter, waylaid her returning home, and dragging her from her carriage, they took her to the church called Caesareum, where they completely stripped her, and then murdered her by scraping her skin off with tiles and bits of shell. After tearing her body in pieces, they took her mangled limbs to a place called Cinaron, and there burnt them.” (loc. cit.)
Her honorable opponent
Bishop Cyril (Saint Cyril of Alexandria), d. AD 444, patriarch of Alexandria (412-44) was held in reverence, or terror, depending upon one’s allegiances, for his relentless persecution of heathens and heretics. He succeeded in driving the Jews from Alexandria.
He was a scholarly archbishop and a prolific writer. Among his exegeses are: Commentaries on the Old Testament, Thesaurus, Discourse Against Arians, Commentary on St. John's Gospel, and Dialogues on the Trinity. He was made a saint some centuries after his death. No formal suggestion has ever been made to decanonize him. “His writings and his theology have remained central to the tradition of the Fathers and to all Orthodox to this day.” (Wikipedia, 2010)
The moral of the tale
If you are an attractive, quantitative woman of good cheer and open and generous nature, held in high regard as a person of influence and virtue, it behooves you to exercise due caution. Even if you do not consciously antagonize the true believer who is a candidate for future corporate sainthood, you must beware his envious malice. He will show no mercy.
Or, as Harvey Mackay mentions in his classic How to Swim with the Sharks: "Lesson 7 Racial and religious prejudice have not been eliminated as of the date of publication of this book."2 -- or of this website either, including gender prejudice.
a) Maria Dzielska, (trans. F. Lyra), Hypatia of Alexandria, Harvard University Press, 1995/96. One of Dzielska´s main sources is Damascius, the last of the Neoplatonists (ca. AD 458, died after AD 538). Born in Damascus, he was the last scholar of the School of Athens. At one point he fled to the Persian court because of persecution, but eventually was allowed to return. The (Christian) Justinian the Great, the Eastern Roman (Byzantine) Emperor from 527 to 565, was antagonistic towards pagan philosophers. (The last emperor to be a native speaker of Latin, he sought to restore the Roman Empire by reconquering the lost western half. He did, in fact, extend it as far as Rome. Byzantine culture thrived in his reign and for Eastern Orthodox Christians he is a saint.)
Maria Dzielska attributes the lack of writings about Hypatia to the fact that most of the contemporary and succeeding historians were Christians. A felicitous description of the circumstances of her death would not reflect well on Christianity or the Church. Therefore this subject was considered one left well enough alone.
b) Michael Deakin, Hypatia of Alexandria: Mathematician and Martyr, 2007. This short biography, just 113 pages, emphasizes her mathematical contributions.
c) Wikipedia articles (2010)
2 Harvey Mackay, Swim with the Sharks Without Being Eaten Alive, William Morrow & Co. 1988, p. 57.
II. Emmy Amalie Noether (1882 – 1935)
Like Hypatia, she was the daughter of a mathematician. (Being Jewish, she is unlikely to have fared any better with Saint Cyril than Hypatia did.) How good was she really? Well, if you only read the article about her in the German Wikipedia, you would think she had been just another fairly notable mathematician, one who had had some minor, inconsequential difficulties along the way for being a woman. (Who knows what issues the author had with her -- jealousy? That is why you need to double-check your sources!)
On 2 January 1935, a few months before her death, mathematician Norbert Wiener1 wrote that
"Miss Noether is ... the greatest woman mathematician who has ever lived; and the greatest woman scientist of any sort now living, and a scholar at least on the plane of Madame Curie."
In a letter to the New York Times shortly after her death Albert Einstein2 wrote:
"In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians."
Still, writing “greatest woman mathematician” might appear as if she were being damned by faint praise. Actually she made groundbreaking contributions to abstract algebra and theoretical physics.
- In her first epoch (1908-1919) her most famous work is on differential invariants in the calculus of variations. Her main proof in this area is known as Noether's theorem. It is regarded as one of the most important mathematical theorems ever proved.3
- In her second epoch, (1920–1926), she did work that "changed the face of abstract algebra."
- In her third epoch (1927–35), she gave the first general representation theory of groups and algebras. This work has been fundamental to the development of modern algebra.
She was taught to cook and clean, and also learned French and English. After earning a certificate with top marks to be an official teacher of those languages, she went to the University of Erlangen. Of the 986 students, she was one of only two women. She completed her dissertation in 1907.
She worked at the Mathematical Institute of Erlangen without pay for seven years! Then in 1915 she was invited by David Hilbert and Felix Klein to join them at the University of Göttingen´s center for mathematical research, which was world-renowned. However professors of philology and history (most of them, one may safely assume, not that good in math, and none of them within lightyears of her intelligence), prevented her appointment. One faculty member protested: "What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?"4
Soon after arriving at Göttingen she demonstrated genius by proving the theorem now known as Noether's theorem. World War I was followed by the German Revolution of 1918–19, a social upheaval which led to women having more rights. As a consequence in 1919 the University allowed her to pursue an “habilitation.”* She completed it instantly, officially passing the examinations the same year.
* The standard German doctorate involves writing a thesis. It does not require the several years of further course work and the comprehensive examination of the U.S. PhD, which is viewed as more demanding on both sides of the Atlantic. However the Habilitation (the second doctorate), which is required for tenure in Germany, is another story entirely. The standards for it are significantly higher than for the PhD.
After she had earned it, the Prussian Minister for Science, Art, and Public Education stalled for a full three years. Finally he reluctantly conferred her the title of “special adjunct professor.” Presumably this unusual designation was made to ensure that she did not get paid. The title gave her no right to a salary. (A year later her colleagues managed to circumvent the system and to arrange a small salary for her.) Thirteen years later she won the prestigious Ackermann-Teubner Memorial Award for her contributions to mathematics. However she was certainly not going to receive tenure, let alone be elected to the Göttingen Gesellschaft der Wissenschaften (the Göttingen Academy of Sciences, full of lesser lights).
When the Nazis came to power in 1933, the Prussian Minister for Science, Art, and Public Education was happily able to expel her from the university for being Jewish. Her colleagues looked in the U.S. to find the sponsor she needed to be able to immigrate legally. One would think Harvard, Princeton, M.I.T., the University of Chicago and Stanford would have gotten into a bidding war for her. Actually Bryn Mawr was the one that expressed interest. (Founded by the Quakers in 1885, it is one of the Seven Sisters Colleges, which at that time were primarily attended by the daughters of the wealthy. It was the first college in the U.S. to offer graduate degrees, including doctorates, to women.)
Albert Einstein and Hermann Weyl had landed at the Institute for Advanced Study at Princeton University. They respected her capabilities and in 1934 she began lecturing there. Einstein and Weyl notwithstanding, she was not well received at Princeton, which did not admit women. She once remarked that she was “not welcome at the men´s university, where nothing female is admitted.”5 Unfortunately her time in the U.S. was brief, as she died after an operation for cancer the next year.
A colleague described her as: "Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all."6 She went so far in this selfless support that she did not object when students, and colleagues as well, would take the credit for ideas of her own.7
The Moral of the Tale
You are not a certified mathematical genius, better than any woman before you in the past 1,500 years, who happens also to be exceptionally good at languages, selfless, friendly and fond of dancing. You are, however, an attractive, quantitative woman of good cheer and open and generous nature, held in high esteem as a person of influence and virtue. You have exercised due caution. You have managed not to antagonize the true believer who is a candidate for future corporate sainthood. You have not even elicited his envious malice. You are still not out of the woods.
Beware the old boys´club. Nowadays it is harder to stall you, and a lot harder to get rid of you, just because you are a woman. The excuse that you belong to the wrong religion – or the wrong race or caste -- will no longer suffice either. But do not underestimate the club. Its members subscribe to two powerful mottos: “Where there is a will, there is a way.” and “What one man can do (squash women), another can do.”
You think this observation is pessimistic? Perhaps, but consider the following comparison. What was the ratio of men to women at the half-dozen leading MBA programs in the world 25 years ago? Three or four, perhaps five or six, to one? These are the places training you for future leadership positions – the kind that take a full quarter century to reach. And what is the ratio of men to women from those programs in the C-suites today in your industry? Three or four to one? (Congratulations, you may well be a fellow executive coach then, as it is one of the few professions in which women have held their own.) Ten to one? Perhaps, but not in the cosmetics or fashion industry, so where then? Or is it more like twenty, thirty or fifty to one?
III. Beating the Odds & Defending the Caveman
The subpage about Madam J. Walker relates the success of a woman who, given the odds against her, makes Oprah Winfrey's rise from rural poverty in Mississippi to billionaire TV mogul almost appear easy.
For a lighter approach to Mr. Troglodyte* and his soul mate, Ms. Mimosa,* one should see Rob Becker's “Defending The Caveman.” He wrote it in 1991 and starred in it for the first 12 years. The one-man comedy show is about how the differences between men and women make us misunderstand one another. Over five million people from more than 20 countries have attended the show in 15 different languages. Below are some milestones quoted from its website (linked above).
1995: "Rob Becker's Defending The Caveman" opens for previews March 26th on Broadway at the Helen Hayes Theater on 44th Street. It runs for almost 2 years. The show had over 700 performances and is still the longest running solo play in Broadway history.
2000: Sacramento grosses almost a million dollars for one week in 2000. The show had now been performed over 2500 times and had grossed over 20 million dollars making it the "Most Successful Comedy Show in History."
2001: Rob: "Without our input these international shows, especially in Germany, seem to flourish.”
The subpage " Diamond Jill, an amusing tale + Die Frau als Haustier - des Auflebens Caveman"gives Bridges' own modest contributions to the interminable war of attrition between the sexes.
* A troglodyte is a member of a primitive people who live in caves or pits. The word is used for modern people whose appearance, degradation and brutality remind one of the worst specimens of the anthropoid apes. Mimosa is a plant whose leafstalk droops and leaflets close tightly when touched. The word in German (die Mimose) is commonly used for an overly sensitive person, a connotation the English word can also have.
1 Clark Kimberling, "Emmy Noether and Her Influence," in James W. Brewer and Martha K. Smith, Emmy Noether: A Tribute to Her Life and Work, Marcel Dekker, Inc., pp. 3–61, (1981), p. 5
2 "Professor Einstein Writes in Appreciation of a Fellow-Mathematician." 1 May 1935, pub. 5 May 1935 in the New York Times. The article in the English language Wikipedia notes that the letter is available online at the MacTutor History of Mathematics archive, linked below.
3 Leon M. Lederman, Christopher T. Hill, Symmetry and the Beautiful Universe, Prometheus Books, 2004, p. 73 The authors, both physicists in their own right, state that Noether´s theorem is "certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics, possibly on a par with the Pythagorean theorem."
4 Lynn M. Osen, "Emmy (Amalie) Noether,"Women in Mathematics, MIT Press, 1974, p. 144 f.
5 Auguste Dick, trans. H.I. Blocher, Emmy Noether: 1882–1935, Birkhäuser 1981, p. 81
6 M. Teicher, M. (ed.), "The Heritage of Emmy Noether," Israel Mathematical Conference Proceedings, Bar-Ilan University/American Mathematical Society/Oxford University Press, 1999
7 Leon M. Lederman; Christopher T. Hill, op. cit., p. 74
© Hypatia: model is Marie Spartali, appearing in Colin Ford's Julia Margaret Cameron (1815 - 1879) 19th Century Photographer of Genius, original in the J. Paul Getty Museum, Los Angeles, public domain - old, scanned 7 Feb. 2010 (Wikipedia); Emmy Noether, from the MacTutor History of Mathematics archives, portrait before 1910, public domain - old; Gyan Web Design 2010