“A portion of the Erdos Collaboration Graph” by Tom Odda, a.k.a., Ron Graham

Who’s Important? A tale from Wikipedia

Ursula K. LeGuin writes, “Greatness, in the sense of outstanding or unique accomplishment, is a cryptogendered word. In ordinary usage and common understanding, “a great American” means a great American man, “a great writer” means a great male writer.”

I think what LeGuin says is true. The meager representation of women in history reflects this bias, and well deserves its nickname ‘written out.’ But do we as a society also believe that greatness is contagious? Can it be passed from one person to another, like a venereal disease? This was a question I began to ask myself as I thought about Paul Erdős.

For those who are not familiar with Paul Erdős, he is one of the world’s most famous collaborators, a brilliant mathematician, well known for working with other mathematicians, who in turn worked with others, who worked with others. A person’s Erdős number represents the degrees from zero that one can trace from oneself back through this collaboration graph. Through it, Erdős is linked to many, many people, but only the 512 people he worked with directly have an Erdős number of one, and those were the names I was thinking about. How many of them belonged to women?

Most of those names appeared to make the gender clear, but I did a web search for each to ensure accuracy. There might, for example, be a George Eliot amongst the collaborators, a woman who used a man’s name to avoid gender bias. I know a number of women who go by their first initial in their bylines for a similar reason.

Of the 512 Erdős Ones, I discovered 21 women. I may have missed a George Eliot; though I almost always found references to a person’s academic work, I could not always find material that confirmed gender. It’s likely that the people I found were the ones I was searching for, but I may also have found a second person with the same name. If a foreign-to-me name returned no useful search results, I used gender-prediction sites to tell me the most likely sex. If I am wrong, I have esteemed company. Princeton admitted a Japanese woman into their mathematics graduate program some years before 1968, the year in which the program began accepting women, because they mistook her name for a man’s.

Historically, mathematics has been a male-dominated field, but here are a few numbers for context. In the mid-1930s, women earned over 14 percent of PhDs in mathematics in the United States. Between 1940 and 1959, the percentage dropped to about 6 percent. In 1966, women received 6.1 percent of the mathematics PhDs; in 1986, 16.6 percent, and 1996, the year Erdős died, 20.6 percent.

Twelve of the Erdős One women had Wikipedia pages, two of which had been nominated for ‘speedy deletion.’ The pages were tagged to be removed because the notability of the subject was questioned. Of the over 250 pages for men, I found eight with requests for speedy deletion and two requests to delete a proposed new page for the same reason (other tags threatened deletion, but in a softer way, simply requesting sources to support claims). All of the pages survived, though in a couple cases, they were deleted and then restored. The point I’m making is this: in this cohort of Erdős Ones, women were over four times more likely to have their importance questioned.

What evidence was being used to establish importance to begin with, I wondered. I began to look more closely at the page histories of the Wikipedia pages themselves.

A Wikipedia page history is often as interesting as the page itself. In the history, one can see the date the page was created, when information was added (or removed), copy edits, requests for citations, and discussions that often pertain to notability. In the history of mathematician Bruce Lee Rothschild’s page, for example, I saw one editor call into question Rothschild’s notability and the next editor demonstrate it, noting that the “Pólya Prize and Erdos number of 1 establishes notability.” The Erdős number was also cited in the page history of Micahel Makkai, with the note: “Erdos numbers 1 considered great honor in math community… they are like prizes…” When the Erdős number was deleted from mathematician Brendan McKay’s page, an editor named McKay restored the number to the page in the subsequent edit.

As I scrolled through page histories, I noticed that the Erdős number was often added early on, as if its absence were a flaw. Before 2008, Erdős numbers were even added as a category. According to the Wikipedia documentation, categories assigned to biographical articles represent ‘defining characteristics,’ which include the subject’s year of birth, year of death, nationality and ‘the reason(s) for the person’s notability; i.e., the characteristics the person is best known for.’

I realized also that the connection between the Erdős number and notability was far from unanimously recognized. One editor struck the Erdős number from Vance Faber’s page with the edit summary ‘so what?’ On other pages, the Erdős number was called ‘trivia’ or ‘puffery’ and deleted. Again and again as I looked at the page histories, my eye fell on the Erdős number, which I now saw as both a reflection of a skewed gender demographic, a result of a long history of discrimination, and a fairly controversial indicator of noteworthiness.

Nowhere were the different perspectives on the Erdős number more apparent than in the discussion regarding the proposed deletion of the Erdős number categories themselves. Like page histories, debates about changes to Wikipedia are archived and can be browsed, and I read all three discussions about the Erdős categories, one for each of the proposed deletions that failed, failed, and at last succeeded.

In the first debate, Editor bunix weighs in to support the Erdős number:

It is significant to us mathematicians. That’s why the American Mathematical Society database, by popular demand, now allows you to compute Erdos number.

In opposition, editor Fastifission writes:

Trivial form of categorization. I’ve yet to hear a good explanation of what meaning it has for mathematicians other than being a little bit of trivia. Knowing someone’s Erdos number only tells you, in effect, their Erdos number; ergo it has no real meaning outside of its own definition, and as such is probably not a useful form of categorization for Wikipedia (it does not, for example, tell you how famous a mathematician is, or how prominent they are, or how prolific they are — at most it might tell you how often they co-author a paper, but even that would be a purely probablistic approach and not work for many if not most mathematicians with Erdos numbers).

All told, over forty people weighed in, with the majority expressing support for the category.

The second time the category was nominated for deletion, twenty-five people participated and no one notified the mathematics community. Editor David Eppstein, who belatedly passed on this information to the mathematics people, notes this surprising omission. The second debate was ultimately characterized as ‘no consensus.’

Eight months later, the category was yet again called into question. This time eighteen people voted. The third debate is the fiercest of the three, with numerous references to Wikimedia policy meant to characterize and combat inappropriate behaviors. After what worked out to be about thirty single-spaced pages of argument, the deciding vote went to the delete side. “Many of the ‘keeps’ relied on the argument ‘nothing has changed since the last time,’ writes the deciding voter, ‘which isn’t a strong argument at all.’ Indeed, as far as I could see, nothing had changed aside from the people participating in the debate itself, as well as the passion of the debaters. One of the participants commented over forty times.

The three debates together illustrate an important point: In the vast gray area between a Nobel prize winner and unpublished newcomer, what and who is notable enough for record cannot be separated from the community that feels passionate enough to document or delete this information. Nor can we separate greatness from the criteria we use to define it. As I thought more about it, judging human excellence seemed no less subjective than judging art.

I found other stories in the Wikipedia pages, too. Esther Klein Szekeres, known for her work on the Happy Ending Problem, a puzzle of combinatorics and geometry, married her collaborator after working on the problem with him, hence the name. The text that describes the romantic timing of their deaths — she and her husband died within an hour of one another — is nearly the same on both of the mathematicians’ Wikipedia pages. However, her info box, which contains the summary information about her career, links to her husband’s page, and his info box makes no mention of her.

Ruth Silverman does not have a Wikipedia page, but I discovered a letter she wrote in 1971:

As a result of surveys on many campuses it becomes apparent that there is a pattern of discrimination against women in all fields …

1) Women are predominantly at the bottom of the pyramid, irrespective of qualifications … and suffer a substantial salary inequity. 2) Many academic departments have no full-time female faculty at all. In many … the percentage of female faculty is far below the percentage of females among qualified applicants. 3) In many departments women with Ph.D.s hold positions below the rank of Assistant Professor and are kept at these low ranks without promotion or significant salary increase. 4) Women tend to be hired on a marginal, temporary, or one-year basis …. Often women teaching part-time have the same teaching load as men teaching full-time. 5) There are departments which make it a policy not to appoint women who are married to members of the faculty …’’

I do not have academic publications, so my Erdős number is infinity and essentially meaningless as a measure of the distance between myself and others on the graph. I will say instead that I am one NOTG (‘Not On The Graph’) away from a woman who was denied employment at a University due to Silverman’s point 5. Not until the nepotism laws were changed — research showed that the spouses affected were invariably women — was she able to work at the University. I am also one NOTG away from a woman who had a math PhD and left the work force to raise her children as this was the decision that made financial sense.

I have read two biographies of Paul Erdős and he is clearly much beloved. He was generous. He was prolific. He loved his work and his love was contagious. When asked by the mathematician Lajos Posa, who at the age of 14 had already collaborated with Erdős on a paper, why there were so few female mathematicians, Erdős answered in his peculiar language: “Suppose the slave children (boys) would be brought up with the idea that if they are very clever, the bosses (girls) will not like them. Would there be then many boys who do mathematics?” I believe he is saying that if boys faced the same societal pressures girls do, very few would enter the field.

Erdős could easily have been thinking of 18th century Sophie Germain, who is known for her work on the proof of Fermat’s Last Theorem. When she was a child, her parents hid the math books (she found them) and removed the light from her room (she obtained her own candles). She was denied entry into the academy (she got the lecture notes) and she signed her letters to leading mathematicians with a man’s name, ‘Antoine-August Le Blanc’ to ensure that she would be taken seriously.

The mathematician Carl Gauss had the following to say about Sophie Germain when he discovered that the young man he’d been corresponding with was actually a woman:

But when a person of the sex, which, according to our customs and prejudices, must encounter infinitely more difficulties than men to familiarize herself with these thorny researches, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, then without doubt she must have the noblest courage, quite extraordinary talents and superior genius.

Here are the women I found in the Erdős One list:

Phyllis Chinn

Fan Chung

Yolanda (Columbus) Debose

Yael Dowker

Maria Klawe

Ewa Maria Kubicka

Carole B. Lacampagne

Jean Larson

Renu Chakravarti Laskar

Wen-Ching Winnie Li

Janice L. Malouf

Anja Gabriele Meyer

Ortrud R. Oellermann

Mary Ellen Estill Rudin

Ruth Silverman

Vera Turan Sos

Hendrika Cornelia Scott Swart

Claudia Alison Spiro-Silverman

Esther Klein Szekeres

Katalin L. Vesztergombi

Foong Frances Yao

I admire the genius of Paul Erdős, as well as every one of his collaborators, but I cannot think of the Erdős Collaboration Graph without also thinking about who is represented and who is not, and why.

Who will history remember?

Our words and our silences will determine this.