Beyond Mathematical Discovery: What Having a Woman Fields Medalist Really Means

There is no Nobel Prize in Mathematics.  And while the Norwegian government has managed to fund a separate prize called the Abel Prize with a similar monetary award and the Israeli government issues a coveted Wolf Prize in the discipline, no mathematical prize means more in mathematics or outside it than the Fields Medal.  The monetary value is only $15,000 Canadian, but the prestige is priceless. This year, for the first time, the Fields Medal, which can be awarded to as many as four people every four years, was awarded to a woman, Maryam Mirzakhani, and awarded to a mathematician from the global south, Artur Avila.  The press is making a big deal of the woman thing and not a big deal about the global south thing, which should not surprise anyone.  The press is also trying to diminish the significance of a woman winning the Fields Medal by stating that no woman has yet won either the Abel or Wolf Prize in mathematics and talking statistics on the sex ratio of Ph.D.s in mathematics.

These prizes are all awarded for mathematical discovery in particular, not pedagogy, compilation of resources, or many of the other things that academic mathematicians do in their work. All but one recipient of the Fields Medal has been an academic.  When you think about mathematical discovery, you think about a bunch of dead white guys having eureka moments in their bath tubs with a crown.  And maybe, if you are the child of mathematicians like me who was the right age in 1994, you think about Andrew Wiles holing himself up in secrecy for seven years to prove Fermat's Last Theorem.  And, if you read the news, you might also think of the one non-academic Fields Medalist Grigori Perelman, who proved the Poincaré conjecture.  Even if you are the child of two mathematicians, you probably don't think about your mother running Maple calculations about complex manifolds while cooking dinner, or a young mathematician taking a break from writing a paper to nurse her child.  And you don't think about how the ability of even a brilliant mathematician to devote the time and energy to amazing discovery and to get the resources she needs is dependent on her gender.  Only 30% of mathematicians are women, and far fewer are tenured faculty at the world's top research institutions.

Before getting to the Fields Medal itself, let me push the other prizes to the side.  The Wolf Prize has only existed since 1978, and it is a lifetime achievement prize.  Its recipients are the authors of your college mathematical textbooks, the provers and conjecturers of Big Theorems, and the founders of new mathematical disciplines.  Among its recipients are many Fields Medalists, and it has no age cap.  This means that the gender bias in its recipients spans not just the last 20 years (assuming start of real mathematical work around age 20) but of the last 50 to 60 - Shiing-Shen Chern received the prize at age 73.  So, when looking at a Wolf Prize awarded in 2014, we need to look at the gender biases in mathematics at least back to 1964.  The Abel Prize has only been in existence since 2001, and despite its 6 million kroner ($1 million US) prize, is not discussed as a goal in mathematics.  Its recipients are mainly winners of the other two prizes, and I think it is still working to establish itself as a legitimate prize, and picking winners helps in that.  It is worth noting that my mother's thesis advisor, Isadore Singer, shared the prize with Sir Michael Atiyah in 2004 for the Atiyah-Singer Theorem, which won a Fields Medal for Atiyah but not for Singer, as singer was too old to win the prize at the time.  Similarly there is no age cut off for the Abel Prize, which is also in the process of making up for its years of not existing.  It is therefore not surprising that it has not yet been awarded to any women.

Now for the Fields Medal, which is awarded for outstanding discoveries by young mathematicians.  For young mathematicians to succeed in quests for discovery, they need to be in the right environment and have support and the time to make their discoveries.  This includes being in a research environment full of other talented mathematicians, usually ones in your own field, and having the support to do independent and collaborative research as well as teach.  Additionally, being able to make mathematical discoveries is not usually a matter of Eureka moments but of extensive contemplation and research, something which taking the time to bear and raise children, even if not taking time off from academic teaching responsibilities, can severely hamper women's progress in mathematicians.  While plenty of men mathematicians spend time raising children and caring for their families, they also have the option of having children later in life (which they do) and passing off care responsibilities to their partners in ways that are not acceptable for women.  The consistent gender imbalance of faculty at elite institutions makes it even harder for women to get the resources they need to overcome these challenges.  Top young women mathematicians are often given excellent positions at 2nd tier schools who are interested in attracting young mathematicians to keep and expanding which fields they have faculty in.  They take these jobs because tenure is hard to come by and they are then set for life.  But it makes incredible discovery harder.

I am hopeful with these latest Fields Medalists.  The inclusion of a mathematician from the global south means that meaningful mathematical educational structures are developing there.  The award going to a woman under 40 at a top American institution means that we are on the way to fixing the gender disparity in mathematics.  If she can now get the support she needs at Stanford, others will be able to as well, and more women will want to become mathematicians.  Programs will have to be more attentive to specific needs and concerns of women.  And maybe fifty years from now, the Fields Medal, the Abel Prize, and the Wolf Prize in mathematics will all be able to be given to amazing mathematicians of many genders on a regular basis.

9 Av

This year I find that my fast has been easy so far, with three hours left to go.  Not that that's the point of Tisha b'Av, but it's noteworthy.  I feel appropriately in touch with brokenness and conscious that our world remains unredeemed. But Tisha b'Av as mourning doesn't feel meaningful, maybe because I'm already mourning.  In addition to the loss of Mr. Boy, this year Tisha b'Av is my grandpa's yahrzeit.  The metaphor of a bottom speaks much more to me this year.  It feels like the world, the people Israel (not to mention the land), and my life have all hit bottom.  I wish I could write more on this, but now is not the time.

Anyway, some 9 Av meditations if you are in need.  Not standard ones.

https://www.youtube.com/watch?v=dRPwFAoQwxc

http://www.theguardian.com/world/2014/jul/20/sayed-kashua-why-i-have-to-leave-israel

If Tisha b'Av falls on Rosh Jodesh, do you fast?

The title of the above refers to a trivia question I once answered.  It's a trick question, because Tisha b'Av means the ninth day of the month of av, so it can never fall on Rosh Jodesh, which is the first day of the month.  That said, if Tisha b'Av falls on Shabbat, you commemorate it the next day instead.

Last night, I attended Mishkan's Tisha b'Av observance, which included Ma'ariv, Reading of Eicha (the Book of Lamentations), and a conversation about our sadness and love when it comes to Israel.  As a Tisha b'Av observance, it was the closest I have come to my Tisha b'Av experiences at OSRUI - meaningful, hot, and at some points frustrating.  The pain in the room was real and the mood somber, but somehow, in leaving with the brokenness of the day, I came out more whole.

I did not grow up with a Tisha b'Av observance in my family.  As someone with staunch Reform upbringing, Tisha b'Av was (for those who knew about it) considered an inappropriate holiday to commemorate because the Reform Movement does not believe the destruction of the Temple to be a bad thing, and therefore does not mourn the event.  However, Tisha b'Av was commemorated at my summer camp, in a beautiful fashion that bestowed the day with contemporary meaning for this mourning.  We talked about sinat jinam, the senseless hatred that Jews see as our part in the destruction of the Temple.  But more than that, the ritual was well-crafted to imbue the day with sorrow and with connection to the history of the Jewish people: tragedies and persecution included.  Living in a time of relative peace and privilege for Jews, this connection was new for me.  I am here because my ancestors responded to persecution by making themselves stronger, because the response to the question eicha has been that part is under our control.  We find things we could have done better even when we recognize that others are responsible for inflicting violence, persecution, and genocide on us.  We could sit in our hatred of them or of God, but instead we reflect on what it is about us and the way we live that exacerbates the damage done to us by others.

I remember that unit heads carried the Torah from our units to Port Hall as the rest of us joined hands and walked singing Don McLean's "By the Waters of Babylon."  We entered Port Hall where we snaked around and joined hands with other units as well until everyone had entered and we sat on the ground.  Passages of Eicha were chanted in Hebrew and read in English, and the list of tragedies that ostensibly occurred on Tisha b'Av was read: destruction of the first Temple, destruction of the second Temple, the start of the first crusade, expulsion of the Jews from England, expulsion of the Jews from France, expulsion of the Jews from Spain, declaration of the Final solution, and the beginning of the deportations from the Warsaw ghetto (not to mention the Toraitic events that the rabbis associated with the day).  The history of how each Torah came to be at camp was recounted, with background information of situations of persecution and how Torahs were rescued if that was the case.  Esa einai was often sung, and we walked back after in silence, which was not a common sensory experience at camp.  The next day (Jewish days start at sundown and go to sundown) we would bury religious texts that were no longer usable in the camp genizah.  I don't know how the custom of adding to a genizah became associated with Tisha b'Av, but my conjecture is that Jews find the loss of text to be of similar importance to the crash of an entire way of life.  I carry nostalgia for that Tisha b'Av experience: the sense of connection to my people when all seems lost, and of being able to take concrete action to mourn the past but also of being able to take concrete action to build a better future.

The observance last night included "By the Waters of Babylon" and traditional kinot.  It included chanting of Eicha and reading it in English.  We sat on a hard floor in the summer heat, and although candles burned, we started before sundown and the effect was not one of darkness.  And we had a "conversation" about Israel, which is a topic that many in the Jewish world see as so divisive that we only talk with like-minded folks.  I put conversation in quotes because it wasn't a conversation in the usual sense. We were first asked to consider where our love comes from when it comes to Israel and where our sadness comes from when it comes from Israel.  We were given paper and pens to write our thoughts and some time (although not enough) to consider.  Then we were asked to listen to those who volunteered to share.  This was an exercise in "vulnerable listening," we were told, which apparently means being attentive and nonjudgmental toward the speaker, but also not to display any emotional reaction you may be having.  Sharers were to take no more than three minutes each and were instructed to give their names at the beginning of what they said, speak in "I language," and say "Thank you for listening" at the end, to which the response from the community was "Thank you." These stipulations led one person to comment that it felt like a "Jews Anonymous" meeting.  I think these regulations were necessary for people to feel safe sharing about a sensitive subject, but by no means did they engender conversation.  Sharers could only focus their comments on their own experiences and feelings, which prevented anything I would call conversation (questions asked an answered, deeper thoughts provoked, progression of ideas possible) from taking place.  It was uncomfortable to listen to people vent their frustrations about Israel.  It was hard to maintain a non-emotional face listening as things I disagreed with or agreed with whole-heartedly were said, and especially as others bared their souls, it was hard to resist impulses to comfort.  The discomfort and pain were fitting for the day.  After the discussion and the reading, we had more space for singing and meditating on loss.  Then we had Ma'ariv (no, not traditional, but again, we started before sundown).  We spoke Ma'ariv, which gives an eerie quality to prayer, and is traditional, as music might increase the enjoyment of the experience, and the idea is that one is praying out of spite because one is in too much pain to do otherwise, and we left, only speaking what was necessary to clean up the space after use.  I walked to the Red Line in silence and rode home, also in silence.  To allow ourselves time to process pain and grow from it is extremely powerful.

Tisha B'av

Perhaps it is problematic that I associate Tisha B'av with haunting music and books - two of my favorite things.  But Eichah trope and other reflective music moves me.  At camp, we used the occasion of Tisha B'av to bury old unusable books with the tetragrammaton in a genizah.  The reverence for books in the Jewish tradition is one that my nerdy self also loves.  The pain of needing to dispose of a book as national pain was a wonderful lesson to learn as a child. Books are powerful and words have the capability to kill or to save lives.

On Tisha B'av, both Temples were destroyed.  Jews were expelled from England, France, Spain, and Portugal on the date.  World War I started on the date.  The rounding up of Jews into ghettos in Poland started on the date, and the deportation from the Warsaw ghetto also happened.  Whether some of these dates were actually on Tisha B'av is unknown, but the commemoration becomes a container for our anguish.

This Tisha B'av, I'm trying to recognize national and personal pain and also the hope of leaving that pain behind.  Tisha B'av starts a season of reflection, self-improvement, and t'shuvah, and we read at the end of Eicha a prayer for God to facilitate our process of t'shuvah.  I'm grateful that in the depths of our sadness, we have hope of a better world.

Indepence Day

I narrowly avoided an argument with my roommate yesterday. The ginkgo girl moved out in the middle of June and one of my other friends moved in with me. There are very few arguments I do not wish to have. There are very few arguments I do not wish to have, but there are three or four that I cannot have and be civil at the same time. One of those is about the founding moments of the United States of America. When my roommate suggested that celebrating Independence Day was irrelevant to modern American life, it took all my strength not to go ballistic. I wanted to throw it back in her face and say that her being able to say that without fear of repercussions is reason enough to appreciate our freedom and form of government. I wanted to say some choice words too, but I simply suggested that I didn't want to have the argument and moved on.

We take our freedom and the struggle for our independence for granted now, perhaps because we feel historically removed from the situation. None of us were there for the continental congress when the Declaration of Independence was signed. We are so far removed from these struggles that when a survey was conducted in the 1960s asking people to identify the source of the first line of the Declaration of Independence, most thought it was from the charter for the radical organization Students for a Democratic Society. The line reads: "When, in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the laws of nature and of Nature's God entitle them, a descent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation." Usually, this confusion is used to point to the failures of American e ducation, which it certainly points to. However, the sentiments of revolution so eloquently captured in Thomas Jefferson's words are relevant not only to the American revolution, but to many subsequent ones.

I don't think the USA is the best country in the world, or that we always live up to the ideals that we have as a nation. But I do know that we are always expanding those ideals: voting is no longer restricted to rich white men, and we abolished slavery. And after the civil war which split our nation in two, President Lincoln assured "malice toward none" who had been in the confederacy. We are in struggles to expand equality further in this country. So, today, I will try not to take the freedom I enjoy for granted, and renew my commitment to helping expand the rights of those who live around me.