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

Peace is a Radical Pursuit: A Poem for Shabbat Jazon

Peace is a radical pursuit

Not the desire of polite society

To avoid the drama and chaos

Of conflicting human instinct

The pundits cry out for the moderates

"Where are the reasonable voices?"

They ask for the confrontation-averse

They call for the champions

Of maintaining the status quo

The wise who would rather

Continue to live in a world

Of unchallenged hypocrisy

Where occupation is sustainable

And terrorism acceptable - for now -

As long as it doesn't flood

The news feed or clog

The air waves or clutter

The rabbi's disagreeable sermon

The pundits cry out for the peacemakers

"Where are the reasonable voices?"

They ask for the confrontation-averse

They call for the champions

Of maintaining the status quo

The wise who would rather

Continue to live in a world

Of unchallenged hypocrisy

Where occupation is sustainable

And terrorism acceptable - for now -

As long as it doesn't flood

The news feed or clog

The air waves or inflame

The imam who is a foreigner

Anyway - from the Bronx

How exotic - And always

Jews first and Muslims after

Peace is a radical pursuit

Not meant for civility

Peace is not easy or quiet

It does not make way

For celebrity gossip

Or whatever it is that

Normal people care about

Peace is abnormal, anomalous

A miracle, I say, all say

Peace means I must care 

About your happiness

As much as I care about mine

It means I must hurt about your pain

As much as I hurt about mine

Peace means that I know

That the word naqba

Emotionally translates to galut

That it is real and

That it will be felt

Statehood or not

For the rest of forever

Until mashiaj comes

To be a Jew means that I believe

With perfect faith that she is on her way

Already, though she delays

To be a Jew means to believe

In the radical notion

That peace is possible

Even now, especially now

Achieving peace as a Jew

Means I must be like the disciples

Of Aaron - loving peace and pursuing it

To be a Jew is to be a storyteller

Of exile - of survival

That inspires the Dalai Lama

To be a Jew is to respond

To the most heated argument

With the affirmation

That these and these are

The words of a living God

The merciful, the compassionate

In which I may not believe

To be a Jew means

To not oppress others

Because I know oppression

To be a Jew means I must beat

My swords into plowshares

And my spears into pruning hooks

And then I must beat my plowshares

Into trumpets and my pruning hooks

Into guitars - to be the folk song army

To be a Jew is to turn

To turn my song into prayer

To be a Jew is to end

All my prayers with prayers for peace

And to pray not only with my words

But also with my feet

Peace is a radical pursuit

Not for those who justify any

Violence against tunnelers

Who are obviously up

To no good at all

Not for those who try

To figure out who

Has the moral high ground

Peace does not blame or shame

Peace is not the absence of violence

It is the hurling of understanding

Against hatred, of love

Against fear, of kindness

Against all types of aggression

Peace is a radical pursuit

It is the humble admission

That I don't know
What it's like to be you

That I will never know

What it's like to be you

But that I wish for you

To have everything that I want

And everything that you want

Peace is a radical pursuit

It is the acknowledgement

of guilt and pain and sorrow

Peace is a radical pursuit

It is an offering

Of the broken self

To experience 

Further vulnerability

Peace is a radical pursuit

Peace is not the prophet's vision

Peace is not the musician's hope

Peace is not the artist's aspiration

Peace is not the poet's dream

It is her job

Peace is as close to us

As the air we breathe

And as perplexing

As that breath we spend

So many hours trying to find

Welcome to the world's

Most hazardous occupation

Peace is a radical pursuit

It is not standing with anyone

It is sitting with everyone

It is for the brave-hearted

It is for the strong-willed

It is for the faithful

Peace is the proclamation

That in the face of every

Unimaginable provocation

As well as the expected ones

We will not feed the trolls

Except at the dinner table

Where they should eat more

Moderation perpetuates

Hatred and violence

It exacerbates

The pain of the status quo

Moderation is unreasonable

Peace is the reasonable alternative

Peace is a radical pursuit

Impatient, chutzpadik, a loud

Call to prayer at sunrise

Peace is a pundit

Demanding that we abandon

Being perpetrators and being victims

Peace is an activist

Fighting for its presence

Peace is an organizer

Asking you: Are you radical enough?