# Age, Gender, and the Highest Award in Mathematics

This fall’s news that Canadian Donna Strickland became the third woman to win a Nobel Prize in Physics filled me with national pride and appreciation for women in STEM. However, it also reminded me of one of math’s greatest disappointments of 2018: the fact that none of this year’s Fields medals went to a woman. These medals are awarded every four years, and only one Fields Medal has gone to a woman: 2014’s award to the late Maryam Mirzakhani.

Why only one? This question has been discussed in many different forums and explanations range from differences in ability between men and women to discrimination and bias. Here, I will write about how one feature of the prize itself — its age requirement — may contribute to the inequity.

### The Fields Medal Age Limit

Donna Strickland was 59 years old when she won the Nobel Prize in Physics. Prior to her, Maria Goeppert-Mayer was 57 when she won a 1963 Nobel Prize and Marie Curie was 36 when she won a 1903 Nobel Prize in Physics. If the Nobel Prize had the same rules as the Fields Medal currently does, only Curie would have qualified. This is because, in 1966, the IMU codified a maximum age limit of 40 years old for Fields medal winners.

Why is the under-40 requirement in place? I have often heard that it is because medalists will have more time to use the award to do great future work, perhaps taking more risks than they would without the security that comes from holding the award. However, the age requirement was actually put in place to ensure greater equity in the awarding of the Fields Medal: in the 1960's age became a proxy for the award’s original goal of identifying previously under-recognized mathematicians rather than piling yet more awards on mathematicians who were already well-known.

A natural question follows: does the under-40 age requirement ensure more equality in the Fields Medal? The record of winners suggests it does not meet this goal when it comes to gender. In fact, I believe that the age limit does harm beyond the elite levels of mathematics.

### “Math is a Young Man’s Game”

One of the most pervasive myths of mathematics is that we do our best work when we are young; as Hardy wrote, “mathematics, more than any other art or science, is a young man’s game.” In her chapter on the myth of youth in mathematics, Claudia Henrion writes that we see mathematicians as “a kind of mental athlete.” Whether or not it played a role in the 1960's decision to impose the age requirement on the Fields Medal, the idea that mathematicians do their best work when they are young is now intricately linked with the award.

#### Why is it a myth?

Is math really a game for the young?

Studying the relationship between age and productivity — whether it be mathematical, scientific, creative, or otherwise — is both complicated and controversial. One key finding is that an individual’s personal career trajectory does not necessarily follow the same curve as that of their peers or colleagues.

Specific to mathematics, Nancy Stern studied the quality and quantity of work done by mathematicians in the late 1970's and concluded: “In short, no clear-cut relationship exists between age and productivity, or between age and quality of work. The claim that younger mathematicians (whether for physiological or sociological reasons) are more apt to create important work is, then, unsubstantiated.” While I have seen more recent quantitative studies in other fields, I do not know of a similar follow-up study for mathematics.

Anecdotally, many mathematicians report that they did better work as they aged than they did when they were young and women may be more likely to report being more productive as they age. One indisputable fact is that many mathematicians do great work when they are older, despite coming into mathematics late. As Fan Chung relayed in her interview with Claudia Henrion, “I think I’ve proved my better theorems recently. I think my last year’s work was my best. People have different paces, especially women. Some people peak later in their lives.”

It is not only the young who excel in mathematics. Further, it is far from clear that the average career trajectory peaks in productivity or quality of work early, particularly when we restrict our attention to women and to those underrepresented in mathematics.

#### Impact of the Myth on Genius and Gender

I’ve heard some mathematicians say that a belief that mathematical discoveries lay in the hands of youth was inspirational and pushed them to work harder during their early careers, but for me it had the opposite effect. I knew that I was not going to change the face of mathematics in my 20's or 30's. I had other priorities for these decades of my life — both personal and professional. Women know that they will have an easier time establishing families, households, and sustainable careers in their 20’s and 30’s than they will in their 40’s or 50’s and the idea of also being expected to reach peak mathematical performance can seem impossible.

The belief that mathematicians are most productive when they are young, however, can have deeper and more damaging consequences since it feeds into the myth of the mathematical genius. If we are more likely to make mathematical discoveries in our 20s than in our 40s, the role of experience, research, discernment, networks, and other characteristics that can only come with more time in the field are diminished and we can only attribute success in the field to innate “talent” or “insight”.

The genius myth is closely associated with the lack of representation of women in mathematics. In a 2015 study appearing in Science, researchers showed that women are less represented in fields that we view as requiring raw talent rather than hard work. Other research shows that people as young as age 6 find it difficult to view women as geniuses. This doesn’t mean that women are any less talented than men, but they are perceived to be less talented.

In short, associating math with youth and with genius makes it less likely that women will participate at all: girls, women, and those around them have are less likely to see them excelling in mathematics due to our biases. Further, when we divide the population into people who are talented in mathematics or not talented in mathematics, stereotypes flourish and we see the field as not open to everyone. We see this belief not only at the elite levels of research, but also as early as elementary school age.

### …But is the Age Requirement Necessary?

While the age requirement of the Fields medal was originally imposed to ensure greater equity, some will argue that it has come to play a number of other important roles.

#### Argument 1: Mathematicians should receive the Medal when they can still benefit from it

The age requirement gives promising mathematicians the security, resources, and recognition that they need to become more productive while they still have time left in their careers. A Fields medalist never needs to worry again about the security of their position in academia and will therefore be more free to take risks in their research. These risks, in turn, could potentially lead to greater rewards than if they had stayed in their current area.

Why I don’t buy it: The evidence noted above demonstrates that it is not only mathematicians under 40 who have time left in their careers to make great contributions. I do not see why any mathematicians who are still active in their careers could not receive the same benefit: the number of years left in one’s career does not necessarily correlate with future output, particularly when it comes to women.

#### Argument 2: The age requirement encourages young mathematicians to work hard

The age requirement encourages young mathematicians to work as hard as they can early in their career.

Why I don’t buy it: The Fields medal is such a rare and high honour that I doubt few people pursue mathematics research because they believe that they will one day be successful enough to win the award. Research about the confidence of men and women suggests that anyone who believes that they will someday receive the medal is likely to be a man. If true, this reasoning for the age requirement actually works to make it less inclusive to women and minorities.

#### Argument 3: The age requirement encourages equality

The original reason for the age requirement is that it would allow us to recognize mathematicians who would otherwise be overlooked.

Why I don’t buy it: While this was the original reason for the age requirement, we don’t hear this argument very much in the popular mathematics community precisely because it hasn’t worked to make the award diverse. For example, a list of countries by the number of Fields Medals is dominated by the United States and European countries, includes just one South American award, and no African awards. A quick look at articles and message boards from the period prior to the announcement of the 2018 medalists shows that Peter Scholze was considered a shoe-in, Alessio Figalli a strong candidate, and Akshay Venkatesh and Caucher Birkar were off of most people’s radars. However, Venkatesh and Birkar were hardly unknown; for example, Venaktesh was one of three named Simons Investigators in math for 2018. The awards went to mathematicians who were already well recognized for their work and certainly did not lift them from obscurity.

### Where to Go From Here

After another round with no female awardees, I hope that the ICM is examining the Fields Medal as a whole, including the age requirement. Has the requirement achieved its goal of recognizing mathematicians who may be overlooked? Is it doing any harm to the field or to the mathematical community? Can we find other ways of making sure that the medal recognizes a diverse set of members of the mathematical community? As the ICM tackles these questions, I am excited to be part of a vibrant community of women of all ages who contribute to mathematics.

My interest in and views about the Fields Medal were greatly influenced by Henrion’s examination of this topic in Women in Mathematics: The Addition of Difference.