The connections between identity diversity and relevant cognitive diversity in mathematics are less obvious. Could gender, race, ethnicity, or physical capabilities influence the representations and analytic tools a mathematician applies?
Many of our complex challenges involve understanding the actions, preferences, and capabilities of diverse people. Thus, identity diversity also contributes relevant cognitive diversity.
The aforementioned efforts to reduce obesity require understanding economic, social, and psychological influences on behavior, as well as the impact of media. Our understandings of those dimensions will benefit from identity-diverse teams. The analysis of the effects of infrastructure will benefit from people from different geographic regions and from urban and rural locations. Overall, identity diversity may weigh in with similar magnitude as disciplinary diversity. To not include any men, or any women, on a team formulating an obesity-reduction program would be as shortsighted as not including a geneticist or a psychologist.
The connections between identity diversity and relevant cognitive diversity in mathematics are less obvious. Could gender, race, ethnicity, or physical capabilities influence the representations and analytic tools a mathematician applies? Sure. In mathematical research, identity is less germane than academic training, though it is possible that a person’s identity could influence how she represents a mathematics problem as well as the problems she chooses to tackle. That’s truer for the frontiers of math, where mathematicians often rely on analogies and knowledge from other experiences.
The lack of an obvious logic linking identity diversity to germane cognitive diversity in fields like math or physics does not mean that those fields do not need to be inclusive. On the contrary, because mathematics community confronts hard problems, it needs cognitive diversity.
Permit me a slight digression to make a larger point linking inclusion to cognitive diversity. Define the capacity of a mathematician as the number of tools she can acquire. A great mathematician might learn about twenty topics, a good one only fifteen. Excluding some identity groups from being mathematicians or making the field less attractive to some groups results in a cohort of mathematicians with lower overall capacity. If a woman with a capacity of twenty opts out of mathematics, and a man with capacity sixteen replaces her, then mathematics suffers. The profession loses talent because she has more capacity, and it loses diversity because of her larger capacity.
Fifty years ago, people chalked up the low representation of women and some racial groups in mathematics, and science generally, to a lack of interest—“Women do not want to become physicists.” As recently as twelve years ago, some attributed the low numbers in these professions (offensively, I might add) to a lack of cognitive ability. Current thinking points to the effects of limited opportunities and exposure, the lack of role models, and the effects of non-inclusive behaviors and discrimination.
Personal accounts of women who entered school with the interest and ability to excel at mathematics and science but pursued other paths reveal the accumulated dampening of interest produced by repeated acts of discrimination. Some actions were overt and direct. Others were subtler. Combined, they made science an unwelcoming place.
As an undergrad, I took a two-year math sequence listed as Honors Track II that students referred to as “math for gods.” Lacking any training in calculus, I struggled during the first two courses. Recently, I looked up three students who had excelled in those classes. All three have enjoyed successful careers. One works as the chief actuary and risk officer at a large insurance company. A second serves as a chaired professor of law at the University of Chicago. The third, the only woman of the three, began her career in engineering, rose to become a senior software engineer, and now works as a life coach, facilitator, and counselor.
Personal accounts of women who tried to pursue scientific careers reveal any number of obstacles, both direct and indirect.1 The fact that the two men remain in technical fields and the one woman opted out is not surprising, but it is disheartening. We lose talent and diversity when environments are not inclusive.
Data gathered by the National Science Foundation reveal low representation of women and minorities in many technical fields, and we cannot but infer lost diversity bonuses. In 2013–2014, 1,200 US citizens earned PhDs in mathematics. Of these scholars, 12 were African American men and just 6 were African American women. From 1973 to 2012, over 22,000 white men earned PhDs in physics, as compared to only 66 African American women and 106 Latinas. Those numbers translate into over 550 white men and fewer than 2 black women earning PhDs each year. Over that same time period, about 15 Asian American women earned physics PhDs each year.2
In addition, recall how mathematics connects to other disciplines and how those connections can produce bonuses. A person may apply his mathematical tools to a problem that leverages identity-based knowledge or interests.
Thus, even if we see no obvious direct links between identity and relevant cognitive diversity within a technical field, diversity and inclusion produce bonuses by increasing the pool of talent and the range of problems studied. Think back first to the complicated graph of mathematical knowledge. People with greater capacity can trace out longer paths in that graph. Their talent adds diversity. In addition, on cross-disciplinarity complex tasks like the obesity epidemic or rising opioid use, identity-based knowledge or perspectives become germane, and identity brings relevant cognitive diversity.
2. Data available from the National Science Foundation and the American Mathematical Society. See William Ysalis Vélez, James Maxwell, and Coleen Rose, "2013-2014 New Doctoral Recipients," Notices of the American Mathematic Society 62, no. 6 (2015): 771-781.