These days our institution is quite concerned with diversity and
broadening participation. Recently we had a presentation devoted to a
single question: Why are there so few women at the
top US mathematics departments?
Popular culture identifies three factors that contribute to individual's success: perseverance, will power and hard work; talent and natural abilities; and supportive environment.
American mythology puts premium on hard work and natural abilities, while modern thinking (as in Gladwell's book "Outliers") points to the environmental factors.
Clearly a tenure at Math Department at Harvard requires plenty of talent, hard work and as much support as one can get. Yet I will argue that environmental factors alone can account for the observable disparity between men and women at the top academic tier of mathematical sciences, and one does not need to look further.
In this context environment relates to a myriad of stimuli, some positive and some negative, that one receives while pursuing professional goals. Each of these stimuli is not significant, and they do not raise to the level of being a behaviour changing factors, yet collectively they shape one's direction, particularly over a long period of time.
The main point is that the overall effect of the environment seems to be exponential. For example, in a large group of students learning a difficult subject one will generally observe that certain percentage of them will drop out after one semester, similar percentage after another semester and so on. In other words, the rate of change is proportional to the quantity that is measured which means that the attrition rate follows an exponential curve. In such situation, even tiny difference in the way one interacts with the environment leads to a dramatic difference twenty years later - a time it takes to climb near the top of the ladder in mathematical sciences. Another simple example illustrating this phenomenon is as follows - suppose that getting tenure is akin to getting certain number of heads in a long sequence of coin tosses (with asymmetric coin). If the probability of getting a head in a single toss is larger than some threshold value then the probability of success is very high and it goes exponentially to one as the length of the trial increases. On the other hand, if the probability of success is lower than the threshold value then the odds of success go exponentially to zero at a rate that depends on the difference between the threshold value and the number of trials.
How would one test the effect of the environment?
We need to find an activity that is somewhat similar to doing mathematics, but where it takes much less time to reach super-star status and (ideally) where the environmental factors are more gender blind. Mathematicians may be upset with this choice but I think that spelling is the right comparison and it proves the point.
Spelling is a curious activity which has a well organized support system. No US kid can escape being pushed to the maximum level that their ability and patience will allow. Spelling talent is easily recognizable, training is straightforward and the very ability to do super-human spelling is not
intimidating. Year after year the group of top 100 US spellers has the numbers of boys and girls, minorities, poor and rich kids, etc., that conform to the anticipated frequency. Statistics that deviate from the expected values are mostly genetic - having super-spellers in the family, etc.
Inescapable conclusion is that both ability and will power to be a super-speller is distributed in the population quite evenly and even-handed system aimed at identifying top performers and eliciting from them several years of hard work to reach the finals of the National Spelling-Bee works well.
Back to mathematics - the path to the comparable status in mathematics takes about twenty years. Mathematics is far more intimidating than spelling and performing at the higher level will not automatically get you in touch with likewise gifted people. Quite the opposite, mathematically gifted kids endure years of boredom at school and often question their own sanity. Assessing mathematical talent and nurturing it is not easy and in this respect the system works moderately well only at the graduate school level. Overall the path is long, steep and arduous.
The educational system favors men when mathematics and other sciences
are concerned. It is not a strong bias but rather a persistent push
which gives a sense of swimming against the current. Women are
constantly discouraged from pursuing mathematics - by teachers,
families, friends and media. Because of the gender imbalance there are far
fewer role models and support networks. On the path to mathematical
pantheon, one has to go through graduate school and one or two
postdoctoral positions. While men can move their families with relative
ease, women often face the phenomenon of an immovable spouse. Dream job requires tremendous level of accomplishment and related commitment of time and energy. It is safe to say that at a time these efforts are needed women have more on their plate than men. To get a job one needs a number of publications in top journals. These days a lot of work is collaborative and it is fairly common that in cases of joint work involving male and female mathematicians, the men's work is often viewed as more substantial. Professional success of female mathematicians that happen to be good looking and attractive often brings another type of speculations - yet another small insult that is painful and difficult to confront.
There is much more to say here but the point is perhaps clear - climbing to the top of mathematical profession is just a tad harder for women than for men. Those who succeeded devoted approximately half of their life to it. Just having a few extra hoops to jump through makes a lot of difference in this endurance race.
If one accepts this argument then there is a natural follow up supported by Bayesian statistics. If one succeeds against the odds then with high likelihood there is a compensating factor. Consequently, women at top math departments were more driven to succeed or they were simply better mathematicians than their male counterparts - both possibilities easily supported by anecdotal evidence.
broadening participation. Recently we had a presentation devoted to a
single question: Why are there so few women at the
top US mathematics departments?
Popular culture identifies three factors that contribute to individual's success: perseverance, will power and hard work; talent and natural abilities; and supportive environment.
American mythology puts premium on hard work and natural abilities, while modern thinking (as in Gladwell's book "Outliers") points to the environmental factors.
Clearly a tenure at Math Department at Harvard requires plenty of talent, hard work and as much support as one can get. Yet I will argue that environmental factors alone can account for the observable disparity between men and women at the top academic tier of mathematical sciences, and one does not need to look further.
In this context environment relates to a myriad of stimuli, some positive and some negative, that one receives while pursuing professional goals. Each of these stimuli is not significant, and they do not raise to the level of being a behaviour changing factors, yet collectively they shape one's direction, particularly over a long period of time.
The main point is that the overall effect of the environment seems to be exponential. For example, in a large group of students learning a difficult subject one will generally observe that certain percentage of them will drop out after one semester, similar percentage after another semester and so on. In other words, the rate of change is proportional to the quantity that is measured which means that the attrition rate follows an exponential curve. In such situation, even tiny difference in the way one interacts with the environment leads to a dramatic difference twenty years later - a time it takes to climb near the top of the ladder in mathematical sciences. Another simple example illustrating this phenomenon is as follows - suppose that getting tenure is akin to getting certain number of heads in a long sequence of coin tosses (with asymmetric coin). If the probability of getting a head in a single toss is larger than some threshold value then the probability of success is very high and it goes exponentially to one as the length of the trial increases. On the other hand, if the probability of success is lower than the threshold value then the odds of success go exponentially to zero at a rate that depends on the difference between the threshold value and the number of trials.
How would one test the effect of the environment?
We need to find an activity that is somewhat similar to doing mathematics, but where it takes much less time to reach super-star status and (ideally) where the environmental factors are more gender blind. Mathematicians may be upset with this choice but I think that spelling is the right comparison and it proves the point.
Spelling is a curious activity which has a well organized support system. No US kid can escape being pushed to the maximum level that their ability and patience will allow. Spelling talent is easily recognizable, training is straightforward and the very ability to do super-human spelling is not
intimidating. Year after year the group of top 100 US spellers has the numbers of boys and girls, minorities, poor and rich kids, etc., that conform to the anticipated frequency. Statistics that deviate from the expected values are mostly genetic - having super-spellers in the family, etc.
Inescapable conclusion is that both ability and will power to be a super-speller is distributed in the population quite evenly and even-handed system aimed at identifying top performers and eliciting from them several years of hard work to reach the finals of the National Spelling-Bee works well.
Back to mathematics - the path to the comparable status in mathematics takes about twenty years. Mathematics is far more intimidating than spelling and performing at the higher level will not automatically get you in touch with likewise gifted people. Quite the opposite, mathematically gifted kids endure years of boredom at school and often question their own sanity. Assessing mathematical talent and nurturing it is not easy and in this respect the system works moderately well only at the graduate school level. Overall the path is long, steep and arduous.
The educational system favors men when mathematics and other sciences
are concerned. It is not a strong bias but rather a persistent push
which gives a sense of swimming against the current. Women are
constantly discouraged from pursuing mathematics - by teachers,
families, friends and media. Because of the gender imbalance there are far
fewer role models and support networks. On the path to mathematical
pantheon, one has to go through graduate school and one or two
postdoctoral positions. While men can move their families with relative
ease, women often face the phenomenon of an immovable spouse. Dream job requires tremendous level of accomplishment and related commitment of time and energy. It is safe to say that at a time these efforts are needed women have more on their plate than men. To get a job one needs a number of publications in top journals. These days a lot of work is collaborative and it is fairly common that in cases of joint work involving male and female mathematicians, the men's work is often viewed as more substantial. Professional success of female mathematicians that happen to be good looking and attractive often brings another type of speculations - yet another small insult that is painful and difficult to confront.
There is much more to say here but the point is perhaps clear - climbing to the top of mathematical profession is just a tad harder for women than for men. Those who succeeded devoted approximately half of their life to it. Just having a few extra hoops to jump through makes a lot of difference in this endurance race.
If one accepts this argument then there is a natural follow up supported by Bayesian statistics. If one succeeds against the odds then with high likelihood there is a compensating factor. Consequently, women at top math departments were more driven to succeed or they were simply better mathematicians than their male counterparts - both possibilities easily supported by anecdotal evidence.
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