The Most Important Problem in Mathematics
Mathematicians sometimes like to say that such and such problem is "trivial". In my experience it doesn't actually mean that they know how to solve it, just that they think they could, and don't want to do it right now. There are various lists of the most important problems in Mathematics. For example, the following will suffice for now:
These are pretty complete lists. WRONG! The above problems might be the most interesting and fun problems, but they are not the most important. The most important non-trivial problem in mathematics, particularly in the US, is trying to figure out how to get more people and more diverse people interested in and working hard at mathematics. I have no idea when or if the problems in the above lists will ever be solved, but I can guarantee you that they are more likely to be solved if more people are interested in working on them. In short, the major problem in mathematics is a human capital problem, and it is never going to be solved if the people that actually know and genuinely like math have no interest in solving it. There are programs attempting to address this problem around the country and they have actually been around for many years, for example, the Ross program, and variations of "Young Scholars Programs" at various universities around the country (University of Chicago, Northwestern come to mind). Here's a new one I just heard about
I applaud such programs and fully support them, but there is one teeny weeny problem they have always had for the last 60 years: the "high end" programs always have kids that look like the kids pictured in the above link. This program is in New York, arguably one of the most diverse cities in the world. Do you mean to tell me you couldn't find ANY visibly black and Latinx kids? Really? In other words these programs typically only address part of the human capital problem and completely ignore the black and Latinx kids. As a word, "diversity" has fallen on hard times lately, but even when everyone was constantly paying lip service to diversity, as far as I can tell it never amounted to much concrete action in STEM that produced results.
The above article is literally showing us the beginning of the dreaded "pipeline" and when you see it and imagine it being multiplied across the country, it is really no mystery that the end of the pipeline, the faculty in US STEM departments, are similarly homogeneous. It is actually straightforward to examine what a sample of US STEM faculty actually look like.
Here is a grid diagram representing the approximate skin colors of a sample of higher ed math faculty in the Chicago area. The x's are just place holders since we used the smallest enclosing square for the shape of our grids. The green faculty member is either Orion or was possibly exposed to gamma radiation. Actually, that's just a bad point which is inevitable when you are doing data science and ML and collecting raw data. We made no effort to curate the data.
We can represent the same population as a point cloud in 3 space where the position of the point is determined by its RGB coordinates. Roughly speaking, the points are clustered towards (1,1,1) because most of the people are lighter and the points avoid (0,0,0) for the same reason. (0,0,0) represents absolute black and (1,1,1) represents absolute white. The plot shows the best 0, 1, and 2 dimensional approximations which are just a point (the mean or centroid), a line, and a plane.
This sample population of math faculty in Chicago is about 83% lighter and 17% darker using a lightness threshold value of .61 with a lightness spread about of about .12. In short, pretty light and not very diverse from a lightness perspective. Things get a bit better when you include CS faculty and all math and cs graduate students however. The point cloud picture is then the following:
We see the same trend obviously, but more diversity of skin tones are present. It is interesting that human skin tones seem to be near a plane in 3 space. This can be made fairly precise using some sort of dimensional reduction technique. One important tool in mathematics, especially applied mathematics and computer science is discretization. In the context of an investigation of skin tones, this idea manifests as skin tone scales, and they play a prominent role in the use of AI in measuring human skin tone. Here are two skin tone scales.
This is the Monk scale (https://skintone.google/ ) alongside a skin tone scale produced by Gemini. Most skin tone scales will likely be in or near this tube which is contained in the above polyhedron. This statement is obviously only approximate. The Gemini scale was produced by requesting a diverse 10 point scale. The Monk scale is also a diverse 10 point scale but the gap in the middle is more useful for choosing a lighter darker threshold.
There are many potential key takeaways that result from this research , but two come to mind immediately:
- Let's stop acting surprised at the results at end of the pipeline, when they are largely determined at the beginning of the pipeline.
- When people are interested in solving problems they measure the results of processes and report the results transparently. The diversity problems in STEM were clearly never going to be solved because granular racial and ethnic data at the level of departments is not being made easily publicly available. Parents and students should be able to look up each department at each university and see a breakdown, based on gender and race/ethnicity, of graduation rates in those departments. For example to answer the question of what percentage of the students graduating as math majors are black or Latinx. This data should certainly be collected, but note that it can be entirely decoupled from admission decisions.
If you would like to learn more about this, here is the link
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