In the Business Section of the New York Times today there is a small piece on microtrends (that is small rends in society that should be recognized and understood) which mentions that at Harvard there are only 77 students studying undergraduate mathematics out of a student body of approximately 6700. This is a tremendously depressing fact, particularly since I suspect (and this would have to be tested) that it disguises the fact that there are likely few non-mathematics majors who are studying mathematics as a significant part of their stream of electives.
Before going to law school I studied mathematics in undergraduate and graduate school, focusing principally on graph and number theory as I moved into the more advanced courses. While I wish I could report that in my daily practice of law I have a steady need to apply the theory of Dirichlet L-Functions or use the insights I gained from studying partial geometric lattices, I can't. However, I can report that every day I apply the skills and, more deeply, the way of thinking that I acquired in those six years of learning about how to analyze problems, to break them down, to re-assemble and to constantly doubt statements like. 'it is obvious that ...' or 'anyone can see it is trivial that ....'.
There has been much written about how the dearth of scientists and engineers being produced by our univeristies does not bode well for our economic future. Frankly, I think this misses the real point -- the abysmal production of educated students across the board who are knowledgeable about mathematics and the scientific method does not bode well for the health of society as a whole. The mindset of the scientist and mathematician -- and I distinguish the engineers as a separate crowd in this regard -- is built around an edifice of doubt but inspired by a deep respect for the idea of insight. That is the scientific undertaking is generally driven by insight that is unproven and untested -- Newton having his flash that the apple falling and the moon orbiting are different manifestations of the same thing. But thre process does not stpo at insight but instead demands that make that the insight be put to the test and every step be put in place before it can be said that the insight is anything more than a nice idea. Thus science and mathematics are not the cold processes of calculating often potrayed in popular culture, but instead the very human processes of having an insight and then doing the hard work to make it real.
When I read the paper or listen to the news what I see too often is the triumph of assumption, prejudice and their close relative superstition. There are so many things where there is little real analysis of what is being said and what underlies it and we are willing to settle into a mindset of blind acceptance of various forms of authority over independent critical thinking.
Where does the fault for this decline lie? I expect that in can be spread far and wide. On the teaching side a lack of elementary school teachers well versed in mathematics and a cohort of univeristy professors who do not value accessibility and style in teaching is part of the problem. A society that is intolerant of any failure is another -- for the very premise of mathemaics and science is one of attempting with a recognition that failure may well follow may also be partly to blame. The disproportionate financial rewards and prestige attributed to other callings is surely also a contributing factor. But I fear that the real reason is that we have evolved in to a society that does not value being disturbed or challenged and particularly does not value being told the truth and these are values that are wholly inconsistent with the mind of the mathematician or the scientist.
Lewis Lapham has commented on how we have become a society of courtiers -- that is a society that flatters and fawns upon those in power and that this creates a mindset incompatible with true democracy. It is also a mindset that is inconsistent with mathemathematical or scientific inquiry. Sadly though, it is mindset that leaves us unprepared for either external or internal challenges. When faced with challenges to preconceptions we are unwilling and more and more seriously unable to rethink those preconceptions.
A great deal of this leads back to the discussion that many people are unwilling to have: that is a real discussion about what is it that underpins what we could loosely call the west. For the most part we have replaced real thought about this with sloganeering ("we are a Christian nation" or "multiculturalism is the core of what we are"). To my mind so much of what we are today in the western world flows from taking on the values of mathematical and scientific ways of thinking -- that is ways of thinking that constantly challenge received wisdom and constantly demand, well, thinking. It is a shame to see the field that places this at the express centre of its being fade away.