Hard problems and soft science

On August 8, 1900 there was a gathering of mathematicians in Sorbonne where David Hilbert presented ten problems that, with subsequent addition of another 13, eventually became what is known as Hilbert’s problems — a list of notoriously difficult, fundamentally important and insofar unresolved mathematical conundrums.

Hilbert didn’t come up with those problems, he merely established them as high-profile targets, and sure enough, there were plenty of people who swallowed the bait and went after them. As a result, only two of the original 23 are left standing today (including the infamous Riemann hypothesis), with the rest being either resolved or deemed to be irrelevant or too vague by today’s standards.

While the problems were certainly important in their own right, the influence of the list far exceeded that of its constituent parts — namely for the reason that it attracted the collective effort of the brightest mathematical minds throughout the 20th century which then laid a foundation for subsequent applications and often spilt over to other subfields. Several of the problems were eventually resolved in a way that Hilbert himself could not have possibly foreseen and that he would likely have found very disturbing. For instance, Hilbert was deeply convinced that in mathematics there cannot be a statement which truth-value is indeterminate — a belief that was proved wrong by Kurt Gödel in 1931. However, this doesn’t really matter, as the fundamental importance of the list was the impetus it provided for countless different people to work on this admittedly small set of problems.

This success has apparently caught some attention in the field of social sciences and a couple of weeks ago a symposium convened at Harvard with a title “Hard Problems in Social Science“, where a dozen scholars from several different fields gave presentations on what they consider the most profound and difficult problems in social science today. I spent an evening to go through most of the videos listed there and, by and large, it is an interesting viewing. Of course, there is an overarching and repeatedly voiced concern with the difference between the hard and soft sciences and whether one can meaningfully pose a problem (and much less solve it) in social sciences the way it is possible to do in mathematics — perhaps referring Clifford Geertz who famously stated that anthropology should “not (be) an experimental science in search of law but an interpretive one in search of meaning”. Nonetheless, the symposium at Harvard gives an interesting glimpse into the state of affairs in social sciences and casts a light on some rather fascinating convergences, both in terms of perceived problems as well as anticipated solutions to them.


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