Does mathematics work like this?

From Trapped in the Virtual Classroom by David Bromwich, in the July 9, 2015 issue of the New York Review of Books [my boldface]:

When H.L. Mencken, an avowed atheist, was asked if he believed in baptism, he replied “Believe in it? I’ve seen it done!” For thirty-eight years, I’ve been a teacher of a discipline of interpretation that is fostered in university departments of literature, philosophy, the history of ideas, and to some extent psychology and political science, a discipline that might best be described as an art that can be taught; and if someone asks, “Do you believe in it?,” I can’t do better than “Believe in it? I’ve seen it done.” The discipline I have in mind is not a religious ritual but an educational practice that can seem to the uninitiated as monkish as some aspects of an alien religion.

This discipline can’t be called a science as a natural scientist would understand the term. It is not progressive. It has few formulas worth memorizing. It doesn’t show its glory in “research programs,” airtight systems of classification, or pathbreaking discoveries that refute a previous century’s scientific orthodoxy. Yet the discipline does have perceptible boundaries and teachable methods of confirmation or falsification, based in large part on the relationship of evidence to assertion, and on the common sense and insight of qualified judges. It imparts a fund of practical wisdom that grows over time and alters its emphasis with the disposition and character of the practitioner.

Is mathematics more like “science as a natural scientist would understand the term” or is it a “discipline of interpretation?”  Bromwich’s article is about mechanization of teaching, but his comments, for example

Does this movement cooperate with a pressure to make human life ever more machinelike? In the process of approval and acceptance, are we being asked to conceive of knowledge itself as mainly constituted by information? And does knowledge come to be seen therefore as a social good that can be disseminated and assimilated in a uniform and mechanical way, so that finally the amount of good accomplished is to be judged by criteria of efficient satisfaction

apply equally well to mechanization of mathematics, a topic already treated on this blog (here, for example, as well as here).

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3 thoughts on “Does mathematics work like this?

  1. Michael Barany

    Allowing that natural scientists do not have a monopoly on saying what even their own sciences are, and that it’s by no means clear they would share Bromwich’s criteria, math does seem to fit his particular bill. It’s a remarkable turn of intellectual history that a Kuhnian revolutionary model of scientific breakthroughs appears for Bromwich not just characteristic of natural science but *definitive*; mathematicians, I’d think, part ways with Bromwichian scientists on that score, though as a matter of history it’s not so clear-cut.
    I was struck by Bromwich’s allusion to “a certain affective range,” and here he seems to share the suspicions of the MWA Author about the ill-fit of mechanization to the deeper pedagogical and intellectual purposes of their respective disciplines.

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  2. Aleksandar Mikovic

    In science and humanities we use logic to arrive at conclusions; however, the main difference between science and humanities is that in science the logical reasoning can be reduced to a formal mathematics, while in humanities this cannot be done. This is because a human language is a more general system than a formal logic systems used in mathematics and also in humanities, beside the truth, one also deals with the concepts like beauty, morals and emotions, which cannot be described in mathematical terms. I don’t believe that the teaching can be mechanized, because one cannot teach anything without a human language, which is more general than any formal logical system.

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