In the academy today, there are powerful forces that aim to dismantle and discard traditional sources of knowledge, and that reject the merit of gaining that knowledge, replacing it with other objectives. The motives are many, but it is possible to discern a reason that many of the disparate motives share: knowledge (and its acquisition and dissemination) is not, or not necessarily, an essential human good. It is not necessarily a human good, for example, if and when it conflicts with what are felt to be other, more important, ends.

Even among those who believe that the acquisition and production of traditional knowledge is good, there are further disagreements. Is such knowledge good because it is useful for some further purpose or end? For the exercise of power over others, for example, or for bending other people to one’s will, or even simply for the provision of material necessities? Or is it good because it is, as some contemporary defenders of the traditional liberal arts put it, “useless”–an end in itself, a good in itself that needs no, and, indeed, can have no further justification? Or some combination of these?

Disagreements about the good of knowledge–whether it is good at all, and what it is good for, if anything, beyond itself–are not uniquely modern (though the motives driving some of the trending policies in academia today do seem, to me at any rate, to be distinctive). The old Italian phrase, “unire l’utile al dilettevole,” which means to unite what is useful with what delights, reflects one interesting position. Namely, that the good of knowledge is comprehensively manifested in the coming together of utility and pleasure or delight.

Here is a book–admittedly in one of the more distant galaxies of the law-and-religion universe–that offers what looks like a wonderful perspective on the good-of-knowledge question reflecting, in certain ways, the point of view in the Italian adage: Why Does Math Work If It’s Not Real? (Cambridge University Press) by Dragan Radulović. The thesis of the book concerns the distinction between “pure” and “applied” mathematics, and it seems to be (if one can surmise from the description) that what in one generation or century seems entirely “pure,” or useless, or delightful for its own sake, can become, in the distant future and entirely unexpectedly, “useful.” So that the union of the useful and the delightful really should be evaluated across extended periods of time–perhaps centuries or even millennia–because it is unfathomable when confronting the good of knowledge at any given moment or point in time, especially the point in time in which the knowledge is acquired or comes to be known.

According to G. H. Hardy, the ‘real’ mathematics of the greats like Fermat and Euler is ‘useless,’ and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this ‘useless’ mathematics. Mobile phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth’s orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is like some magic hand had guided the ancient mathematicians so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck’s discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.

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