Very Formal Affairs

Abstract

If social and behavioral scientists have harbored “physics envy” as some have wryly claimed—envy of its explanatory and predictive success— then computer scientists may be said to have suffered from “mathematics envy.” Interestingly, this envy was less a characteristic of the pioneers of digital computing of the 1940s and 1950s, the people who shed first light on the design of digital electronic computers, the first programming languages, the first operating systems, the first language translators, and so on—though most of them were trained as mathematicians. They were too busy learning the heuristic principles of computational artifacts. Rather, it was in the 1960s when we first find signs of a kind of mathematics envy, at least in some segments of the embryonic computer science community. It was as if, having discovered (or invented) the heuristic principles of practical computational artifacts, some felt the need to understand the underlying “science” of these artifacts—by which they meant its underlying mathematics and logic. Mathematics envy could be assuaged only by thinking mathematically about computational artifacts. Computer science would then be raised to the intellectual stature of, say, physics or indeed of mathematics itself if computer scientists could transform their discipline into a mathematical science. One cannot blame computer scientists who thought this way. The fact is, there is something about mathematics that situates it in a world of its own. “Mathematics is a unique aspect of human thought,” wrote hyperprolific science (fact and fiction) writer Isaac Asimov. And Asimov was by no means the first or only person to think so. But wherein lies the uniqueness of mathematical thinking? Perhaps the answer is that for many people, mathematics offers the following promises:The unearthliness of mathematical objects. The perfectness and exactness of mathematical concepts. An inexorable rigor of mathematical reasoning. The certainty of mathematical knowledge. The self-sufficiency of the mathematical universe. These promises are clearly enviable if they can be kept; usually, they are kept.