Dijkstra acknowledges Booleans as one of three significant contributions introduced with Algol 60 which he considers the founding of computing science. transcript

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The next milestone of ALGOL 60 that I must mention is ALGOL 60’s introduction of “boolean” as a full-blown type, i.e. not only with boolean expressions but also with boolean constants, variables, arrays, procedures and parameters. From a programming point of view it was not so shocking: besides “integers” whose values can be represented by some finite number of bits, one can introduce a type for which a single bit suffices, but in a wider culture it is making a major difference.

Even for programmers, who saw that there was no implementation problem at all, the introduction of the boolean variable was --and probably still is-- a big leap, as is convincingly illustrated by the fact that for years one would still find even in published programs clauses like:

if c = true then ....

when of course

if c then .....

would suffice.

Evolutions do take time. Mathematicians have used boolean expressions at least since 1557, when Robert Recorde introduced the equality symbol “=” as infix operator, but a formula like “n=5” was not recognized as an expression, not syntactically and not semantically, because for lack of the type boolean, “n=5” was not something that could have a value.

This changed in 1854 when George Boole introduced the type we now name after him, an invention, however, that the mathematical community had not yet absorbed a century later: for the average mathematician, and even for the not so average one, in 1954, a boolean expression was not something with a value, but as in 0 <= n <= 10, a condition or a statement of fact, and, say, 2+3=7 was not a complicated way of writing the constant false, it was just wrong, an attitude that precludes the manipulation of uninterpreted formulae containing boolean subexpressions. I now see more and more people doing calculational mathematics such as formulating a theorem as a boolean expression and calculating that its value is true.

This new style of doing mathematics embodies a major simplification of the mathematical argument. Computing Science developed it because it needed and had the potential to do so; ALGOL 60’s promotion of the type boolean has played a historically significant role in that development.

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