This is a slight piece, but I just learned that Giuseppe Peano spearheaded the creation of Latino sine flexione, an attempted auxiliary language. The name gives away the plan: “Latin without inflections”. That is, without the nouns and verbs changing form to reflect the role they play in a sentence. I know very little about languages, so I admit I don’t understand quite how this is supposed to work. I had the impression that what an Indo-European language skips in inflections it makes up for with prepositions, and Peano was trying to do without either. But he (and his associates) had something, apparently; he was able to publish the fifth edition of his Formulario Mathematico in the Latino sine flexione.
Giuseppe Peano is a name any mathematician would know and respect highly. He’s one of the logicians and set theorists of the late 19th and early 20th century who straightened out so much of the logical foundations of arithmetic. His “Peano axioms” are still the standard axiomatization of the natural numbers, that is, the logic that underlies what we think of as “four”. And into the logic of mathematical induction, a slick way of proving something true by breaking it up into infinitely many possible cases. You can see why the logic of this requires delicate treatment. And he was an inveterate thinker about notation. Wikipedia credits his 1889 treatise The Principles Of Arithmetic, Presented By A New Method as making pervasive the basic set theory symbols, including the notations for “is an element of”, “is a subset of”, “intersection of sets”, and “union of sets”. Florian Cajori’s History of Mathematical Notations also reveals to me that the step in analysis, when we stop writing “function f evaluated on element x” as “f(x)”, and move instead to “fx”, shows his influence. (He apparently felt the parentheses served no purpose. I … see his point, for f(x) or even f(g(x)) but feel that’s unsympathetic to someone dealing with f(a + sin(t)). I imagine he would agree those parentheses have a point.)
This is all a tiny thing, and anyone reading it should remember that the reality is far more complicated, and ambiguous, and confusing than I present. But it’s a reminder that mathematicians have always held outside fascinations. And that great mathematicians were also part of the intellectual currents of the pre-Great-War time, that sought utopia through things like universal languages and calendar reform and similar kinds of work.