Leopold Kronecker Quotes
God made the integers, man made the rest.
Weber, Heinrich. "Leopold Kronecker." Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 2, 1893, p. 19.
3rd Earl Russell of Kingston. In mathematics the numbers can count people, autos, sins, molecules, or paintings. The mathematician does not know or care. And the mathematics is the same regardless. And the fundamentals themselves are unknown. For example, what is a number? It’s not the symbol we write; that is a numeral. Some say that it is an abstract idea that represents a quantity like 5. But what is 5? That itself is an abstraction. So few mathematicians and no layman know what they are talking about when they do mathematics. Lord Russell, with his colleague Whitehead, built up a system where they could define a number as a set with certain properties. But they take 3 large volumes full of equations in a small type font to just get to 3rd grade arithmetic and knowing what they are talking about. In politics, we also often do not know what we are talking about, but that is for a much simpler set of reasons.
Leopold Kronecker was a German mathematician who worked on number theory, algebra and logic. He criticized Georg Cantor's work on set theory, and was quoted by Weber (1893) as having said, "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" ("God made the integers, all else is the work of man"). Kronecker was a student and lifelong friend of Ernst Kummer.
