Kazimierz Kuratowski

At Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), the premier mechanical and electrical engineering school in Mexico; I took a Calculus course. The textbook was: Introduction to Calculus, by Kazimierz Kuratowski, which you can freely download from the link above.

From the Wikipedia note on him, one reads that the ``identification of the ordered pair (x,y) with the set {{x},{x,y}};'' was one of his contributions.

When I learned this in my Mathematical Analysis class, I was not told who the author of the idea was, but I was impressed by the depth of the concept.

Now that I am reading Karl Menger's calculus book, I am impressed by how much notation affects our perception of mathematics. Kuratowski was successful, where Menger wasn't; even though his notation is well thought, maybe too very well thought, he did not convince his peers around the world to accept it.

I believe that his care is very much needed, both to teach new students, and to write mathematics for computer processing.

Notation may not be all; but definitely it is the beginning.