Mathematics and Mediaeval History

The end of history is, alas, also the end of the dustbins of history. There are no longer any dustbins for disposing of old ideologies, old regimes, old values. Where are we going to throw Marxism, which actually invented the dustbins of history? (Yet there is some justice here since the very people who invented them have fallen in.) Conclusion: if there are no more dustbins of history, this is because History itself has become a dustbin. It has become its own dustbin, just as the planet itself is becoming its own dustbin.

Think of it: of the infinity of real numbers, those that are most important to mathematics—0, 1, √2, e and π—are located within less than four units on the number line. A remarkable coincidence? A mere detail in the Creator's grand design? I let the reader decide.

Extension and abstraction without apparent direction or purpose is fundamental to the discipline. Applicability is not the reason we work, and plenty that is not applicable contributes to the beauty and magnificence of our subject.