What an astounding development it must have been in 1961, when Abraham Robinson introduced his theory of nonstandard analysis. This theory, arising from ideas in mathematical logic and based on what are now called the hyperreal numbers ℝ*, provides a rigorous method of handling infinitesimals, having many parallels to the early work in calculus. I look upon this development as a kind of joke that mathematical reality has played on both the history and philosophy of mathematics.
