ABSTRACT

If derivation constitutes the content of the discipline of mathematics, it is straightforward to see why Hegel holds the view that he does. He states that mathematics simply ‘moves along the line of equality’, from equation to equation. The spirit of Hegel’s view of mathematics is no doubt experienced by anyone who has taken a mathematics course. Ultimately, the proof displays the intelligence of its composer in the form of an externally imposed necessity. Again, anyone who has struggled to prove a mathematical theorem would have some feel for how the author of the proof does all the work. Indeed, many great mathematicians have held this view of mathematics. One may think that this is simply philosopher of mathematics reading some of his own philosophical training back into a history of another discipline. However, because the development of the Mathematical Concept has logic of its own, we can resist simply handing over the history of mathematicians to sociologists and historians.