> From time to time a definition of what mathematics > s is is offered or > requested--I don't know why. Here is one due to > Donald Monk: > > As a tentative definition of mathematics we may > may say it is an a > priori, exact, abstract, absolute, applicable and > and symbolic scientific > discipline. > > [Foot of page 1 of J. Donald Monk, Mathematical > logic, GTM 37] > > It might be amusing to identify seven things which > aren't mathematics > that satisfy all but one (a different one in each of > the seven cases) of > - a priori, > - exact, > - abstract, > - absolute, > - applicable, > - symbolic, > - scientific; > thereby demonstrating their independence. Actually, > the definition of > scientific is just as controversial. On page 2 op. > cit. Monk explains > that by absolute he means 'not revisable on the basis > of experience.' > > (The book arrived today, and it's going to be a tough > read. If I need > any help I will, of course, seek it in one or both of > the scis dot logic > and dot math.) > > My second thought (the first related to 'scientific') > was that > 'symbolic' is nugatory: every discipline uses written > language, and the > special symbols of mathematics are just taking the > place of words in > natural language ((i)for reasons of brevity and (ii) > for > understandability among people who use different > natural languages, I > suppose). > > Third thought: absolute seems to rule out the > possibility of a published > result being found to be wrong subsequently. I > suppose it depends on > what one means by experience. >
As every human activity, mathematics is a "would be" which is distorted by reality.