Conceptually Complicated

Conceptually Complicated

A Book Review on Reuben Hersh’s “What is Mathematics, Really?”

           

            What is Mathematics, Really? is a 1997 informative book by Reuben Hersh that dwells on the nature of mathematics --- its origin and its sole nature. Hersh explores and rejects the concept of Platonism, formalism, and intuitionism. Rather, he introduces the concept of humanism wherein he offers mathematics to be understood as “a human activity and a social phenomenon.” Hersh explains Platonism is the idea that “mathematical entities exist outside space and time, outside thought and matter, in an abstract realm independent of any consciousness, individual or social.” Formalism states that math is a “meaningless game played arbitratrily.” Hersh seemed to react stronger against this concept saying that it is not actually a game but is actually determined by history through the workings of society. Intuitionism accepts the concept of natural numbers as the basis of mathematics towards more complex ones. This is really more of a construction of one’s mind by ordering, arraying concepts and inclusion of sets. The humanist point of view adds another string to the philosopher’s view [which are physical and mental]. This additional string to the standard kinds of existence is the social kind. According to Hersh, there isn’t any more need to dig deep into the world for answers; the answer lies in the application of our activities every day.

            It was rather entertaining to see Mathematics in another light. It seemed like most people just over analyze the subject which makes things a lot more complicated. Maybe, that is the reason why not a lot of us like Math. It’s the social trend that when it’s numbers, it’s going to involve numbers/calculations and super analysis. But maybe, just maybe, the way we look at it including mindset) is on the wrong lens.

            So, in the more personal side of the reading I did, I came to the point of relating the thought of Mathematics to Science. By Science, I mean, the on-going experiments that are happening in big laboratories and in space (e.g. search for black matter). It left me the impression of “blind-walking”, or at least, that’s what Hersh’s words did. The difference was that, based on my comprehension, Science is more governed of laws and proven theories while Math is usually more of conceptualizing and providing proof to validate assumptions. However, Science is nothing without Math. I think, although Mathematics is mostly assumptions and concepts, society would accept it because it’s easier to have something to believe in rather than not have nothing to govern us at all especially in analyzing and interpreting the natural world.