Viewing Mathematics in a Different Perspective (A Review on Reuben Hersh’s What is Mathematics Really?)

Mathematics had been always thought of just something about objective computations, solutions to certain problems, numbers and equations, and other such things. Basically that was how math was interpreted and understood by many most especially those who are not much into mathematics. People always had the impression of it as being very difficult and those who excelled in mathematics are either geeks or geniuses. Mathematics had always been the center of stereotyping.  But in Reuben Hersh’s book, What is Mathematics, Really?, he pointed out how mathematics is not just some objective application of rules and theorems, mathematics could also be a part of human culture, a socio-political phenomena per say. He continued on discussing that mathematics has a broad scope more than what is basically taught in school. He went on by categorizing the nature of math in two principal views: the Platonist and the Formalist.

The Platonist was more traditional as it has a stand that “In math, there are right answers”. For me, that is traditional because it was focused more on the application of the earlier theorems discovered years ago. While the Formalist was, I think, more contemporary because it questions the very existence and credibility of the rules earlier discovered by the mathematicians. Here comes the improvisation of the activities that modern mathematicians resist on being purely rule-governed activities. According to Hersh, Formalists believe that “one cannot understand math just by the rules” which means that more thorough ways of learning and looking at math is needed. Formalists wanted to look at newer and a different perspective, outside of the objective computation in mathematics. Formalists tend to ask questions, perhaps those never been asked. That was basically how Hersh introduced the two principal views of mathematics.

He wanted the readers to view mathematics as not simply a physical or a mental activity, like how mathematics is generally viewed everywhere. Hersh wanted mathematics to be viewed as something that “could only be done in socio-cultural-historic terms.” Viewing mathematics in a different and a whole new perspective is quite interesting because it only justifies and sorts of explains the importance of mathematics in the sense of its application. Many of us don’t even know what the use of complicated mathematical computation is for except inside the classroom. Hersh pointing out that mathematics is more than that, that it could actually be a social and historical activity, opened to new mathematical understanding. In one chapter, Hersh mentions the significance of viewing mathematics this way is.

Recognizing that mathematics is a social-cultural-historical entity doesn't

automatically solve the big puzzles in the philosophy of mathematics. It puts

those puzzles in the right context, with a, new possibility of solving them.

This is like a standard move in mathematics—widen the context.

            Note the phrases “in the right context” and “new possibility of solving them”. This suggests that indeed the act of recognizing mathematics as it really is opens new door to better opportunities, newer and better discoveries.

            All throughout the book, Hersh might have had caused some forms of confusion with the readers, as juxtaposing math with philosophy will normally do, still I believe he was successful in defining what mathematics really is. His attempt to show mathematics in a different light was effective and impressive for me. Personally, I became to have a different appreciation of mathematics, not just for the objective computation.