The Unending Uncertainties

A book review on the book; What is Math, Really?

1, 2, 3,... If I would be given a lifetime where I can finish counting limitless numbers, then it’s just plain crazy.

Philosophy needs math as much as math needs philosophy. But the question is that do they even exist? Like Hersh’s thinking, there are these doubts circling in my head. Alterations should be done; modification is a continuous process just to build a foundation being math’s stronghold. Mathematical philosophy talks about providing an explanation on how math exists, what is its nature. Math is not just a study, it is the activities men do, and it brings life.

To assume, account, and even imply. Mathematics is a connection revolving towards the core of understanding. In the book, the author highlights men. It is an anthropological approach being bias on our part. He does not believe on math having a universal scope as what I have comprehended. I don’t agree to this but I’m with him when he said math is a part of our culture, history and evolution. Hersh starts his writing explaining the 4 types of cube, having a pattern in each of its dimension. There’s this argument about the existence of the 4D cube, if it is just created in an imaginary world why can we understand the mechanism of its dimension? There are things in life where we can’t limit our explanations and therefore we obtain a wide range of answers in seeking for the truth.

Hersh rejects the mainstreams in philosophy like Platonism, formalism and intuitionism because according to him it cannot sustain mathematics. He limits to reality contradicting Platonism. As for my view, in mathematics it is essential to explain the universe, especially time that can be found in any galaxy. Mathematics cannot be touched but it can be felt. I agree with him rejecting formalism, math has no rules. It is not arbitrary! Like Hersh having a strong objection, I consider evolution as a permanent change in math therefore no one can say math is a random idea. Math has bases and it is not stagnant. Intuition is powerful, it is a sense; to infer by witting. Intuitionism contradicts the universality of numbers and deals only on a finite set. So Hersh being an unsettled and brilliant man continues to seek for what is math, really. His explanation about not searching for other meanings in math but to settle on the social-cultural-historical meaning has a point. This is the start of his comprehension, the humanist perspective. Mathematics is not just about mental and physical manipulation but it has an impact on the society as a whole. Humanism says mathematics is not unique. I firmly object, math consists of infinite symmetry, it is not plain. Humanism focuses on the past, what has already been done rather than what is it to modify. Is it me or Hersh’s ideas are a bit constricted?

In totality I don’t like Hersh’s approach on trying to define math. It’s quite frustrating how he critics some philosophies and ended up on an unstable one which is humanism. Math cannot just rely on it, to have a great foundation it needs a wider scope and broad knowledge that can be found in fused ideologies. He points out education at the start of the book but did not discuss it well in the succeeding pages. For me, philosophy and education goes together no matter if it’s banked or de-banked. As long as philosophy concerns math, math should also be a tool for education like philosophy is for math.

“It is not infinite that our mind/brains generate, but notions of the infinite” (Hersh, 1997). These three go together; intuition, logic and infinity ∞