Beyond Our Minds

What is mathematics really? When I get to meet ugly equations, and whenever I  come across a math problem that I can’t solve, I ask myself, what is mathematics, really? When I see mathematicians, I ask myself, why do these people keep on torturing their brains? How come they soared in this subject feared by many? I am not saying that I despise math, but why do I need to tire myself with this one? Luckily, I am not the only one. Perhaps, this someone currently reading my review is also asking it to himself/herself. To know what is mathematics really, what is its nature and how people accept it in different ways, here is a bit of information which came from Reuben Hersh.

Just in the previous century, the philosophy of mathematics became a big issue to the mathematicians. They kept on asking themselves, how this language appeared? What does it really mean? What was its origin? And because no one have ever explained it to them, they began to hypothesize. These hypotheses soon became their basis in every mathematics they create.

In the argument for the nature of mathematics; formalism, platonism and intuitionism were the top three perspectives. Formalists’ point of view tells us that mathematics is just composed of symbols that were formally manipulated not basing on any axiom. Platonists argued that mathematics can be compared to experimental science wherein you study subjects that exist but not physically, as in a material. However, Intuitionists’ perspective had the highest degree, they believed that all mathematics is an unending human creation. Unfortunately, this argument has not yet been resolved.

Hersh wrote his book in order for us to question ourselves. What is really mathematics to us? He wrote his book in order for us to have an involvement in this argument. And because of this  reason, he argued that most writings about mathematics is ignorant about what it really practices. Hersh have given his insights as to what mathematics is. He tried to involve the history of the philosophy of math. Then he even included philosophical and political issues to explain the nature of mathematics in connection with philosophical positions.

Another issue to Hersh was certainty. We can never be certain if a mathematical statement  is true unless supported by a  mathematical philosophy. According to Hersh, it is incorrect to aim for certainty. Mathematics requires humans to do hard work and mathematical truths, just like any other truths, are uncertain.  But if we treat mathematics  as a human creation, we must account such great feeling that mathematical objects really exist independently. When we think of these objects they go far beyond our minds and then we are now able to create it. Hersh called this view as humanism.

I am quite pleased with what Hersh was trying to deliver to his readers. Although there were some of his points which I did not understand, still, he really did a good job in blowing my mind. Nevertheless, his points became an additional information to me. It is my first to encounter such brilliant interpretation of mathematics.