How is it that we can deal with mathematical problems of increasing sophistication? Is this a property that humans inherently have, or is it our ability to understand the abstract? And if the latter, why are we evolved to understand the abstract so well? Is it a consequence of language or is it something to do with consciousness in general?
Basically, no one really knows.
On my “to be read” shelf so I can’t vouch for the contents, but it certainly seems to be relevant to the OP;
The Math Gene: How Mathematical Thinking Evolved & Why Numbers Are Like Gossip, by Keith J. Devlin.
I read another of his books which was very good, so I feel safe in mentioning this one.
This is GD material. Anyway, you have made value judgements. Who is to say that humans deal “so well” with abstract thought? Well, we consider ourselves better relative to other life on this planet, but there is no absolute standard. As for uniqueness of ability to understand the abstract, animals can’t tell us.
On preview, speaking of books, here’s a relevant one.
I’d say that we’ve evolved a superior ablility to communicate. Being able to pass information from one individual to another and from one generation to another is most assuredly a survival trait.
This communication ability involves highly-developed prefrontal lobes in our brains, which allow us to manipulate symbols with high facility. Mathematics is all about symbol manipulation.
So, while I don’t think that being able to add 2+2 in itself helped our ancestors pass on their genes, being able to tell your kids where the local leopard lives or how to find the best melons did improve the survival of that ability in later generations. The ability to talk includes the ability to think about the world, and therefore the ability to do math.
I’ve also heard that much of human mental ability is simply the result of runaway sexual selection. The premise is that even if algebraic topology or functional calculus of variations doesn’t have any survival value, some folks might find such ability attractive in members of the opposite sex, so folks with those abilities might have an easier time reproducing and passing on their smart genes.
Or at least, that’s the theory. I can hope, can’t I?
Let me be the first to skewer this horrible notion that math has anything inherently to do with numbers. Mathematics is the art of thinking precisely and with logical rigor. It’s distilled abstract reasoning. Just because the most common abstract in daily life is number, people have identified the two.
Incidentally, this gets back to the OP: people who developed the capacity for reasoning and inference could learn more about their world and improve their ability to survive in it.
Exactly. Numbers (and rules of quantity) provide the ideal inspiration and launching pad to develop mathematics. But that’s an inaccurate conception of the gestalt of mathematics.
Wikipedia has a good article on mathematics:
Well, I’ve got my gripes with that article too. Mostly it’s the use of “the formalist view”, which is an outdated philosophical position based on how mathematics was done a century ago. Mathematics has changed since then, some philosophers of mathematics have moved on with it (notably the structuralists), but the popular debate is mired in ancient platonist/formalist schisms.