The philosophical difference between math and science

Contemporary society lumps math and science as one thing, but they are not the same. Reading a passage in Simon Blackburn’s Think, I saw some insight about this, which I will paraphrase and expand on here.

Math is based on abstractions, and relationships between abstractions. Abstractions in math are generally absolute truths, meaning it is impossible that the abstraction is not true. Very few things that are accepted in mathematics get retracted later. New abstractions can be formed from existing ones, usually from those that are absolute truths, and these new abstractions can be formed by simply sitting at a desk and thinking about it long enough: there’s an adage, a mathematician is a machine that turns coffee into theorems.

The basis of science is empiricism. One observes something about the natural world, and tries to create their own model of how it works or occurs—they try to turn it into math. When the conversion is successful, we can use the new math to create technology, to invent and engineer new things.

Verification of a model is usually not absolute, and through repetition and logic something is “believed” to be true when as far as anyone can tell there’s no evidence that it is false. The only way to verify something in science is to repeat it: you’re not going to get the next scientific breakthrough by only sitting at your desk. Because science is often not based on absolute truths, many things in science that are once accepted get retracted from days to centuries layer.

This philosophical difference I think explains how there can exist child prodigies, and their distribution among math and the sciences… There are many children who are math prodigies, fewer who are prodigies of physics, and almost none of chemistry. Child prodigies in biology and the life sciences are completely unheard of.