Discovery Or Invention?

[Maine farmer]

In my studies of Mathematics, I got as far as one semester of Differential Equations, where I somehow managed to get a C average. I am aware of how crucial math is to science, and everything in nature seems to follow some mathematical formula, so my question: Is Mathematics a discovery or an invention? My instict is that it is a discovery, but I remember being taught that Isaac Newton "invented" calculus at about the same time as some other guy whose name I don't recall. Which is it?

[CraigD]

Is Mathematics a discovery or an invention? My instict is that it is a discovery, but I remember being taught that Isaac Newton "invented" calculus at about the same time as some other guy whose name I don't recall. Which is it?

This question requires the adoption of a philosophical position to be answered. I'll answer it from that of my favorite philosophical position, formalism.

 

Mathematics is a collection of formal techniques, so is invented.

 

These techniques allow theorems to be derived from postulates. These theorems are discoveries in the non-physical world defined by their requisite postulates.

 

A particular collection of postulates, those of arithmetic and various geometries, allow mathematical formalism to be applied to empirical reality. Measurements of empirical reality are discoveries. The confirmation, or refutation, of mathematical predictions are also discoveries.

 

Most people, most of the time, don't invent new mathematical techniques, but learn previously invented ones. In some cases, people discover math via textbooks, lectures, and explanations. In others cases, they invent mathematics that has been previously invented by others.

[Boerseun]

Interesting question, and interesting reply, Craig.

 

However, for the sake of the debate, I would hold the position that mathematics is a discovery. The way I see it, mathematics is a way to describe the relationship existing between several entities, be they physical or imaginary or whatever. And there is only one correct way to do so. Of course, new methods like Newtons' calculus might be just around the corner that might easily describe several complex issues that today's maths battle with, but the concept stays the same. Much as Einstein "discovered" relativity, I would say that maths is a "discovery", almost a Law of Nature, if you will.

 

It has been said that if we ever make contact with an alien species, at least we will have mathematics in common. Which gives me the impression that the techniques involved in maths (common and advanced) is more a universal "Law of Nature" than a local "invention".

 

I might have the cat by the tail, and it might even be the wrong cat, but that's my impression of it.

[C1ay]

IMO mathematics is an invention. It is a set of man-made procedures used for finding values and a collection of man-made notation used as a means of communicating that. Yes, man discovered things like the Golden Ratio in nature but he invented the method used to make that discovery and the notation used to define it. The use of the Fibonacci rectangle in calculating this ratio in the conch shell is one such example.