Numbers

Number is a fundamental concept in mathematics that does not have a formal definition. The usual tenet sounds like “it’s the thing that we use to count, and measure”. Most mathematicians take it as a given and move ahead without much interest or thought about the subject.

Isaac Newton thought about mathematics as God’s laws. Leopold Kronecker was quite satisfied with “God made the integers; all else is the work of man”. Modern mathematicians tend to shy away from theological language. Their prefer terms like “natural”, “transcendental”, “real” to obfuscate the issue even further. Any formal definition of number would require some polite name for “we don’t have a clue”.

Cave man could probably use mammoth bones to measure their cave. That is very primitive process. Mammoth bone is not a very precise tool. Nevertheless it brings indisputable practical advantage. We just assume that all bones are absolutely identical and we don’t care about the difference. Here we have number concept born. It’s mostly practical human ignorance and experience. There is not much more to it.

There is no doubt that mathematics and numbers were extremely useful tools in human experience. They are used everywhere. Nevertheless they are just a tools. Attempt to find some sacral mystical meaning would be just wrong.

Defining numbers as “practical ignorance” and math as “just a tool” helps to keep things sane. Infinity bigger than infinity (Cantor theorem/paradox) and Lobachevsky geometry can be really puzzling and confusing. As a remainder both Cantor and Lobachevsky ended their life in mental institutions.

Mathematical apparatus is humongous. “Just a tool” consideration might help you filter out a lot of junk information, which is an absolute necessity in the modern information age.