Math is invented, not discovered. It can't be discovered because it doesn't exist until someone makes it up. As a matter of fact, numbers themselves don't exist. They are a convenient, but abstract, idea that were invented like mathematics. But no, math was not discovered.

Numbers and math may be

*abstractions,* but they were

*abstracted* from empirical observations of the natural universe. Two plus three equals five in reality, not just in the abstract. You can try it with your fingers, with sticks, or with the dead polecats you're bringing home for the tribe to make for dinner, and it will always come out the same. This is something that someone discovered.

So is the ratio of the circumference of a circle, and π, the constant that keeps showing up in the natural universe every time we turn around. So are the formulas for the areas of squares and triangles, the volumes of various objects, the sines and tangents of angles, the Golden Mean, and

*e,* the base of natural logarithms. For that matter, so is

*i,* the square root of -1, which threw itself in our faces as soon as we discovered electricity and the relationships between its various measures.

It's just as easy to argue that we didn't invent any of these things, we discovered them.

But math is a technology and we can have the same intellectual argument over many of the earliest technologies. Did we invent agriculture or discover it? We

*discovered* how animal and plant metabolism and reproduction work (science), then we

*invented* ways of making them work for us (engineering). Metallurgy? We

*discovered* that really hot rocks will melt and separate into different component materials (science), then we

*experimented* with them and

*discovered* that blending the tin from one city's rocks with the copper from another city's rocks created bronze, an alloy that was stronger than either (more science), then we

*invented* tools made of that alloy (engineering).

Numbers have to start somewhere. Until we got into agriculture and started living in static communities, numbers wouldn't have been more than concepts like "more" and "less", "together", "apart", and so on.

Primitive people typically had only the numbers 1-5 or 1-10. The Indo-European root

*phenqwe,* "five," (cf. Greek

*penta,* Latin

*quinque,* German

*fünf,* Sanskrit

*pancha,* Russian

*pyat*) also shows up as the Germanic word "finger."

*Dekm,* "ten," was the largest number the Indo-European tribes had a root word for.

*Kmtom* (cf. English "hundred," Latin

*centum,* Russian

*sto,* Sanskrit

*satem*) is a compound word formed on

*dekm* with the D eventually elided, with the basic sense "big ten." Just as the Germanic tribe went on to form

*thus-hund,* "swollen hundred."

*The Meaning of Tingo* delves into the number words of a few of the world's last remaining Neolithic peoples and the pattern is common. In one language the word for "eleven" is "have to go down to my toes."

When we needed to start counting things to keep track of them, and who owned what, we started counting things in discrete groups - the Babylonians had a complex (ac)counting system that was base 60 or something, which survived for a fair while.

Sixty shows up a lot in early civilizations. We still have 60-second minutes, 60-minute hours and degrees, and 360-degree (60x6) circles.

The Romans had a fairly inept math formalism, but it functioned well as a counting system - it must have or they would have abandoned or changed it instead of using it for all those centuries.

People become very comfortable with their numbers. When Fibonacci brought the Hindu-Arabic positional decimal number system to Europe in the 1200s, absolutely no one except mathematicians adopted it for several hundred years, not even shopkeepers. Look at my country's uncompromising rejection of the metric system. 128 ounces in a gallon, 63,360 inches in a mile.

It wasn't until we needed to start thinking about geometry and so on that math got past arithmetic.

Although that happened rather early in all six of the world's civilizations. The Olmec, Inca, Egyptians, Chinese, Indians and Mespotamians all figured out the orbits of the heavenly bodies because they were key to religious rituals. And IIRC they all had a decent value for π.