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Depends on how one defines discovery and invention.

Discoveries are something we haplessly stumble upon, or seek out, that may or may not have an eventual purpose. A rainbow would be an example of a hapless discovery with little purpose, and oil would be an example of something we discover, but with intent (in modern times) that has purpose.

An invention is something that has utility or purpose, that we manufacture with intent from discoveries. A car engine for example, is an invention. If one wants to be disagreeable though, they could. The fact is, the design for a combustion engine has always been in the ethos. It just took a lot of discoveries prior to its manufacture, such as steel, before we could assemble the pieces. It was a series of discoveries and subsequent inventions that lead to the combustion engine.

You have to take math in order. Numbers would have to come before math. Numbers are logic driven. While I'm not sure we can claim the invention of some numbers, mainly 1 and 0, we can certainly take credit for the invention of the rest. We can also take credit for the decimal place. All of the numbers were the result of a logical redundant linear labeling system designed with intent and purpose to extend indefinitely, allowing us to endlessly expand on a base set of 10 labels or digits, obviously derived from our fingers. It allowed us to track a 1000+ fingers. And all of those arose out of the necessity for trade and commerce, NOT science. We needed to coherently communicate the same number labels/symbols and mathematical processes to other human beings, in order to trade with them.

Necessity truly is the mother of invention.

It's almost always about the money.

That numbers and math worked for science was a discovery. But that almost certainly was not the intent of either. It was 12 magical sea shells for 6 awesome pelts, which now gave the pelt merchant 37 magical seashells in his pocket, and 6 less pelts in inventory.

Contrary to what some might think, numbers and math were more likely physical or visual discoveries, not abstract concepts. When you hold up 5 fingers, and then close 3, we have 2 sticking up. We could physically see numbers and math right in front of our face, and put it to work. All we needed was a rudimentary labeling system for 10 fingers.

But it all begins with the simple notion of something versus nothing.

So, we most certainly discovered numbers and math on the most rudimentary level. And then we expanded (invented) on that fundamental base knowledge with a redundant logic for the sole purpose of commerce.

That it works for science is not all that remarkable, if you give it a moment of thought. The universe is driven entirely by motion. Motion is analog, but also represents a natural underlying perfection in linear order. You cannot skip a step in motion. Numbers also represent perfect linear order which can emulate the perfect analog of motion. Motion is a derivative of motionless space, and time is a derivative of motion. It's three fundamental analogs driven by motion that make up the universe. Of course it behaves with mathematical perfection. There is no other way for it to exist, because motion drives it.

Motion is the analog numbering system of the universe.

Math is an analog to digital converter. It cannot capture the entire scope of the underlying analog, which is infinite, but it gets pretty darn close with finite values. Numbers are discreet, but the underlying universe is an analog continuum.

Numbers from a scientific perspective are simply increasing the resolution of the underlying analog. The higher the resolution, the better picture we see of the universe. 10 digits was pretty crappy resolution.

Infinite is analog.

Finite is binary.

|1| > ∞ > |0|

We're in the middle.

I think there is a danger in looking at math or numbers from the perspective of discovery, as if 3.1415 has some ethereal meaning beyond its utility that we discovered mathematically. It gives numbers and math a cult like religious interpretation. This is basically what led to numerology.

Math and number are both a discovery, and a subsequent invention. There is nothing mystical or magical or supernatural about either. They’re no more special than a hammer and nails. Math is like the hammer, and numbers are like the nails. They’re tools we apply to the universe so we can better understand and manipulate nature to suit our needs and desires. They help us communicate and survive in the modern world.