I often wonder did humanity invent mathematics or did we discover it.
I don't like the use of the terms.
we invented symbols to explain things we observed, then used those symbols to model unobserved possible things.
2+2 = 4 was neither invented, nor discovered, it was observed, those symbols are simply the language we use to describe the observation.
the gravitational constant was "discovered" in a very broad use of the term, but it's use in mathematics was a matter of observation.
if I had only these two terms to use, I would say that mathematics is a language we invented to describe the relationship to things we discovered, although calling simple observations "discoveries" has always stuck in my craw a bit.
One only need ask the question, ‘would an alien species have ‘discovered’ the same mathematics, or would they have ‘invented’ a language completely foreign to our brightest mathematical minds?’ I am of the opinion that physics is what we discover, and mathematics is a language we invent, not only to describe our universe, but to theorize about it, and what may be beyond.
I can go with that, although I think that an alien species would have much of the same mathematics, they would just have different symbols. they may have discovered different aspects of physics, but much of it would be common, because the physics themselves are universal.
One example only: the Fibonacci numbers which are to be found throughout nature. They also create the golden ratio which dominates nature and our art. They have always been there.
Alright, a second one that plagued me in high school: geometry. Note how easy Egyptian geometry came to us as we started to build and note how to do so in the best manner. It took the Greeks to discover or create Euclidean geometry which is just a means to list reasons and properties for why Egyptian geometry worked even before explanation.
Newton invented Calculus, Calculus is the mathematical study of continuous change
I believe Newton's contemporary invented the Calculus we use today: Leibnetz. I believe Newton's calculus was algebra based, and Leibnetz' was not, and the world went with his. I could be wrong.
@t1nick i think you are correct, but the point here is "was it discovered, or invented?"
@magicwatch true, my bad. Actually I think some of both. Its totally an invented convention, but invented to describe natural phenomenon
Certain concepts and properties are constant but the math to express them was invented. I have always wondered if we would have had only a total of 8 digits on both hands, three fingers and a thumb, would we be counting in base eight instead of ten.
The Yuki language in California and the Pamean languages[1] in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves
I love that thought
1+1 has always equaled 2, we just put language to it....
10 + 10 in decimal = 14 in Hexadecimal
Depends on the base system.
There us a funny video if a teacher getting fired for stifling a student's thought by telling him his answer is wrong. His answer for 1+1 was 11. After the teacher is fired the superintendent is adding up her compensation and says one plus one is two. To which the teacher replies no it is eleven.
Just like we didn't invent gravity, inertia, or the light spectrum.