@helenS i have been discovering statitics. DONT YAWN! Much of it was invent'd gamblers. It has re informed me of the counterintutive nature of reality. Regression to the mean,, all that
As a math graduate student, I can honestly tell you that math is an endless cycle of discovery and invention. You discover a reality, and then you create some label or notation for it. Then you use that notation or label, apply logic, and you discover a new reality. Now you invent a label for that reality. Rinse and repeat.
Discovered. Just like any Scientific law math was created when the universe was. And math is innate in many plant and animal species not just us humans.
@helenS No. I mean this post when it was first asked. I still believe that although certain values such as the circumference of a circle were discovered, the system with which we manipulate said values, was most definitely invented. You can only discover what already exists. There was no math before math. Even the base 10 Hindu–Arabic numeral system we use is invented. The ancient Babylonians used a base 60 system for their Math. You still see remnants of it in things and is why we have 60 seconds in a minute and 60 minutes in an hour.
Personally, I think mathematics is a universal language, and it was created to gain a better understanding of our universe. Some of what we know was discovered along the way, which led to new knowledge and/or the amending of old knowledge.
@SW-User She blocked you?? Why would anyone block you!
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@helenS Well, you know she is always posting, "I am in a bad mood." Well, I asked her if she was infested with Gnomes. I explained Gnomes can do that, and that you can get rid of them with Raid the same stuff which gets rid of cockroaches and ants. I even explained you don't even have to spray the stuff, just display the cans in strategic areas where the Gnomes can see them, and they will vanish.
Anyway, long story short, she was not amused. She blocked me, I still hope the Gnomes leave her alone.
@revenant @revenant A large part of mathematics is deductive and an ongoing puzzle is how it applies to physical reality at all. Laws of nature are empirical and seem not to have necessity as an ingredient. e=mc(squared) seems to be different from 1+1=2 in that e might have been equal to mc cubed! It took Einstein to figure out that it was c squared.
Kind of both...because, while it is created from ideas about number, etc., its success in being used to model, describe, predict (e.g., with physics) the natural world is a testament to the fact that it has a truth in it beyond a simple made-up set of ideas.
One of the most striking examples is that the separation constants used in solving the Schrödinger equation for hydrogenic (1-electron) atoms by the separation of variables end up being the quantum numbers which describe the state of the electron in any orbital...amazing!
Surely mathematics is simply a human derived shorthand (thanks particularly to middle ages Islamic scholars who gave us the modern method for writing it and for algebra etc.) to explain the natural world around us.
I have 1 Goat my Wife's Dad gives me another goat - I have ... 1+1=2
It's then that along comes the lord of the manor and says - You all need to pay me 1 groat for every goat you have... so writing down maths is important... etc.
In the same way the two pages of squiggles my son publishes explains (probably) how Saturn's current fields interact with it's gravity etc. It's a language to explain a concept in a way people can interpret uniformly
@SW-User That's an explanation of bookkeeping/low-level accounting, which is very different from mathematics in general.
That the idea of number can be tied, in counting, directly to real objects (and through this, you can demonstrate positive integers & real numbers) demonstrates that THAT aspect of mathematics is definitely reality-based. Add in trade and the notion of owing someone something, and you have justified negative numbers.
Counting & trade give you addition & subtraction. Multiplication is fast addition, division is fast subtraction, so the four basic math functions are easily derivable.
But the theoretical side--à la Descartes, etc.--is grounded enough that solutions to equations used to model reality end up describing things we may not yet have even seen, showing that our mathematics models reality amazingly well. Examples include Newton's mechanics & law of universal gravitation; Laplace's & Hamilton's reformulations of Newtonian mechanics; Maxwell's compilation of results from studies in electricity & magnetism to give the equations of electromagnetism; Hertz's derivation of electromagnetic waves; Bohr's model of atoms; Sommerfeld's quantization rule; Einstein's derivations & explanations of Special Relativity, E = mc^2, Brownian Motion, the Photoelectric effect, General Relativity; Planck's generation of his constant; Bell's derivation of his inequality; the predictions in particle physics of Gellman & Nishijima's "Eight-fold Way"; the particle predicted by Higgs et al.; etc., etc., etc.
It is discovered, uncovered, created, but based enough in reality that it describes it well, including the use of imaginary numbers to represent real waves...
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@SomeMichGuy not sure Saturn Aligned Current Fields is low level accounting. My point being that much of maths is used to relay the physical world whether counting goats or determining the power within the atom.
Yes, mathematics has a level of reality behind it as shown by the fact that predictions we make with it can be born out in reality, even in realms where we have no direct experience (macroscopic/cosmological & microscopic length scales).
Discovered by many people over thousands of years. Issac Newton essentially found calculus, over an extended summer holiday. Probably the smartest man in history. Something that takes most people years to learn, he discovered in months.
@Thespis YES! And try to solve the two-body problem with only his level of calculus...
This is why I go apoplectic when I hear parents throwing around "genius" as term for their child...most people have no idea what genius is, and Newton is an iconic example.
Which kind? Euclidean, Newtonian, Laplace Transforms, Statistics... Most were developed by specific people and then built on into bigger and bigger things. Pi, the Golden Ratio, and the natural log have been around for a long time.
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There is a great documentary called The History of the Number 1 hosted by Terry Jones(of Monty Python fame) that explains this question pretty good...oh the things you watch at 2am when you cant sleep lol
@helenS Yes, I had the first semester of calculus, too. lol
But infinitesimals are creatures of continuous things, not discontinuous ones...and someone who quotes Kronecker probably knows that values associated with HIS δ are discrete (unlike those associated with the Dirac δ, which are continuous)...
Both. Math already exsisted in nature, it is the building blocks of literally everything. The invention part is the naming and recognition of patterns, logic, and structure of our natural world. We have also supposed theorms that arent yet proven so this in a sense is invention but the math is simply the rosetta stone for reality and we are just seeking to quantify and understand what is which in turn allows us to better manipulate our reality (invent).
@Elessar disagreed, we simply interpreted math in a way we could understand, we cannot take credit for math any more than we can take credit for the ocean or the sky or electricity, electricity was harness not invented, as was math.
@xSharp Well, some concepts have been abstracted to the point that I would almost say they've been invented, than just interpreted from the observation of real world phenomena. 🤔
Math exists in some invisible spiritual realm, where it was discovered by mystics first and then eventually millenniums later was put practical uses, at which point people claimed to have invented it.
@SW-User greeks did not invent it, even the zoroastrian persian empire had it first, syria was a place of learning open to the entire world, until the Islamic reform came around and burned all the books
math is built into the universe, like the golden mean and pi, it was discovered thousands of years ago even before Pythagoras and his therum, math is the language of the universe
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The methods, numbers, definitions etc. Are invented. But the mathematics itself was discovered as it has been there since the beginning of time.