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'The weapon of criticism cannot, of course, replace criticism of the weapon, material force must be overthrown by material force; but theory also becomes a material force as soon as it has gripped the masses.' - Karl Marx
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Is mathematics discovered or invented? I my opinion I suspect that math is discovered, if so, that imply that there's a "true" reality that is independent of human invention and opinions, so, what's the LeftyPol opinions about the nature of mathematics?

< The concepts of number and figure have not been derived from any source other than the world of reality. The ten fingers on which men learnt to count, that is, to perform the first arithmetical operation, are anything but a free creation of the mind. Counting requires not only objects that can be counted, but also the ability to exclude all properties of the objects considered except their number — and this ability is the product of a long historical development based on experience. Like the idea of number, so the idea of figure is borrowed exclusively from the external world, and does not arise in the mind out of pure thought. There must have been things which had shape and whose shapes were compared before anyone could arrive at the idea of figure. Pure mathematics deals with the space forms and quantity relations of the real world — that is, with material which is very real indeed. The fact that this material appears in an extremely abstract form can only superficially conceal its origin from the external world. But in order to make it possible to investigate these forms and relations in their pure state, it is necessary to separate them entirely from their content, to put the content aside as irrelevant; thus we get points without dimensions, lines without breadth and thickness, a and b and x and y, constants and variables; and only at the very end do we reach the free creations and imaginations of the mind itself, that is to say, imaginary magnitudes. Even the apparent derivation of mathematical magnitudes from each other does not prove their a priori origin, but only their rational connection.

(Anti-Dühring, Friedrich Engels)

>>22935
>i have 10 fingers so numbers are real
least retarded engels take

>>22934
Math is discovered insofar as it describes material relations (space itself according to Hegel in the introduction to the Logic) and invented as ideas of these reflected in our minds, whose representation is even now still subject to many whims of their creators.

Math is a discovery.
The symbols and formulas we use is just the sentient translation of math.

Theres still much to matg we dont know about.
I was never good at algebra when I was little but I could recite my timestable up to fifteen without calculator

Math is discovered insofar as we are figuring out things about the logical structure of the universe.
Math is invented insofar as we are developing methods to do the math, like proofs.

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>>22934
Mathematics is discovered and the formulae are invented

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If it were discovered, that would challenge the concept of invention as being distinct from discovery, wouldn't it?
What's the difference between figuring out you can fill a bag with hot air to fly and figuring out you can make a seashell spiral with squares using a compass?
If invention is a coherent concept, then both would be inventions

>>22949
With inventions, there are multiple different ways you could do it. For the classic example, there's lightbulbs. You can discover that an electric current can induce a glow in certain metals under the right conditions. But the actual invention of the lightbulb entails designing the specifics, like the amount of light vs heat you want or the shape of the bulb. There's more than one "right" way to do it. Learning how the physics works is discovery. Applying it is an open-ended creative process called invention.

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Are old threads discovered or invented? >>2320

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Maybe Conway's Game of Life would be a good example to understand the distinction here? It's a simple set of rules invented by Conway, but the consequences of these rules, like that there's a "glider" pattern that keeps moving, are discovered.

Counting and the relation 2 + 2 = 4 are interesting examples, as you could probably convey them to alien cultures simply through a series of sound pulses . .. … …. .. .. ….

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>>22936
Not what he said

>>22978
brandon rogers stuff n sam

I‘d say it‘s both. The natural world is based on quantitative relations of various sorts and through observation we have inferred them by abstracting them from concrete processes. However, how we display in symbols and our axiomatic models are actually constructions, that are developed in an exchange between them and further observations when we apply them to practical matters.

A bit of both. Math is ultimately a language for describing quantities and the relationships between these quantities. The language itself is invented, but it describes patterns that are very much real.

This is not a trivial question. We need first settle down the question that if mathematics even exists? And philosophers can not reach a satisfying answer.

If you want to learn more about philosophy of mathematics I recommend https://plato.stanford.edu/entries/philosophy-mathematics/

>>22934
Math is discovered not because it has any concrete relation to material phenomena but because every mathematical principle follows from a certain set of well-defined axioms. So all the properties of mathematics already exist based on those axioms, it is only the responsibility of mathematicians to discover their consequences.

Don't authentically remember what my stance was on this, but have thought the following:
Think mathematics can feel discovered because results are formally entailed.
However, these formal languages, and results had to be invented, or evolved.
One could argue that there isn't even number on the near impossibility of two things being identical.
Even number had to be evolved.

>>22934
both
people too often see mathematics as "hard natural truth", when they're as much constructs of the mind than any other concept describing reality. Having the 0, imaginary numbers, shit like that had to be brought forward and debated, and took time to be accepted despite their usefulness.
And once you've established the basis of the rules, the system of numbers, axioms, operations, graphical representation etc ("invented mathematics"), there is a lot to be "discovered" in those systems.

Discovered implied that mathematics is a thing in the world rather than a way we understand the world. All of logic is a tool for us. We have the initial premises and all follow from them. Those premises aren't handed down by any god that told us how to think.

its discovered and is just one manifestation of the higher order or Absolute

>>22934
Discovered but indelibly partial due to the interfacing of human limitations, so both 'real'/a fragment of the absolute, symptomatically, and also insufficient/a construct of the human mind in correspondence to its perceptible immediacy.
In other words, it is partially discovered and partially invented.

HOLY IDEALISM

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>>24214


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