Mathematics Is An Invention Or A Discovery?

[Newstein]

Mathematics is the language of science and has enabled mankind to make extraordinary technological advances. There is no question that the logic and order that underpins mathematics, has served us in describing the patterns and structure we find in nature.

The successes that have been achieved, from the mathematics of the cosmos down to electronic devices at the microscale, are significant. Einstein remarked, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

So since also it is the oldest branch of study, I want to know about its origin. Actually it was invented or it is simply a discovery. 

Please make your strings. 

 

 

Advance Thanks!!

 

[exchemist]

Mathematics is the language of science and has enabled mankind to make extraordinary technological advances. There is no question that the logic and order that underpins mathematics, has served us in describing the patterns and structure we find in nature.

The successes that have been achieved, from the mathematics of the cosmos down to electronic devices at the microscale, are significant. Einstein remarked, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

So since also it is the oldest branch of study, I want to know about its origin. Actually it was invented or it is simply a discovery. 

Please make your strings. 

 

 

Advance Thanks!!

Haha, what a good question. 

 

I have always taken the position that it is a human invention, being a quantitative branch of logic. However, being a branch of logic, it contains things that are unambiguously and objectively true, once the starting axioms are defined. This leads some people - wrongly in my opinion - to think that mathematics somehow exists in nature as it were, and is a physical thing, to be discovered, when it is in fact abstract. 

 

But I'd be interested in what others think. 

[DrKrettin]

I just can't bring myself to think of a Mandelbrot Set just as an abstract concept. It was always there, and we, or rather Mandelbrot, discovered it.

[Turtle]

Mathematics is the language of science and has enabled mankind to make extraordinary technological advances. There is no question that the logic and order that underpins mathematics, has served us in describing the patterns and structure we find in nature.

The successes that have been achieved, from the mathematics of the cosmos down to electronic devices at the microscale, are significant. Einstein remarked, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

So since also it is the oldest branch of study, I want to know about its origin. Actually it was invented or it is simply a discovery. 

Please make your strings. 

 

Advance Thanks!!

The question is as perennial as the grass. FarmingGuy asked it here a scant 6 years ago.: >> Discovery Or Invention?

 

My string is ho-hum: What difference does it make what you call it? Math is as math does; just do it. :smart:

[Super Polymath]

Math is an uncovering, or decoding, of operations from nature to concepts in digitized (language such as the numerical or signs systems) form.

 

However, if you don't conceptualize why an operation is the way it is, sure you might be able to solve according to formula, but you won't be able to uncover or decode anymore new operations. 

 

Those who take the longest to learn math, always end up becoming the best at it. Which is why academics has utterly failed in the math department. Our schools dish out the crappiest mathematicians. There are no recognized modern Isaac Newtons. A lot of modern geniuses don't even have college degrees & would probably score poorly on standardized IQ tests, & - in the case of William James Sidis & Bobby Fischer - are anti-authority & end up shunned. Because authority, or the powers that be, are definitely doing things *** backwards. For instance, String Theory has branches of inconceivable, & probably irrelevant, mathematics based on dimensions that are - to any plausible observational analysis - scientifically unobservable. 

Edited June 6, 2017 by Super Polymath

[DrKrettin]

Math is an uncovering, or decoding, of operations from nature to concepts in digitized (language such as the numerical or signs systems) form.

 

However, if you don't conceptualize why an operation is the way it is, sure you might be able to solve according to formula, but you won't be able to uncover or decode anymore new operations. 

 

Those who take the longest to learn math, always end up becoming the best at it. Which is why academics has utterly failed in the math department. Our schools dish out the crappiest mathematicians. There are no recognized modern Isaac Newtons. A lot of modern geniuses don't even have college degrees & would probably score poorly on standardized IQ tests, & - in the case of William James Sidis & Bobby Fischer - are anti-authority & end up shunned. Because authority, or the powers that be, are definitely doing things *** backwards. For instance, String Theory has branches of inconceivable, & probably irrelevant, mathematics based on dimensions that are - to any plausible observational analysis - scientifically observable. 

 

 

I think you surpass even yourself in utter bollocks in that post. 

[exchemist]

I just can't bring myself to think of a Mandelbrot Set just as an abstract concept. It was always there, and we, or rather Mandelbrot, discovered it.

I see what you mean. I suppose you can see it as  a discovery in the sense that it follows logically from the structure of maths as previously established up to that point, rather than being made up arbitrarily, as it were. However I would say something like that is not a discovery in the sense of things that were pre-existing before they were developed by the person who formulated them. So I would say that complex numbers and calculus, for instance  are better described as "invented" rather than "discovered". 

 

But perhaps I ought now to go and read the previous thread that Turtle has drawn our attention to. 

[Super Polymath]

I see what you mean. I suppose you can see it as  a discovery in the sense that it follows logically from the structure of maths as previously established up to that point, rather than being made up arbitrarily, as it were. However I would say something like that is not a discovery in the sense of things that were pre-existing before they were developed by the person who formulated them. So I would say that complex numbers and calculus, for instance  are better described as "invented" rather than "discovered". 

 

But perhaps I ought now to go and read the previous thread that Turtle has drawn our attention to. 

Even Einstein was against Quantum Mechanics.

 

He'd say that String Theory is "bollocks".

 

BTW, this is the 21st century, idc where in Britain you're from, nobody uses the word bollocks anymore. 

Edited June 7, 2017 by Super Polymath

[Turtle]

I see what you mean. I suppose you can see it as  a discovery in the sense that it follows logically from the structure of maths as previously established up to that point, rather than being made up arbitrarily, as it were. However I would say something like that is not a discovery in the sense of things that were pre-existing before they were developed by the person who formulated them. So I would say that complex numbers and calculus, for instance  are better described as "invented" rather than "discovered". 

 

But perhaps I ought now to go and read the previous thread that Turtle has drawn our attention to. 

 

It won't take you long to read and as here, it's just opinions. Whether math is invention, discovery, or some pet woo, it just doesn't have any bearing on how math is done. :cup:

[Super Polymath]

I think you surpass even yourself in utter bollocks in that post. 

I meant scientifically unobservable, making the math moot. 

[exchemist]

It won't take you long to read and as here, it's just opinions. Whether math is invention, discovery, or some pet woo, it just doesn't have any bearing on how math is done. :cup:

I have done and I agree, nothing very special there.

 

But I have a passing interest in this, as there is a nutter on another forum who has fallen for the views of that bloke Tegmark (ne Shapiro, but changed his surname to that of his mother, Shapiros being two a penny in the N E USA), who affects to believe that physical reality IS mathematics, or something. I have little time for this and Tegmark seems to be close to being a self-proting charlatan, but he has quite a following, apparently.

[Turtle]

But perhaps I ought now to go and read the previous thread that Turtle has drawn our attention to. 

Now if you really want to make me glow by following my draw, read Hofstadter. Arguably he too is offering an opinion, but the rigorous critical thinking he uses to form that opinion is impeccable.

[Turtle]

I have done and I agree, nothing very special there.

 

But I have a passing interest in this, as there is a nutter on another forum who has fallen for the views of that bloke Tegmark (ne Shapiro, but changed his surname to that of his mother, Shapiros being two a penny in the N E USA), who affects to believe that physical reality IS mathematics, or something. I have little time for this and Tegmark seems to be close to being a self-proting charlatan, but he has quite a following, apparently.

I'm not familiar with Tegmark, but even if physical reality IS mathematics, what does it matter?

[Turtle]

OK. So I read the Wiki bio on Tegmark and will quote a wee germane bit.

 

... Tegmark has also formulated the "Ultimate Ensemble theory of everything", whose only postulate is that "all structures that exist mathematically exist also physically". This simple theory, with no free parameters at all, suggests that in those structures complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically "real" world. This idea is formalized as the mathematical universe hypothesis,[12] described in his book Our Mathematical Universe. ...

The assertion "all structures that exist mathematically exist also physically" seems on the face to contradict Gödel, much less set up a non-falsifiable condition. But on SASs insofar as the quote is accurate, it is this very subject that Hofstedter's strange loops deeply investigates.

 

PS The bio goes on to say:

... Tegmark was elected Fellow of the American Physical Society in 2012 for, according to the citation, "his contributions to cosmology, including precision measurements from cosmic microwave background and galaxy clustering data, tests of inflation and gravitation theories, and the development of a new technology for low-frequency radio interferometry". ...

Props then to Tegmark ne Shapiro for doing the math. :thumbs_up Edited June 6, 2017 by Turtle

[exchemist]

OK. So I read the Wiki bio on Tegmark and will quote a wee germane bit.

 

The assertion "all structures that exist mathematically exist also physically" seems on the face to contradict Gödel, much less set up a non-falsifiable condition. But on SASs insofar as the quote is accurate, it is this very subject that Hofstedter's strange loops deeply investigates.

 

PS The bio goes on to say:Props then to Tegmark ne Shapiro for doing the math. :thumbs_up

Well exactly. By saying this he is claiming that any piece of maths that we can conceive of (I would say construct or invent) somehow pre-exists, independently of human minds. So complex numbers existed long before we devised them and so did calculus.  Sorry, but I really struggle with that notion.  

 

As you say, it is an unfalsifiable assertion and as such is a metaphysical rather than a scientific statement. But as we know, metaphysics with a specious quasi-scientific endorsement is all the rage: "quantum woo" etc.  

 

I have not read Hofstedter, I admit. 

 

Teggers is a clever fellow, no doubt of it, but that does not stop a person getting grandiose ideas, unfortunately.

Edited June 6, 2017 by exchemist

[Super Polymath]

Math is how the pieces fall together, it is the mechanics of nature. It exists with or without our linguistic expression or sensual perception of it. 

 

Linguistically I suck at math. But sensually, my perception of it would probably destroy anyone's. 

Edited June 6, 2017 by Super Polymath

[Turtle]

Well exactly. By saying this he is claiming that any piece of maths that we can conceive of (I would say construct or invent) somehow pre-exists, independently of human minds. So complex numbers existed long before we devised them and so did calculus.  Sorry, but I really struggle with that notion.  

 

As you say, it is an unfalsifiable assertion and as such is a metaphysical rather than a scientific statement. But as we know, metaphysics with a specious quasi-scientific endorsement is all the rage: "quantum woo" etc.  

 

I have not read Hofstedter, I admit. 

 

Teggers is a clever fellow, no doubt of it, but that does not stop a person getting grandiose ideas, unfortunately.

Aye, no end of clever fellows falling prey to grandiosity. This is what makes Fuller one of my favorite whipping boys. 'Course no end of shite-pokes skipping clever and going straight to grandiositude as we know so well. :lol:

 

Now Hofstadter, I will beat his drum but ne'r his person. (Well, some gentle ribbing may be in order. ) His softcover I Am A Strange Loop is a mere 15 quid. It's not for the faint of heart, but I think a stalwart bloke like yourself would find it of more interest than not.

 

Back on the topic of invent vs. discover...