I don't quite understand what you're asking. Care to explain a bit better?

It is not actually a question, but a subject for debate related to the title of the post: If somehow evolution has equipped us with mathematical minds, it is fair to hypothesize that the "book of nature is written in the language of mathematics" just because we see it that way. Of course, this does not account for answers to other philosophical problems related to applicability of mathematics (such as Wigner's puzzle). Still, the (philosophical) investigations to such problems tended to ignored those biological-anthropocentric factors. If I have to draw a question, it would be this: Can theoretical philosophy be more multi- or inter-disciplinary at least for this topic? Isn't it that philosophy generally avoid science in collaborating on philosophical topics?

What gets me excited is if math was invented. Did we invent/create the universe? The Western extroversion as opposed to the Eastern introversion is then not a mistake for the path outwards leads back inwards: the human mathematical enterprise is a journey of self discovery. Is there anything human about math? I asked a woman I know to leave a unique mark (no, not by urinating) on her projects so people would immediately recognize it was her handiwork (a calling card of sorts). Let's sift through all the math we know. Do you think we'll find features that reveal/betray a human touch?!

Truth be told, math seems to bear cultural signatures e.g. the Greeks were anti-infinity and couldn't fathom how nothing could be something (zero). The Indians were more receptive with respect to both these concepts/ideas. The Chinese were using negative numbers. :chin:

there are anthropocentric and evolutionary features that the philosophical investigations on this topic have not focused on much: — Doru B

I agree with the linked article that perceptual processes are the place to look for the basis of mathematical reasoning, but rather than ‘innate’ I’d suggest instead they perceptual processes are constructive, forming mathematical concepts as metaphors arising from embodied perceptual interactions with the world.

However, there are anthropocentric and evolutionary features that the philosophical investigations on this topic have not focused on much:

https://medium.com/@cb_67963/human-mathematics-and-gods-mathematics-682ac8e7bba — Doru B

Interesting article. Thanks. I don't think it will convince anyone one way or another on the issue of the nature of mathematics. I come down on the side of math being a human invention. There are studies that indicate that numerical ability may be present very early in a baby's development.

My 'anti-platonist pragmatics' (finitism?) comes to this: pure mathematics is mostly invented (re: pattern-making) and applied mathematics is mostly discovered (re: pattern-matching).

Interesting article if a bit long-winded. Two nit-picking comments:

1.

Well, the history of science has proved that whatever complex concepts mathematicians created, they finally came to be applicable in the mathematics of physics or even to directly describe an empirical context.

The massive amount of "pure" mathematical knowledge produced in the last three hundred years suggests this statement is unsupportable.

2.

In 1950, Nicholas Bourbaki, who shaped the concept of mathematical structure and types of structures from a set-theoretic perpective, asked in his influential The Architecture of Mathematics whether the unity of mathematics is the outcome of formal logic or simply this scientific fertility.

It would appear from this statement that "Nicholas Bourbaki" is an actual individual, when in fact it's a name a group of math people created when pooling their resources and producing a number of respected textbooks.

Nevertheless, an entertaining read. Thanks.

My 'anti-platonist pragmatics' (finitism?) comes to this: pure mathematics is invented (re: pattern-making) and applied mathematics is discovered (re: pattern-tracking) — 180 Proof

Pure math stems from explorations in applications frequently, though not exclusively. The stuff I have done for years was pure up front and has remained so. It's a combination of discovery and invention.

From Wiki:

In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics.

Was mathematics invented or discovered? — Doru B

logic is a processing structure encoded genetically into our mind which comes from the way reality moves

math is a reduced abstraction of reality, based on logic(the way reality moves)

The massive amount of "pure" mathematical knowledge produced in the last three hundred years suggests this statement is unsupportable. — jgill

Glad you said that - I had the same thought.

The question seems a correspondent of the most popular question “Was mathematics invented or discovered?” and relates to the nature of mathematics as well as to the philosophical problem of applicability of mathematics. However, there are anthropocentric and evolutionary features that the philosophical investigations on this topic have not focused on much — Doru B

The idea of naturalizing mathematics is not new. It is how the thesis that mathematics and mathematical truth are discovered (as opposed to constructed or pulled from an ideal Platonic realm) is often cached out.

Though the research in "perceptual mathematics" cited in the article is recent, the general finding that there are innate proto-mathematical capacities should not come as a surprise. This doesn't resolve the question of whether mathematics is invented or discovered, but perhaps the question should be dissolved as a false dilemma. We might gravitate towards certain mathematical structures due to innate predispositions. We also invent mathematics to deal with empirical problems. We also invent mathematics with no practical goal in mind and then, having a ready-made tool at our disposal, opportunistically find a use for it. Nowadays we also invent a load of completely useless mathematics, of which perhaps a small fraction will ever find an application, and the rest will gather dust in mathematical journals and specialist books. Then again, pure mathematicians share the same cognitive apparatus with the rest of humans, they develop in largely the same environment, and their work is influenced by past mathematical culture.

So, what to make of this tangle? That it's not either-or - it's both and then some.

Nowadays we also invent a load of completely useless mathematics, of which perhaps a small fraction will ever find an application, and the rest will gather dust in mathematical journals and specialist books. — SophistiCat

I agree. Many years ago I was on a USAF Office of Scientific Research grant. At the time I was grateful for the financial support, but I wondered why they would fund the sort of things that interested me.

I mentioned 135 math research papers a day received at ArXiv.org . Today it was 269.

What motivates all those math people? Tenure/promotion considerations. Prestige within a community. Delight in the exploratory aspects of a subject with few constraints arising from the physical world - free rein for one's imagination.

From my vantage point as a very senior citizen, the first thing I note is the huge number of people pursuing activities compared with 60 years ago. I haven't a clue as to numbers of mathematicians then and now. But at that time the outdoor sport I became involved with had perhaps a couple of thousand fairly serious devotees here in the USA. Now there are well over six million. World-wide there may be ten million or more. It staggers the mind.

What motivates all those math people? Tenure/promotion considerations. Prestige within a community. Delight in the exploratory aspects of a subject with few constraints arising from the physical world - free rein for one's imagination. — jgill

Yeah, I think imagination, curiosity and play are underestimated in these reductionist accounts of mathematics, even though they are as much a feature of our psyche as anything else.

From my vantage point as a very senior citizen, the first thing I note is the huge number of people pursuing activities compared with 60 years ago. I haven't a clue as to numbers of mathematicians then and now. But at that time the outdoor sport I became involved with had perhaps a couple of thousand fairly serious devotees here in the USA. Now there are well over six million. World-wide there may be ten million or more. It staggers the mind. — jgill

Ha! You think there is a connection? :) From my own experience, I've known a few physicist and astronomer climbers, but can't recall any mathematicians off the top of my head.

Isn't it that philosophy generally avoid science in collaborating on philosophical topics? — Doru B

Not in the way you put it. Philosophy asks a question in a different sense because reality, to philosophy, can be inquired upon in a different sense. However philosophy draws empirical examples and evidence from science.

Ha! You think there is a connection? :) From my own experience, I've known a few physicist and astronomer climbers, but can't recall any mathematicians off the top of my head — SophistiCat

Yes, I do think there is a connection. I knew and climbed with ten or so fellow math guys from different locales over the years. For me it was problem solving and exploration. Short rock climbs are frequently referred to as "problems". A great combination of intellect and athletics.

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logic is a processing structure encoded genetically into our mind which comes from the way reality moves — Miller

That's nonsense. It's the same as saying God is genetically programmed in our genes because that's how reality is. Math isn't programmed by our genes. It's just a way of looking to nature.

point is logic is abstraction related to empiricism

point is logic is abstraction related to empiricism — Miller

Yes. And?

the brain is not a crystal ball. it has a genetic structure

there is no free will, only biological determinism

what you dont have the genetics to process you will never understand

the brain is not a crystal ball. it has a genetic structure — Miller

Only the DNA in my neuron nuclei have. The processes on my neuron network can "resonate" with processes in the real world. But they just as well go contrary. They are not programmed by my DNA. It just happens or not.

They are not programmed by my DNA — AgentTangarine

before you were born you were nothing but a strand of dna

there was no brain

the dna created the brain as it wanted it to be. then later the brain is born and then it is completely bound by its genetic reaction to the environment. neither of which it chose.

its reactions shape it which then reacts again and shapes it more. over and over until you die

causation

before you were born you were nothing but a strand of dna — Miller

I was nothing but the stuff around it. I just used my genes to develop. They only gave me proteins. They were not involved in any programming. My brain can act like a computer but it isn't one. The physical world can resonate in the brain. This resonance can be structured by math. But only for certain well defined experiments to fit the math. Most of the physical world can't even be approximated by math. There is no math formula corresponding to a piece of music. Any attempt to fit all phenomena in math is doomed.

There is no math formula corresponding to a piece of music. — AgentTangarine

a piece of music is nothing but a pattern. you just call it music since it alleviates your boredom and raises your dopamine

a piece of music is nothing but a pattern. you just call it music since it alleviates your boredom and raises your dopamine — Miller

That's not why I listen to music. That's how you see it. A sad, almost terrifying fact. The soundwave pattern of music cannot be thrown in a mathematical formula. Only short pulses of music can. So what use has math? Not to mention the feeling you get when listening. Just a pattern on the neural network resonating with the music waves. But it feels great! How you explain that?

Computers play music.

feels great! How you explain that? — AgentTangarine

masterbation feels great

im one with god

Computers play music. — jgill

But the pattern of sound coming from them can't be caught into a superposition of sines. Unless the music consists out of sine waves in the first place. Can an arbitrary piece of music be Fourier transformed? Only short pieces, not? Short pieces compared to the wavelength. Music pulses.

masterbation feels great — Miller

Now that feeling comes close to a mathematical contemplation.

The soundwave pattern of music cannot be thrown in a mathematical formula. Only short pulses of music can. — AgentTangarine

I don't necessarily think thats correct. Music is sound, and sound is illustrated by mathematics, therefore it should follow that you can illustrate music by math, and math by music.

I have read most of the article your link leads to. Among other things it talks about "non-mathematician mathematicians" which can be only taken figuratively, since obviously it is quite a conflicting expression! Anyway, I can't see what is the point the author of the article the position is trying to make besides that we are all mathematicians and we apply math in our everyday life. Well, this sounds like what I say sometimes about philosophy, namely that everyone is a philosopher and has a philosophy on life and various subjects. But I think we have to address Math as a scientific subject, i.e. the discipline and study of numbers, formulas, relational structures, shapes, etc.
For example, are we inventing mathematical formulas or discovering them?

So, instead of non-mathematicians, let's talk about Mathematics and other sciences themselves.

Now, since I am not a scientist myself, first I bring in some data I found from a short research I did. Then I will tell my views as a non-scientist, from a philosophical view (even if I am not an actual philosopher myself :smile:)

The term "Mathematical universe" leads to "Mathematical Universe Hypothesis", according to which "the physical universe is not merely described by mathematics, but is mathematics (specifically, a mathematical structure)" (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis).

"Mathematical universe" also leads to Max Tegmark, who wrote a book entitled "Our Mathematical Universe".

Tegmark says, "our external physical reality is a mathematical structure. That is, the physical universe is not merely described by mathematics, but is mathematics (specifically, a mathematical structure). (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)

Tegmark explores the possibility that "math does not just describe the universe, but makes the universe."
(https://www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/

(The book is discussed in detail at https://space.mit.edu/home/tegmark/mathematical.html)

***

Now, about my view on the subject:

Maybe we should start with talking about numbers, the basis of Math. It is supposed that the numeral system was discovered by Egyptians, but this is not important in this topic. It only shows that numbers are apparently human-made. So, we have to ask ourselves, is there a numerical system in the physical universe --independent and different from ours-- based on which the universe "works"? For example, there are three trees out there in the field. Does it matter for the universe? Does the universe use this as information to "act" or "behave" in some particular way? Would it matter if there were four trees or one tree or none? We certainly cannot say.
But this is something more or less concrete. Can such a concepts like "zero", "infinite", etc. have a meaning for or application by the universe? What about "calculus", "combinations" and hundreds of other math methods? I mean, not as terminology but what these represent? In other words, if the nature of the universe or a characteristic of it is mathematical, if the universe has its own way of using what we call "mathematics", how could we ever understand it?

So, on a purely logical basis, a "mathematical universe" makes no sense to me. On the other hand, a "mathematical mind" does.