We cannot know that, before maths existed, 2+2=4; however, we can certainly build a picture of a universe in which 2+2=4 for all universal time and show that it is consistent with observation. I don't see how you can do better than that.

Oh Prof !!!!! Let me tell you something , as much as we want to believe in creator and us , I want to believe that we have the ability to create many many many things . Math included ...

Story of famous young mathematician , Srinivasa Ramanujan - his Prof (G H Hardy ) asked him how he was writing the proof(s) in arithmetic . He replied saying , "a goddess comes to me in my dream and dictates all that".

Well , in Hinduism we associate a great significance to "0" , philosophically / spiritually / prayers and reciting and mathematically ...

We cannot know that, before maths existed, 2+2=4; however, we can certainly build a picture of a universe in which 2+2=4 for all universal time and show that it is consistent with observation. I don't see how you can do better than that.

The affirmations or axioms that have been elaborated or expressed in relation to Mathematics, exist since this tool was invented by man.

• The Universe with its matter and energy, cosmos and entropy, already existed before there was conscious life in it, which developed as a miracle, as a singularity in islands of "neguentropia".
• The man to exist, he perceived with his senses and organized in his mind and consciousness such phenomena, that to describe and explain them better, he invented auxiliary tools to enhance his intelligence; and one of these inventions, are Mathematics.

The question posted here can also be stated as follows: Is math an invention of the human brain? Or does math exist in some abstract world, with humans merely discovering its truths? For this question, the astrophysicist, Mario Livio answers, "The debate about this question continues to rage today. Personally, I believe that by asking simply whether mathematics is discovered or invented, we forget the possibility that mathematics is an intricate combination of inventions and discoveries. Indeed, I posit that humans invent the mathematical concepts—numbers, shapes, sets, lines, and so on—by abstracting them from the world around them. They then go on to discover the complex connections among the concepts that they had invented; these are the so-called theorems of mathematics." (http://www.pbs.org/wgbh/nova/blogs/physics/2015/04/great-math-mystery/) I agree with this answer by Livio.

This question has been addressed at length in other threads, see for instance Derek Abbott's on RG:

https://www.researchgate.net/post/Is_mathematics_a_human_contrivance_or_is_it_innate_to_nature

Is mathematics a human contrivance or is it innate to nature? Question Sep 2013

Do we invent mathematical forms as we need them and then merely discover their emergent properties later? Or are those mathematical forms innate to nature, and are hence discovered rather than…

6,559 Answers 51,406 Reads

& many such other threads on RG ( https://www.researchgate.net/search.Search.html?type=question&query=was%20mathematics%20discovered%20or%20invented )

If we view "mathematics" as i) a science, or ii) as a philosophy of numbers and relationships, or iii) as a language for expressing, i and ii, then mathematics as we know it is a construct that has been developed by sentient beings and does not exist in the absence these sentient beings.

Balanced against this, however, there is an aspect of this question which invites a different type of consideration. Namely, we are all familiar with the question posed to philosophy classes "If a tree falls in a forest and no one is around to hear it, does it make a sound?" In other words, is there anything about "mathematics" that is not dependent on human observation and interpretation? If we say "no", then everything is relative. Thus, 2+2=4 is not true in all conditions and circumstances. If we say "yes" then there are some basic properties that are existentially, perhaps even ontologically, true apart from human observation and interpretation and 2+2=4 would always be true.

2+2=4 is an empirical formula, till now human observations confirm this formula. Logic can not guaranteed that this formula is correct elsewhere in the universe or if it is eternal.

Dear Talib, if I may, I don't believe it's an empirical formula - I really think it's just a plain vocabulary definition ..... 1 and 1 is defined as 2, and 4 as 2 and 2 , merely because it is quite impractical to say things like 1 and 1 and 1 and 1 .... and hence vocabulary shortcuts are needed

Dear H. Ransford,

I mean 1+1=2 also empirical and based on observations. I just agree with @Tony Maine.

I too agree with Tony Maine...

Math was always valid and present in the practical world, but the abstract expression of it was largely absent. Quantum Physics on the other hand has a long standing problem of definition in the absence of human scientists to take measurements. My own opinion is that a measurement occurs when two information streams mix together, no matter who or what else is present or observing.

@Tony Maine: We cannot know that, before maths existed, 2+2=4; however, we can certainly build a picture of a universe in which 2+2=4...

One of the elusive things about Mathematics is that it works with structures that are ideal, not physical. Keying on what @Tony Maine has succinctly observed, we can build a picture of the universe in which assertions such as 2+2 = 4 hold true, even though we would be hard pressed to find a "2" or a "+" or a "4" in the physical world.

What is incredible is that we can introduce mathematical structures that satisfy Mathematical assumptions and which approximate our experience and the objects that we perceive in the physical world.

My take is that at least in terms of space-time geometry that what is called mathematics, in terms of causal relations, between measurable sets has always existed. Yes, mathematics can be formed which have no connection to physics, James, but I also believe that in terms of differential geometry structure , that space-time metrics would exist, in terms of causal relations, mapped by other beings, regardless if or not human kind existed.

Dear Kirk MacGregor ,

Everything ( Science (Creation of universe from single point ) ) is created even the before the existence of human being.

Now Mathematician or Scientist are just discovering it whether it is 2+2=4 or how atoms work.

Thanks

Of course 2+2=4 is always four whether human is there or not. Man developed/formulated Scince/Mathematics/Economics. Aryabhata and Ramanujan (The man who taught infinity: how GH Hardy tamed Srinivasa Ramanujan’s genius) are famous Indian personalities.

Aryabhata

(https://www.britannica.com/biography/Aryabhata-I)

(https://en.wikipedia.org/wiki/Aryabhata)

Ramanujan

(http://theconversation.com/the-man-who-taught-infinity-how-gh-hardy-tamed-srinivasa-ramanujans-genius-57585)

Mathematics

(https://en.wikipedia.org/wiki/Mathematics)

Dear Kirk,

At first glance, it seems a ( simple question), but in deep, it is a serious issue to understand our initial conscious of our surrounding world. In this concern I quote Kant's point of view:

[ Kant, however, contests this: he claims that elementary mathematics, like arithmetic, is synthetic a priori, in that its statements provide new knowledge, but knowledge that is not derived from experience. This becomes part of his over-all argument for transcendental idealism. That is, he argues that the possibility of experience depends on certain necessary conditions — which he calls a priori forms — and that these conditions structure and hold true of the world of experience. In so doing, his main claims in the "Transcendental Aesthetic" are that mathematic judgments are synthetic a priori and in addition, that Space and Time are not derived from experience but rather are its preconditions. Once we have grasped the functions of basic arithmetic, we do not need any empirical experience to know that 100 + 100 = 200, and so it appears that arithmetic is analytic. However, that it is analytic can be disproved by considering the calculation 5 + 7 = 12: there is nothing in the numbers 5 and 7 by which the number 12 can be inferred. Thus "5 + 7" and "the cube root of 1,728" or "12" are not analytic because their reference is the same but their sense is not — the mathematical judgment "5 + 7 = 12" tells us something new about the world. It is self-evident, and undeniably a priori, but at the same time it is synthetic. Thus Kant proved that a proposition can be synthetic and known a priori].

https://en.wikipedia.org/wiki/Immanuel_Kant

A bit like the question of the tree falling in the forest, and the sound it makes?

I'd say, for certain, what the formula 2 + 2 = 4 describes existed from the time of the big bang. Humans merely contrived, and continue to contrive, ways to model the universe that they observe around them. We don't change how things work, we merely derive a language that explains the way things work. Math, physics, chemistry, biology, everything these sciences address existed from the beginning. What would a mere 40K years of human existence, or whatever the somewhat longer estimates we see now, have to with the fundamental laws? The universe has existed 13+ billion years with these laws, and this solar system some 4.6 billion.

Aliens from other solar systems, potentially from much more ancient cultures than ourselves, possibly already extinct, may very well have invented very similar models to describe the universe. We have no reason to believe, yet, that the laws of science in the rest of the universe are fundamentally different from what they are in our corner. So, you know, even they will/would have a way of expressing that when you group two planets with two more planets, you will see a group of four planets. As far as we can tell, this is the case in all solar systems and all galaxies. And was already the case 40K years ago, for certain!

I guess yes, math merely reflexes a state of affairs in the world, and how it will be formed depends on this or that formula

Old question, still interesting.

Please refer to my Aforismi 2019 (it’s in English) for a detailed answer. See especially Nos 301-2, 353-7, 623-46. I suggest you read also Nos 458-63, 527-33, if that suits you. Here:

Preprint Aforismi 2019