Is mathematics real or just a human invention?

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I'd say it real. Saying it wouldn't exist without humans is as absurd as saying the physical cosmos wouldn't exist without humans.

I think it has been around since the dawn of time it was merely discovered by humans a few thousand years ago to calculate and measure things more effectively and efficiently.

Mathematics is discovered, it isn't invented. If intelligent alien life exists elsewhere in the universe they will discover the same mathematical principles - except maybe Pythagoras' theorem would probably be known a Zog's theorem and Zog may look something like:

Mathematics are an abstract concept that we use as a handbook to understand the concrete world. Human beings didn't "invent" mathematics, they "translated" what they were seeing in the concrete world to another "language" to find its logic, set patterns...

that alien race would use base6 over base10

What do you mean by 'real'?

Yep. This.


The world - the raw mass of data and events - is under no obligation to make sense to us. That it so often does, and to the extent that we can manipulate and affect the world to the degree we do, is remarkable.

Our notations about it and many attempts to describe mathematics are invented though. Aliens will have similar concepts to ours, but they might be using a completely different radix to express their numbers. Etc, etc, etc.

all of that is only translation though.

Yes indeed and as someone else pointed out, our little alien friend here would also likely count using base 6. I'm referring solely to the fixed principles or "laws" of mathematics rather than the techniques, terminology and methodology used to express those principles.

iMathematics is an abstraction--it does not exist in any concrete sense.

Some elements of mathematics do relfect patterns that we seen in the natural world, of course. If I have a pile of two apples and another of three apples, I put them together and I have a bigger pile. So I can demonstrate the concept of addition.

But many of those natural analogies break down as soon as we leave the natural numbers.

I can give you one apple. I can give you three apples. But how can I give you -1 apples? I could take one from you--and while this is mathematically consistent, we have altered the action from giving to taking. Or you could give me one--but we have changed the subject and the object of the action. We are bending the notion of "giving" to comply with our understanding of negative integers.

Let's move on to the rational numbers. I can give you a rock. But how can I give you half a rock? If I break a specific rock in two, I have two rocks, each of which might (but most probably aren't) half the size of my first rock--but each of them is a rock, not a half rock.

How can we find i in the natural world? And by extension any of the complex numbers?

We have created the language of numbers to describe the things that we see. It is the language of patterns. But it is as much a human invention as the language of words that we have used to discuss this question.

When I was a physics student (long time ago) i cropped up quite a lot, especially in electrical theory. I found it somewhat puzzling at the time just how useful complex numbers were in describing the physics of reality.

Remember that mathematics is our way of understanding the world's phenomenons, it is a science, the alien would maybe think differently to us, and may not interpret the laws of the world in the same abstract form as we do. They may need to do it in another way, a completely different way maybe? Is the physical cosmos real in the first place? Is maths, if you think about in this way, then, real?

Which is fairly easy to deal with, there are conversion programs that exist that can convert base10 to binary, or to base8, base16, base32, etc.

Things will get a little more interesting with base6, but a conversion program can be made.

What if they count by using a new symbol for each prime and naming composites by their prime factorization.

1 = *
2 = A
3 = B
4 = AA
5 = C
6 = AB
7 = D
8 = AAA
9 = BB
10 = AC
11 = D
12 = AAB
.
.
.
this would make them as annoying as hell.

Hard to say. But I think our version of mathematics has been made by us for our understanding, and the fact that we use it makes it very real.

By giving an antimatter apple that destroys one of the matter apples.



You could look at it as a rock or half a rock. I mean it's part of a rock that was broken in half. in what sense is that not half a rock?



Math is not a science. Science follows scientific method. Math does not.