Is mathematics the same language in every country?

[MessyPaint]

@Mangosteen

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My wife was taught the following method to solve the problem above.

The 6 is bigger than the 9 so you borrow a one from the tens column. The one becomes a “ten” in the ones column. Subtract the 9 from this ten and you get 1. One plus 6 equals 7.

Although this method may look slower and more complicated, it is used because its easier and faster to figure out subtraction problems using 10 minus a number.

i’m a little confused on how the 6 is bigger than the 9 and thats why you borrow…and where you are borrowing from…and why nothing is beneath the 6

[Mangosteen]

Sorry, I meant the 6 is SMALLER than the nine.

[Topologist]

@Chronos

Suppose I were to meet a Martian mathematician.

Back to the OP, any terrestrial research mathematician will be aware of the worldwide mathematical community and the way in which it expresses itself in journal articles. In any language, that involves not only common symbols but a stylized way of using the language, meant to express the logic of an argument as unambiguously as possible while still being readable. (Well, the better ones manage to produce readable articles, anyway.) Because of that, it’s usually easy to translate a journal article from one language to another and preserve at least the mathematical content. In the way I express myself professionally, I probably have more in common with a Chinese mathematician than I do with an American physicist. You could argue that there is only one worldwide mathematical culture.

But, what if we were to meet a Martian mathematician? If we could recognize it as a mathematician, I suspect that means in part that we would recognize the way it expresses itself, the logical underpinnings of what it does. I wonder, though, about the substance of its mathematics. Would it have algebra, analysis, and topology? Or would it have fields that we haven’t come close to thinking of? How much of what we’ve developed is necessary, and how much is there just because that’s what lay on and near the path we’ve chosen to take, as opposed to a different path the Martians took?

[MessyPaint]

@Topologist

But, what if we were to meet a Martian mathematician? If we could recognize it as a mathematician, I suspect that means in part that we would recognize the way it expresses itself, the logical underpinnings of what it does. I wonder, though, about the substance of its mathematics. Would it have algebra, analysis, and topology? Or would it have fields that we haven’t come close to thinking of? How much of what we’ve developed is necessary, and how much is there just because that’s what lay on and near the path we’ve chosen to take, as opposed to a different path the Martians took?

right. exactly. would mathematics even be in their thinking structure, and whatever type of mathematics were, would it even fit here, to our understanding?

i want to bounce questions off of other animals, like- if there is some kind of mathematical skeleton in an animals brain structure - or if we (humans) are the only ones in touch with being able to see these patterns, does anyone know of any researchers who have tried to test an animals understanding of this?

it’s such a mystery, math is like wind- you feel it mostly

[ultrafilter]

@MessyPaint

i want to bounce questions off of other animals, like- if there is some kind of mathematical skeleton in an animals brain structure - or if we (humans) are the only ones in touch with being able to see these patterns, does anyone know of any researchers who have tried to test an animals understanding of this?

Some other animals have basic counting abilities, but being able to abstract counting to numbers is very likely unique to humans.

@Topologist

But, what if we were to meet a Martian mathematician? If we could recognize it as a mathematician, I suspect that means in part that we would recognize the way it expresses itself, the logical underpinnings of what it does. I wonder, though, about the substance of its mathematics. Would it have algebra, analysis, and topology? Or would it have fields that we haven’t come close to thinking of? How much of what we’ve developed is necessary, and how much is there just because that’s what lay on and near the path we’ve chosen to take, as opposed to a different path the Martians took?

This probably deserves a thread of its own.

[iwakura43]

@Mangosteen

Although this method may look slower and more complicated, it is used because its easier and faster to figure out subtraction problems using 10 minus a number.

I learned my arithmetic in New Jersey. Just how did the rest of you learn to subtract on paper, if not this method? (I certainly don’t ‘carry the one’ for simple calculations, but if I have to subtract big numbers from each other, I certainly would).

[The_Flying_Dutchman]

@Kiminy

Real discrepancies would occur if other counting systems than Base-10 are taken as the norm. The hoopla that prime numbers are somehow “universal” (allowing us to use them to commicate in some way with alien cultures), for example, is ridiculous. Our prime numbers (numbers that are divisible only by themselves and 1) are only “prime” in a base ten system. If an alien culture were to use base 12, base 15, or some other counting system, their “prime numbers” would be completely different.

@Oldguy

Not true “Seventeen” is prine in any (integer) base system. It is true that 17 in base nine which is “sixteen” is not prime but the number seventeen is.

Okay, I must be missing some fundamental concept here.

If I consider the definition that I’ve always understood and provided by Kiminy, “Our prime numbers (numbers that are divisible only by themselves and 1)…”, I can experiment as follows:

Consider the prime number thirteen.

I pull out thirteen pennies and put them on the table.

Can I arrange them in even groups like I can with twelve?

With twelve I can have two groups of six each, three groups of four each or four groups of three each.

Obviously I can’t divide thirteen up evenly in any way shape of form.

Note that in my description of the experiment I purposely avoided base-10 notation. The quantity represented by the number thirteen can be described in any other base system.
Could you please explain how prime numbers are not universal?

Thankyou.

[Hypnagogic_Jerk]

@The Flying Dutchman

Could you please explain how prime numbers are not universal?

No, you’re right. Kiminy was wrong to say that prime numbers are dependent on notation, and Oldguy and ultrafilter corrected him. As Oldguy says, the number “seventeen” is a prime number however you express it, be it (17)[sub]10[/sub], (11)[sub]16[/sub], (10001)[sub]2[/sub] or XVII, or anything else.

[ultrafilter]

@ultrafilter

This probably deserves a thread of its own.

So I started it.

[CalMeacham]

Mathjematics is pretty universal across the world – the symbols have become pretty standardized in most cases, and I find that, with an appropriate language dictionary, I have been able to follow a papwer written in a foreign language that’s mostly math symbols.
I’d like to note two provisos, though:
1.)Sometimes the symbols are a little different. Older German texts use a caret (^) in place of a “cross” (basically a big “X”) to indicate the vector product (“cross product”), which confused me at first. It’s common European use to have the period and commas mean the opposite of their meaning in the US.

2.) Having never been in the Middle East myself, I haven’t seen this, but I understand the numbers are written differently. I’;ve seen depictions of them, but not in actual use. Despite the fact that we call them “Arabic numbers”, the form used in the West differs from the form in the Middle East, and by enough to be confusing. (Someone with more knowledge and experience will doubtless straighten me out here.)