1. ## What is mathematics?

I'm a math major and therefore need to be able to define "mathematics" in a sentence. A few years ago, I would've said "the study of numbers", but with topics like "Set Theory" that have little to do with numbers, that definition seems inadequate.

2. ## Re: What is mathematics?

Originally Posted by alexmahone
I'm a math major and therefore need to be able to define "mathematics" in a sentence. A few years ago, I would've said "the study of numbers", but with topics like "Set Theory" that have little to do with numbers, that definition seems inadequate.
I the area known as the philosophy of mathematics it is generally agreed that mathematics is the science of patterns.

For a longer exploration of this topic, I recommend What is Mathematics Really by Reuben Hersh.

3. ## Re: What is mathematics?

I wouldn't use the word "science" but the study of patterns, certainly. It might be slightly better to say the "study of relationships" as a little more general.

4. ## Re: What is mathematics?

Originally Posted by HallsofIvy
I wouldn't use the word "science" but the study of patterns, certainly. It might be slightly better to say the "study of relationships" as a little more general.
Actually I agree with you there. But I was a student of the philosopher Micheal Resnik who was a Quine PhD. That was his definition.

5. ## Re: What is mathematics?

"Study of relationships" is awfully broad - study of relationships among what? This sounds like something a genealogist would claim, or a family psychologist. A quick google search suggests "the science that deals with the logic of shape, quantity and arrangement."

6. ## Re: What is mathematics?

Originally Posted by ChipB
"Study of relationships" is awfully broad - study of relationships among what?
That's actually the whole point- NOT relationships among specific things but just "relationships" in the abstract.

7. ## Re: What is mathematics?

Originally Posted by HallsofIvy
That's actually the whole point- NOT relationships among specific things but just "relationships" in the abstract.
Maybe, "The study of abstract and concrete relationships".

8. ## Re: What is mathematics?

Are there other kinds of relationships, that are neither "abstract" nor "concrete"? If not how is "abstract and concrete relationships" different from "relationships"?

9. ## Re: What is mathematics?

Originally Posted by HallsofIvy
Are there other kinds of relationships, that are neither "abstract" nor "concrete"? If not how is "abstract and concrete relationships" different from "relationships"?
In common English, the word "relationship" has connotation that is implied when not modified by any adjectives. By adding adjectives, it becomes more clear that the connotations normally associated with the word may not apply. Even this phrase is not necessarily clear, and could likely be improved upon.

10. ## Re: What is mathematics?

This is an interesting discussion. I was looking for the origin of the word 'physics' and googled 'ancient physics'. I found an article on explorable where physics is viewed as a child of mathematics and philosophy.

11. ## Re: What is mathematics?

Originally Posted by HallsofIvy
I wouldn't use the word "science" but the study of patterns, certainly.
I don't think Mathematics is a science at all. Science, by definition, uses experiment to verify or disprove hypotheses - the scientific method. Maths doesn't, it's an exercise in pure logic. I would say that Mathematics was developed as a tool for the study of Physics and Accountancy, and that Physics was originally Natural Philosophy which seems like a very accurate description. Perhaps you might describe it as an amalgam of Philosphy/Theology and observation - maybe Applied Philosophy.

A single sentence answer would perhaps be "the study of relationships between abstract objects", but as has been illustrated here, a single sentence isn't really sufficient - you could write a book on the subject.

12. ## Re: What is mathematics?

You are right; mathematics is not a science, and yes the answer could stretch into a book. I also like the way many subjects separated out into individual ones, but today many rejoin in interesting intersections. It's like our vocabulary to explain the ecosystem we live in is morphing - all the time.