Many people enjoy puzzles. For example, the recent craze for Sudoku - that's maths. Rubic cubes. Sliding block puzzles. Shunting puzzles. Peg solitaire. Anagrams. "Find a word" type puzzles. Those are all mathematics, normally called "recreational maths".
Some like doing calculations too. But that's of more limited appeal, and modern mathematics is often much more like puzzle solving than it is like calculations.
Some mathematicians are good at calculations, and some aren't just like non mathematicians.
So, if you want an "in" into understanding why mathematicians enjoy maths, start with puzzles :).
For instance try the sliding block puzzles and other puzzles here:
Play it now at Coolmath-Games.com
If you enjoy puzzles, you might well enjoy maths - if it was taught to you as like puzzle solving :).
If you solve a sliding block puzzle, for instance, your series of moves is actually a proof by example that there is a solution to that puzzle. It could be turned into a logical proof in an axiom system based on the requirements of the puzzle.
And just as you operate at a higher level and don't work it all out from basic axioms to solve the problem - same also in maths. You know the rules - but you think about things at a much higher level. And it often involves a lot of trial and error and unexpected insights. Sometimes you go to sleep puzzling over how to solve something in maths and then get the answer when you wake up in the morning. Or suddenly it comes to you. Those "aha" moments when you suddenly see a solution to something you've been trying to solve, maybe for months, are perhaps the most satisfying part of mathematics, as they are for puzzle solving.
And just like some people like some kinds of puzzles and others like other types of puzzles - mathematicians also like different types of maths. You might love group theory but set theory just doesn't appeal. Or you think fourier analysis is great, but can't see the fun and interest in complex analysis or number theory. Or vice versa.
Some people also enjoy calculating. That's more like practical maths. E.g. using maths in astronomy or physics or biology etc - if you like the subject and like puzzle solving, it's great to be able to combine them both. I like the way that with a few simple calculations and a bit of lateral thinking, you can sometimes solve problems that at first seemed very complex.
Before you can become a professional mathematician - normally you'd be expected to have a general understanding of maths, for instance you'd be expected to understand integration and differentiation as an undergraduate - and much more complex topics than that - even if you never need those for the area of maths you chose to specialize in.
And - some areas of maths require you to understand concepts that are quite hard to grasp, you may need to study for some time in some fields even after you graduate before you can say you fully understand it, well enough to start researching into it yourself. In most subjects, if someone talks about their research, you can expect to have some idea of what they are talking about even if you have never studied it at all, they can explain some of their ideas to you. But in maths, then often even other mathematicians in closely related fields can't understand the research. When I was doing postgraduate research into maths, I went to seminars on logic and set theory, a field I specialized in, and though some were easier to understand - with some of them I only understood a few sentences in the entire talk - and that's not because I was especially dim as a mathematician - it's normal. They could as easily have been talking in Japanese :). I think more so in maths than in any other subject that I know of.
But others involve concepts anyone can understand easily.
As an amateur mathematician, you just need to understand the particular area you are interested in, and some areas of maths require only a few simple concepts to understand them. Including recreational maths, and some areas of geometry for instance. So the fun of maths is accessible to everyone.
As a child I loved Martin Gardener's "Mathematical games" books and his column in Scientific American. They are still good fun reads to this day.
You can get them all on CD here:
Martin Gardner’s Mathematical Games: The Entire Collection of His Scientific American Columns on one CD
Or from Amazon: Martin Gardner's Mathematical Games: Martin Gardner: 9780883855454: Amazon.com: Books
Or some of them as individual books: Amazon.com: Martin Gardner: Books, Biography, Blog, Audiobooks, Kindle
Here are a few of his puzzles online: Page on theguardian.com
But the books are so much more than just a collection of puzzles, highly recommend them.
Some like doing calculations too. But that's of more limited appeal, and modern mathematics is often much more like puzzle solving than it is like calculations.
Some mathematicians are good at calculations, and some aren't just like non mathematicians.
So, if you want an "in" into understanding why mathematicians enjoy maths, start with puzzles :).
For instance try the sliding block puzzles and other puzzles here:
Play it now at Coolmath-Games.com
If you enjoy puzzles, you might well enjoy maths - if it was taught to you as like puzzle solving :).
If you solve a sliding block puzzle, for instance, your series of moves is actually a proof by example that there is a solution to that puzzle. It could be turned into a logical proof in an axiom system based on the requirements of the puzzle.
And just as you operate at a higher level and don't work it all out from basic axioms to solve the problem - same also in maths. You know the rules - but you think about things at a much higher level. And it often involves a lot of trial and error and unexpected insights. Sometimes you go to sleep puzzling over how to solve something in maths and then get the answer when you wake up in the morning. Or suddenly it comes to you. Those "aha" moments when you suddenly see a solution to something you've been trying to solve, maybe for months, are perhaps the most satisfying part of mathematics, as they are for puzzle solving.
And just like some people like some kinds of puzzles and others like other types of puzzles - mathematicians also like different types of maths. You might love group theory but set theory just doesn't appeal. Or you think fourier analysis is great, but can't see the fun and interest in complex analysis or number theory. Or vice versa.
Some people also enjoy calculating. That's more like practical maths. E.g. using maths in astronomy or physics or biology etc - if you like the subject and like puzzle solving, it's great to be able to combine them both. I like the way that with a few simple calculations and a bit of lateral thinking, you can sometimes solve problems that at first seemed very complex.
Before you can become a professional mathematician - normally you'd be expected to have a general understanding of maths, for instance you'd be expected to understand integration and differentiation as an undergraduate - and much more complex topics than that - even if you never need those for the area of maths you chose to specialize in.
And - some areas of maths require you to understand concepts that are quite hard to grasp, you may need to study for some time in some fields even after you graduate before you can say you fully understand it, well enough to start researching into it yourself. In most subjects, if someone talks about their research, you can expect to have some idea of what they are talking about even if you have never studied it at all, they can explain some of their ideas to you. But in maths, then often even other mathematicians in closely related fields can't understand the research. When I was doing postgraduate research into maths, I went to seminars on logic and set theory, a field I specialized in, and though some were easier to understand - with some of them I only understood a few sentences in the entire talk - and that's not because I was especially dim as a mathematician - it's normal. They could as easily have been talking in Japanese :). I think more so in maths than in any other subject that I know of.
But others involve concepts anyone can understand easily.
As an amateur mathematician, you just need to understand the particular area you are interested in, and some areas of maths require only a few simple concepts to understand them. Including recreational maths, and some areas of geometry for instance. So the fun of maths is accessible to everyone.
As a child I loved Martin Gardener's "Mathematical games" books and his column in Scientific American. They are still good fun reads to this day.
You can get them all on CD here:
Martin Gardner’s Mathematical Games: The Entire Collection of His Scientific American Columns on one CD
Or from Amazon: Martin Gardner's Mathematical Games: Martin Gardner: 9780883855454: Amazon.com: Books
Or some of them as individual books: Amazon.com: Martin Gardner: Books, Biography, Blog, Audiobooks, Kindle
Here are a few of his puzzles online: Page on theguardian.com
But the books are so much more than just a collection of puzzles, highly recommend them.
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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