My math teacher says that they do math for fun, and I wonder how they do that? I want to do math in my free time. Where can I find problems to solve that will engage me and will take a while to complete?
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2Self-plug: Check out Brilliant.org. – Calvin Lin Jun 30 '21 at 00:05
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You may find this one to be fun, which can be solved (for example) by only knowing the binomial expansion formula: Show that $10^{2k+1}+1$ is divisible by 11 for all positive integers $k$. If this is not fun, ignore it, there are a lot more fun-type problems. For example, find the "fraction of positive integers" that are divisible by either 2 or 3. – Michael Jun 30 '21 at 00:10
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6Martin Gardner's many book on recreational mathematics are high-quality resources for problems in a wide variety of areas. – Andrew D. Hwang Jun 30 '21 at 00:11
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3Also going to recommend anything by Martin Gardner. You could also ask your teacher. – Jair Taylor Jun 30 '21 at 00:13
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There are many ways and you should follow your interests. One option is to maybe check out The Art of Problem Solving, Volume 1: The Basics. If it doesn't connect with you, do something else. – littleO Jun 30 '21 at 00:27
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Worth repeating: ask your teacher for advice. Besides (hopefully) getting some direction appropriate to your level and interests, but math fun can be even more fun if you have someone nearby to share with. – dxiv Jun 30 '21 at 03:47
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Perhaps qbyte.org might interest you. – Sarvesh Ravichandran Iyer Jun 30 '21 at 05:20
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A simple way to get fun problems is to watch the [tag:recreational-mathematics] tag! – Trebor Jul 02 '21 at 17:36
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Not directly responding to your question about sources, but an important bit of advice, I think: to have fun, do not pay any attention to anyone's judgement on the prestige or coolness or whatever of whatever you want to do. When you are doing math for fun, you yourself are the sole arbiter and judge of what is "good" or not!!!
In fact, I'd recommend the same for professionals, but it's more complicated.
paul garrett
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Dive in! Pick a problem or two here every day and try to work through them. Read and work through solutions to others.
A rural reader
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I would say I do the same thing. After finishing my A-levels (UK 18yo exams if your not familiar) I continued looking into concepts I found interesting, and websites like this are good as you can find problems and try to solve them, and if you can't someone else likely can so you learn from their answers. There are lots of cool obscure theorems too which I love finding. As others have mentioned, there are also online courses (some free) to take you beyond what you learn at school. Personally, I have found the maths I have learn on my own much more interesting than anything I was taught at school, but It is a good building block.
Henry Lee
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