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David Ketcheson
David Ketcheson
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I believe @Mangara's comment is very relevant here:

Number theory, combinatorics and geometry (the areas Project Euler mainly draws from) actually have lots of accessible problems that are still unresolved.

Accessible here means that the problem can be easily explained. However, unresolved problems that anyone can understand tend to be extremely difficult. If they weren't, then someone would have solved them!

Get a copy of Richard Guy's Unsolved Problems in Number Theory. There you can find some problems that constitute "real mathematical research" but are more or less in the vein you describe.

You can usually only (get paid to) do this research in a university, you have to be very talented to get a tenured job in these areas, and it's a long road. Also, due to the highly interconnected nature of mathematics, the techniques used to solve these problems are often vastly different from what you might expect -- for a famous example, see the proof of Fermat's Last Theorem via algebraic curves. So if you want to work in (say) number theory, you'll still need to learn deeply about and use other areas of mathematics.

I believe @Mangara's comment is very relevant here:

Number theory, combinatorics and geometry (the areas Project Euler mainly draws from) actually have lots of accessible problems that are still unresolved.

Accessible here means that the problem can be easily explained. However, unresolved problems that anyone can understand tend to be extremely difficult. If they weren't, then someone would have solved them!

Get a copy of Richard Guy's Unsolved Problems in Number Theory. There you can find some problems that constitute "real mathematical research" but are more or less in the vein you describe.

You can usually only do this research in a university, you have to be very talented to get a tenured job in these areas, and it's a long road. Also, due to the highly interconnected nature of mathematics, the techniques used to solve these problems are often vastly different from what you might expect -- for a famous example, see the proof of Fermat's Last Theorem via algebraic curves. So if you want to work in (say) number theory, you'll still need to learn deeply about and use other areas of mathematics.

I believe @Mangara's comment is very relevant here:

Number theory, combinatorics and geometry (the areas Project Euler mainly draws from) actually have lots of accessible problems that are still unresolved.

Accessible here means that the problem can be easily explained. However, unresolved problems that anyone can understand tend to be extremely difficult. If they weren't, then someone would have solved them!

Get a copy of Richard Guy's Unsolved Problems in Number Theory. There you can find some problems that constitute "real mathematical research" but are more or less in the vein you describe.

You can usually only (get paid to) do this research in a university, you have to be very talented to get a tenured job in these areas, and it's a long road. Also, due to the highly interconnected nature of mathematics, the techniques used to solve these problems are often vastly different from what you might expect -- for a famous example, see the proof of Fermat's Last Theorem via algebraic curves. So if you want to work in (say) number theory, you'll still need to learn deeply about and use other areas of mathematics.

Source Link
David Ketcheson
David Ketcheson
  • 36.6k
  • 10
  • 110
  • 163

I believe @Mangara's comment is very relevant here:

Number theory, combinatorics and geometry (the areas Project Euler mainly draws from) actually have lots of accessible problems that are still unresolved.

Accessible here means that the problem can be easily explained. However, unresolved problems that anyone can understand tend to be extremely difficult. If they weren't, then someone would have solved them!

Get a copy of Richard Guy's Unsolved Problems in Number Theory. There you can find some problems that constitute "real mathematical research" but are more or less in the vein you describe.

You can usually only do this research in a university, you have to be very talented to get a tenured job in these areas, and it's a long road. Also, due to the highly interconnected nature of mathematics, the techniques used to solve these problems are often vastly different from what you might expect -- for a famous example, see the proof of Fermat's Last Theorem via algebraic curves. So if you want to work in (say) number theory, you'll still need to learn deeply about and use other areas of mathematics.