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> Some of the problems in this book are HARD, but they are generally well posed problems of actual research interest to mathematicians Could you share a few ex
by psykotic 15y ago
> Some of the problems in this book are HARD, but they are generally well posed problems of actual research interest to mathematicians
Could you share a few examples? I've looked through the books from Gelfand's correspondence course (which are indeed excellent) but don't remember any problems that fit your description. Some of them would certainly be challenging for young children--I'm more interested in the second half of your statement.
I'll volunteer one potential example. There was a sequence of problems that dealt with the solvability by radicals of palindromic polynomials. That certainly motivates some ideas of Galois theory in no small way, but it's very basic and of no interest to research mathematicians.
Addendum: Now that I have looked it up in the book, I see it was a single problem, Problem 270, not a sequence of problems. That sequence of problems was from a mathematics competition for young children.
- Drbble 15y agoParent meant problems that were in the past of interest to research mathematicians. Someone(s) published the first papers exhibiting Catalan numbers underlying various counting problems. Obviously we don't expect elementary students to be at the forefront of modern cutting edge research.
- psykotic 15y agoIf so, that's a much weaker and not terribly interesting claim. The concrete example of counting with Catalan numbers is more compelling; it would be very challenging for children who lack experience with recursive definitions and inductive proofs. Systematic enumeration, albeit elementary, is distinctly modern.