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October 29th, 2017, 01:28 PM   #1
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Lightbulb Can Anyone solve these 5 Very Simple Math Problems?

Here is a link to the problems.


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October 29th, 2017, 03:10 PM   #2
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Someone will likely get around to proving them (if they can be proven) somewhere in the next few centuries. I'm not going to wait around for it, though.

-Dan
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October 29th, 2017, 04:17 PM   #3
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What do you mean by "simple"?

Just because it is easy to explain a problem does not mean it is simple. For example, the Collatz conjecture might seem simple because a child can iterate it. However, the actual question involves deep ideas about the nature and existence of invariant sets in non-smooth dynamical systems. Results in this area have been made. However, the Collatz conjecture itself asks about the global dynamics of a non-smooth map. Considering the fact that classifying global dynamics is an extremely difficult problem even for the classical cases arising from differential equations or iterating continuous maps, its highly unlikely this problem will be solved this century.

In other words, the Collatz conjecture is about as far from a "simple" problem as I can imagine. The same can be said for the moving sofa problem.

Also #3 is a completely trivial fact proved by calculus students daily. This is far from an unsolved problem. See the following link:

https://en.wikipedia.org/wiki/Euclidean_distance
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