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It sometimes amazes me how utterly random problems like this end up being their own fields in mathematics. This ended up being a pretty fascinating problem, but

by soheil 5y ago

It sometimes amazes me how utterly random problems like this end up being their own fields in mathematics. This ended up being a pretty fascinating problem, but coming up with an arbitrary equation like this and then checking to see if it satisfies yet another arbitrary requirement doesn't seem very difficult to do. Am I completely missing something here?

yupper32 5y ago
> doesn't seem very difficult to do. What makes you think this? You just had area experts tell you otherwise. Do you think that mathematicians are lying to you?
- spoonjim 5y ago
  Mathematicians don't really claim that creating Collatz-like conjectures is difficult... they claim that proving Collatz is hard.
  - yupper32 5y ago
    I read "checking to see if it satisfies" as "proving", but I could be wrong.
- soheil 5y ago
  I think you misunderstood the answer with the problem. Coming with the answer to this problem is clearly difficult. But what makes 3x+1 as a problem so hard to come up with?
spoonjim 5y ago
The conjectures where the condition is very simple (Collatz, Goldbach, Fermat) but the proof is very elusive are not as common as you think.
- soheil 5y ago
  I guess even if they're not common, clearly the person who first came up with 3x+1 didn't know it was going to be so hard to solve. So it was a random simple problem to formulate that ended up being very difficult to solve.
  - spoonjim 5y ago
    The entire mathematical world realized how interesting the Collatz conjecture was as soon as it was put forward. And it took until 1937 when Euclid figured out most of geometry 2000 years ago.
    - smegger001 5y ago
      Euclid figured out most of geometry 2000 years ago... *for flat planes. there was this thing about parallel lines he got wrong
- jones1618 5y ago
  FYI: Many variations of Collatz (Mx+N where M and N are different numbers, imaginary numbers, etc.) have been explored. If I remember right many behave trivially/uninterestingly or are equivalent to Collatz only not as simple. So, Collatz is uniquely simple yet complex.
demosito666 5y ago
I don't get why this is being downvoted. For me math is pretty much a mystery, in a sense that it seems so arbitrary once you move from simple concepts that were initially grounded in a real world (like counting pebbles or splitting a circle). And it's not because I'm particularly badly educated, after all I believe we all can agree that Eugene Wigner [1] knew a bit of math and he still was wondering the same thing [2]. So soheil's question doesn't seem ignorant of meaningless to me. One could probably reframe it to become something similar to philosophy of Gödel's theorems, in lines of "there may (or may not) exist an infinite number of problems in number theories that are very simply formulated but are impossible/hard to prove or disprove". Consequence of that being that our abilities to have a definitive proof of statements are negligible and we're thus fundamentally trapped in an infinitely small space of outer mathematical universe. I'm sorry if I'm saying something stupid here (or on the contrary, some well-known fact), like I said, I know nothing about mathematics so the two are equally possible to me. [1] https://en.wikipedia.org/wiki/Eugene_Wigner https://en.wikipedia.org/wiki/Eugene_Wigner [2] https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...

by soheil 5y ago

yupper32 5y ago

> doesn't seem very difficult to do. What makes you think this? You just had area experts tell you otherwise. Do you think that mathematicians are lying to you?

spoonjim 5y ago
Mathematicians don't really claim that creating Collatz-like conjectures is difficult... they claim that proving Collatz is hard.
- yupper32 5y ago
  I read "checking to see if it satisfies" as "proving", but I could be wrong.
soheil 5y ago
I think you misunderstood the answer with the problem. Coming with the answer to this problem is clearly difficult. But what makes 3x+1 as a problem so hard to come up with?

spoonjim 5y ago

The conjectures where the condition is very simple (Collatz, Goldbach, Fermat) but the proof is very elusive are not as common as you think.

soheil 5y ago
I guess even if they're not common, clearly the person who first came up with 3x+1 didn't know it was going to be so hard to solve. So it was a random simple problem to formulate that ended up being very difficult to solve.
- spoonjim 5y ago
  The entire mathematical world realized how interesting the Collatz conjecture was as soon as it was put forward. And it took until 1937 when Euclid figured out most of geometry 2000 years ago.
  - smegger001 5y ago
    Euclid figured out most of geometry 2000 years ago... *for flat planes. there was this thing about parallel lines he got wrong
jones1618 5y ago
FYI: Many variations of Collatz (Mx+N where M and N are different numbers, imaginary numbers, etc.) have been explored. If I remember right many behave trivially/uninterestingly or are equivalent to Collatz only not as simple. So, Collatz is uniquely simple yet complex.

demosito666 5y ago

I don't get why this is being downvoted. For me math is pretty much a mystery, in a sense that it seems so arbitrary once you move from simple concepts that were initially grounded in a real world (like counting pebbles or splitting a circle). And it's not because I'm particularly badly educated, after all I believe we all can agree that Eugene Wigner [1] knew a bit of math and he still was wondering the same thing [2]. So soheil's question doesn't seem ignorant of meaningless to me. One could probably reframe it to become something similar to philosophy of Gödel's theorems, in lines of "there may (or may not) exist an infinite number of problems in number theories that are very simply formulated but are impossible/hard to prove or disprove". Consequence of that being that our abilities to have a definitive proof of statements are negligible and we're thus fundamentally trapped in an infinitely small space of outer mathematical universe. I'm sorry if I'm saying something stupid here (or on the contrary, some well-known fact), like I said, I know nothing about mathematics so the two are equally possible to me. [1] https://en.wikipedia.org/wiki/Eugene_Wigner https://en.wikipedia.org/wiki/Eugene_Wigner [2] https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...