6 ms·

Mathematics has this funny habit of throwing around "it is easy to say that ...", or in this case, calling a proof that eluded mathematicians for decades "simpl

Mathematics has this funny habit of throwing around "it is easy to say that ...", or in this case, calling a proof that eluded mathematicians for decades "simple."

philipov 10y ago
Simple (easy to say) is not the same as being easy to deduce. A needle is a simple object, but finding one in a pile of hay takes a lot of work. Likewise, it is hard to pick out the features that make a problem simple when they are embedded in a sea of complexity. It becomes easy to say once you are no longer faced with the difficulty of knowing the right thing to say.
- cr0sh 10y ago
  > A needle is a simple object, but finding one in a pile of hay takes a lot of work. 1. Gather all the hay in multiple trash bags (this assumes that the needle remains with the hay and doesn't fall out) 2. After gather the hay, use a roller-magnet pickup tool over the area the hay was at to find the needle if it fell out of the hay (assumes needle is made of ferrous magnetic material) 3. Place each bag, one by one, inside the torus of a CT scanner. Turn on CT scanner. 4. Remove bag of hay. Check inside of CT scanner torus for needle. 5. Repeat as needed with other bags. Alternatively, one could set the hay pile on fire, then run over the ashes with the magnetic pickup tool.
  - Aron 10y ago
    Alternatively I could step on the hay with a bare foot, because if the needle is in there, I'll step on it for sure.
    - hifigi 10y ago
      Or you could just burn the hay.
- mehaveaccount 10y ago
  >Simple to say is not simple to deduce. Case in point: Fermat's Last Theorem, or Collatz Conjecture
  - Chinjut 10y ago
    Well, no, the point isn't that simple propositions may have complex proofs, the point is that a proof may itself be simple, though hard to discover in the first place.
cperciva 10y ago
You just need to understand the language. "Trivial" = "regularly covered in undergraduate courses" "Easy" = "a good topic for an undergraduate honour's thesis" "Non-trivial" = "a good PhD thesis topic" "Distinctly non-trivial" = "a groundbreaking result which will establish a professor's reputation in the field"
- tnecniv 10y ago
  I had a professor who liked to talk about how "elementary" did not mean easy, it just means "uses only the foundations." This proof is a perfect example of that statement. Formulating the problem the right way -- which is most often the hardest part -- was the real challenge here, not the mechanisms needed to do the formulation or the proof.
  - huhtenberg 10y ago
    Not sure why, but this reminds me how we had a professor that would say Let y(x) = a*x^4 + b*x^3 + c*x^2 + d*x + e, whereby e is not _necessarily_ the base of natural logarithm
    - cperciva 10y ago
      My favourite along those lines was "let epsilon be a small number which is not necessarily greater than zero". Everybody who spent the preceding year on epsilon-delta proofs did a double-take at that.
  - FabHK 10y ago
    There's a wonderful book, by the way, Proofs from THE BOOK, of, well, simple beautiful proofs. The book is named after > mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book." https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK
- sacheendra 10y ago
deleted 10y ago
[deleted]
mygo 10y ago
Easy to prove =/= Easy to discover (+). It is simple to say E=MC^2. That doesn't take away from the fact that it was very hard for it to be discovered. And it's a good thing. It's a good thing that things which were hard to discover can be communicated easily. Otherwise we wouldn't be able to compress thousands of lifetimes worth of discoveries into a one-semester lecture. --- (+) footnote: well, unless P=NP.

Mathematics has this funny habit of throwing around "it is easy to say that ...", or in this case, calling a proof that eluded mathematicians for decades "simple."

philipov 10y ago

Simple (easy to say) is not the same as being easy to deduce. A needle is a simple object, but finding one in a pile of hay takes a lot of work. Likewise, it is hard to pick out the features that make a problem simple when they are embedded in a sea of complexity. It becomes easy to say once you are no longer faced with the difficulty of knowing the right thing to say.

cr0sh 10y ago
> A needle is a simple object, but finding one in a pile of hay takes a lot of work. 1. Gather all the hay in multiple trash bags (this assumes that the needle remains with the hay and doesn't fall out) 2. After gather the hay, use a roller-magnet pickup tool over the area the hay was at to find the needle if it fell out of the hay (assumes needle is made of ferrous magnetic material) 3. Place each bag, one by one, inside the torus of a CT scanner. Turn on CT scanner. 4. Remove bag of hay. Check inside of CT scanner torus for needle. 5. Repeat as needed with other bags. Alternatively, one could set the hay pile on fire, then run over the ashes with the magnetic pickup tool.
- Aron 10y ago
  Alternatively I could step on the hay with a bare foot, because if the needle is in there, I'll step on it for sure.
  - hifigi 10y ago
    Or you could just burn the hay.
mehaveaccount 10y ago
>Simple to say is not simple to deduce. Case in point: Fermat's Last Theorem, or Collatz Conjecture
- Chinjut 10y ago
  Well, no, the point isn't that simple propositions may have complex proofs, the point is that a proof may itself be simple, though hard to discover in the first place.

cperciva 10y ago

You just need to understand the language. "Trivial" = "regularly covered in undergraduate courses" "Easy" = "a good topic for an undergraduate honour's thesis" "Non-trivial" = "a good PhD thesis topic" "Distinctly non-trivial" = "a groundbreaking result which will establish a professor's reputation in the field"

tnecniv 10y ago
I had a professor who liked to talk about how "elementary" did not mean easy, it just means "uses only the foundations." This proof is a perfect example of that statement. Formulating the problem the right way -- which is most often the hardest part -- was the real challenge here, not the mechanisms needed to do the formulation or the proof.
- huhtenberg 10y ago
  Not sure why, but this reminds me how we had a professor that would say Let y(x) = a*x^4 + b*x^3 + c*x^2 + d*x + e, whereby e is not _necessarily_ the base of natural logarithm
  - cperciva 10y ago
    My favourite along those lines was "let epsilon be a small number which is not necessarily greater than zero". Everybody who spent the preceding year on epsilon-delta proofs did a double-take at that.
- FabHK 10y ago
  There's a wonderful book, by the way, Proofs from THE BOOK, of, well, simple beautiful proofs. The book is named after > mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book." https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK
sacheendra 10y ago

deleted 10y ago

[deleted]

mygo 10y ago

Easy to prove =/= Easy to discover (+). It is simple to say E=MC^2. That doesn't take away from the fact that it was very hard for it to be discovered. And it's a good thing. It's a good thing that things which were hard to discover can be communicated easily. Otherwise we wouldn't be able to compress thousands of lifetimes worth of discoveries into a one-semester lecture. --- (+) footnote: well, unless P=NP.