Elementary proof.

Question

What actually elementary proof means ?

If there is an elementary proof for a conjecture , then is it a theorem ?

I saw papers on some conjectures proving stating as elementary proof. Then it means the conjecture is proved ?

Is there any site that correctly tells about status of a conjecture ? thanks in advance .

The search for "elementary proof" on Google returns this page as the first result, which seems to answer your question. — Clayton, Dec 04 '13 at 13:12
An elementary proof is just a proof that is elementary. You just need to pick up a dictionary. — Tim Ratigan, Dec 04 '13 at 13:12

score 3 · Answer 1 · answered Dec 04 '13 at 13:34

I would argue that when we say elementary proof we mean a proof which doesn't use techniques from seemingly more complicated mathematics theories.

For example, a proof of the Prime Number Theorem --- which is a statement about $\mathbb{N}$ primarily --- that uses complex analysis is not considered elementary.

score 2 · Answer 2 · answered Dec 04 '13 at 13:13

2

Elementary proof is a proof which uses some basic mathematical tools, rudiments of mathematics etc. Please also check http://en.wikipedia.org/wiki/Elementary_proof

answered Dec 04 '13 at 13:13

Deyton

246

score 1 · Accepted Answer · answered Dec 04 '13 at 16:28

"Elementary proof" can mean several things: 1. A proof that doesn't use big machinery; 2. A proof that is short and sweet; 3. A proof by a crackpot claiming to have solved some famous conjecture; 4. A proof that is too fiddly to write down, so the author says it is "elementary" so that he/she doesn't need to spend time figuring out a good way to write it properly; 5. A proof that everyone in the field is aware of, but has never been written down, so if you are new to the field you don't have a chance of figuring it out.

Item (4) is more usually denoted "it is clear that..." And (5) is more usually denoted "it is well known that..."

Elementary proof.

3 Answers3