Forum Introduction

[Robert]

Theorems and Conjectures
Added to forums on Oct 22, 2005

Purpose
This forum was added to the mathematics category to focus discussions on some of the more interesting, famous and important theorems and conjectures of mathematics. Many of these represent fascinating enigmas, quandaries or conundrums. By discussing these mathematical curiosities new insight could be gained into the mathematics of the Theory of Everything.

Background
There are many theorems and conjectures. Some are quite famous, with entire books devoted to them, such as Godel's incompleteness theorems, Fermat's last theorem, and Cantor's diagonal argument. Some conjectures, such as the Riemann hypothesis (1859) or the Collatz conjecture (1937) were formulated many years ago and yet remain unsolved to this day.

Some definitions:

• Conjecture - A mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove.
• Theorem - An proposition that has been or is to be proved on the basis of explicit assumptions; A statement that can be proven using logical (deductive) reasoning.

So basically, a conjecture is probably true, but has not been proven while a theorem has been proven to be true. Fermat's last theorem was actually a conjecture until it was proved in 1995, at which point it became a true theorem.

Posting Guidelines
You just need to keep your posts on topic. Your posts should usually revolve around known mathematical enigmas rather than your own personal theorems of the math world. If would like to present a Theorem of your own, that is well thought out and presented in a serious way, you may do so and solicit comments from others. If you would like to present a theorem as a segue into your perspective on other mathematical or scientific concepts, that should also be fine.

When you start a thread, be sure to provide the name and a short description of the mathematical theorem or conjecture you wish to discuss. Also, provide links to outside resources when possible. One more thing, please use the spell checker before submitting your post. It's a great tool and gives your post a more professional look.

Post your questions to this thread and I'll respond and may update to introductory post if a clarification is needed.

Regards,
--Robert

[Guille]

This forum is a great idea, I have oads of threads to start.

But I have a question: What are the definitions and thus differences and similarities of the ideas of "conjectures" and "hypothesis" in mathematics?