Great Theorems of Mathematics

[gnome]

Pixy already named my two favorites in the OP.

Third place is the already-mentioned Euclid proof of infinite prime numbers.

The Goldbach Conjecture will always have a special place for me as well, because as a youth I spent a good deal of time searching for a proof I even came up with a reversed form of mathematical induction to try to cope with it.

 

[jadey]

Pigeonhole principle. When you have m boxes, and n > m objects, at least one box contains at least 2 objects. Generalized statement: if you have m boxes and n > k*m objects, at least one box contains k+1 objects.

Fixed that for you. The almight Jadey was prepared to debunk a great theory.

 

[Cuddles]

Pigeonhole principle. When you have m boxes, and n > m objects, at least one box contains 2 objects. Generalized statement: if you have m boxes and n > k*m objects, at least one box contains k+1 objects.

That's only true if you specify that the objects go in the boxes. Otherwise it just ends up looking like my floor at home.

 

[ddt]

Fixed that for you. The almight Jadey was prepared to debunk a great theory.

If a box contains 3 objects, it also contains 2 objects, doesn't it?

That's only true if you specify that the objects go in the boxes. Otherwise it just ends up looking like my floor at home.

Have you seen my floor?

 

[arthwollipot]

If a box contains 3 objects, it also contains 2 objects, doesn't it?

Three different sets of two objects, in fact.

 

[jadey]

If a box contains 3 objects, it also contains 2 objects, doesn't it?

That's a fargin' trick question you cork sucking bastage!

 

[AvalonXQ]

Three different sets of two objects, in fact.

Whoa! That makes six objects!

 

[Philosaur]

Whoa! That makes six objects!

Three objects, three sets of two objects:

A + (B + C)
B + (A + C)
C + (A + B)

There's three more sets! Giving us *nine* objects total!

Oh wait--there's also the set of all objects:

(A + B + C)

Ten! Do I win something?

 

[AvalonXQ]

Yes! In fact, you win ten of them.

 

[Philosaur]

Yes! In fact, you win ten of them.

Awesome! Though it's a good thing my payroll department doesn't think like this...

 

[jadey]

Awesome! Though it's a good thing my payroll department doesn't think like this...

Good? For who?

 

[leon_heller]

It's not a theorem (yet) but I've always liked Goldbach's Conjecture - every even number is the sum of two primes.

Leon

 

[ctamblyn]

Three objects, three sets of two objects:

A + (B + C)
B + (A + C)
C + (A + B)

There's three more sets! Giving us *nine* objects total!

Oh wait--there's also the set of all objects:

(A + B + C)

Ten! Do I win something?

Hang on just a minute... There are three singletons {A}, {B}, {C}, three two-element sets {A,B}, {A,C}, {B,C}, the set {A,B,C} and the empty set {}. As well as the three original objects. I make that 11 in total.

 

[Philosaur]

Hang on just a minute... There are three singletons {A}, {B}, {C}, three two-element sets {A,B}, {A,C}, {B,C}, the set {A,B,C} and the empty set {}. As well as the three original objects. I make that 11 in total.

Touché...

 

[arthwollipot]

Do we have any advance on 11? Going once... going twice...

 

[ddt]

Do we have any advance on 11? Going once... going twice...

Oh but that's simple. There is not only {} (the empty set), but also { {} } (the set containing only the empty set as element), and { { {} } } and { { { {} } } } and { { { { {} } } } } etc. You get the point: without even needing a single element, you have a countably infinite number of sets. That's before you posit there is something like a countably infinite set (which is one of the axioms of ZFC set theory).

 

[arthwollipot]

*bang* Sold to ddt for an infinite sum of money. Please redeem by cheque or money order as we haven't space for an infinite amount of cash.

 

[epix]

Strange that no one has mentioned the most frequently used theorem of them all: the Pythagorean theorem.

 

[arthwollipot]

Oh come on. A² + B² = C² is about the dullest of the things Pythagoras achieved.

 

[epix]

Oh come on. A² + B² = C² is about the dullest of the things Pythagoras achieved.

Most of the "great theorems" don't have much of an application outside abstract math that doesn't connect with any useful application. Interesting is that at the time of the conception, Pythagorians guarded the idea as a secret, and I believe that they killed someone who was talking too much.