• Best of luck to the class of 2019 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • Like us on facebook here

Interesting mathematical statements (1 Viewer)

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,477
Location
Outside reality
Gender
Male
HSC
2016
I know lol. This is one of the biggest mind gobbling problems to pure mathematicians apparently; WHY?
The thing is, we don't even know how to begin to approach this problem. Paul Erdos has already commented on this problem.
Looks like we'll just have to wait for the next
Euler/Erdos/Tao/Gauss/Noether/Polya/Hilbert/Russell/Lagrange/Riemann/Hardy/Poincare/Fermat/Grothendieck/Newton/Leibniz/Weierstrass/Cauchy/Descartes/Dirichlet/Cantor/Fibonacci/Jacobi/Ramanujan/Hamilton/Godel/Pascal/Apollonius/Laplace/Liouville/Eisenstein/Banach/Peano/Bernoulli/Viete/Fourier/Huygens/Chebyshev/Lebesgue/Turing/Cardano/Minkowski/Littlewood/Legendre/Birkhoff/Lambert/Poisson/Wallis/Tarski/Frege/Hausdorff/Neumann/Galois
to come around and resolve the problem.

 

glittergal96

Active Member
Joined
Jul 25, 2014
Messages
418
Gender
Female
HSC
2014
If you have a small ball in 3 dimensional space, it is possible to decompose it as a union of a finite number of sets, which can be moved by rotations and translations such that the pieces never overlap and such that the final object constructed is an arbitrarily large ball.

Colloquially, one can cut a pea into a finite number of pieces and reassemble it into something the size of the sun.
 

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,805
Gender
Male
HSC
2015
Can we keep our posts restrained to at least MX2 level and not making bad usages of mathematics lmao
 

KingOfActing

Well-Known Member
Joined
Oct 31, 2015
Messages
991
Location
Sydney
Gender
Male
HSC
2016
Zeta regularisations are important

1 + 2 + 3 + ... =/= -1/12, but is rather 'assigned' that value
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,097
Gender
Male
HSC
N/A
I like the 1 + 2 + 3 + 4 + … = -1/12 result, and find it also quite amazing that this is used in physics and gives some experimentally verifiable results. There's a lot of 'weird' stuff like this in this series of lectures on Mathematical Physics by Carl Bender that can be found on YouTube.

Also, I think this thread should be in the maths Extracurricular Topics forum.
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,477
Location
Outside reality
Gender
Male
HSC
2016
If you have a small ball in 3 dimensional space, it is possible to decompose it as a union of a finite number of sets, which can be moved by rotations and translations such that the pieces never overlap and such that the final object constructed is an arbitrarily large ball.

Colloquially, one can cut a pea into a finite number of pieces and reassemble it into something the size of the sun.
Only if I accept the axiom of choice. : PPPPPPP
 

glittergal96

Active Member
Joined
Jul 25, 2014
Messages
418
Gender
Female
HSC
2014
Only if I accept the axiom of choice. : PPPPPPP
Even if you don't accept the axiom of choice (which is a bit limiting, but some minority of mathematicians don't), you would not be able to prove that such a reassembling of the pea into the sun is impossible. (Because the axiom of choice is consistent with the other axioms of set theory.)

This is still pretty unintuitive.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top