# Famous Mathematician's Theorems

## Can you name the famous mathematicians who created these theorems?

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Summary of ResultNameSubject
Used to prove that there are uncountably many irrational numbers.Set Theory
In a right angled triangle, the square of the hypotenuse, equals the sum of the squares of the two right angled edges of the triangle.Geometry
A conjecture concerning the distribution of the zeros of the classical zeta function.Analysis
For n > 2, no three integers a, b, c satisfy: a^n + b^n = c^n.Number Theory
Every even integer greater than 2 can be expressed as the sum of two primes.Number Theory
Any convex polyhedron with V vertices, F faces, and E edges is such that: V - E + F = 2.Topology
There are infinitely many prime numbers. If there were finitely many, then the number obtained from multiplying all the primes then adding 1, would be divisible by a new prime.Number Theory
Every non self intersecting loop in the plane divides the plane into an inside region and an outside region.Topology
Every continuous function from a closed ball in Euclidean space, into itself, has a fixed point.Topology
Any coloring of a sufficiently large complete graph contains a monochromatic complete subgraph of a given size.Combinatorics
If parallel lines are drawn at a distance t apart, and a needle of length L < t is dropped, then with probability 2L /(pi)t, the needle will intersect a line.Probability
The complement of the union of sets A and B, is the same as the intersection of the complements of A and B.Set Theory
The number of elements in any subgroup of a finite group, divides the number of elements in the group.Algebra
Every partially ordered set in which every totally ordered subset has an upper bound, contains at least one maximal element.Set Theory
Every simply connected closed 3-manifold is homeomorphic to the 3-sphere.Topology
Summary of ResultNameSubject
L^p is a complete normed vector space.Analysis
There does not exist a set whose members are exactly those sets that are not members of themselvesSet Theory
Given an ergodic dynamical system, then the space average equals the time average almost everywhere.Dynamical Systems
For sufficiently large n, then the number of distinct prime factors of n has the normal distribution with mean and variance log ( log (n) ).Probability, Number Theory
The sequence of prime numbers contains arithmetic progressions of arbitrary length.Combinatorics/ Dynamical Systems
If A and B are complete measure spaces, f an integrable function on A x B, then the integral of f with respect to the product measure, is the iterated integral of f on A, then B.Analysis
A subset of euclidean n-space is compact if and only if it is closed and bounded.Analysis
If two paths connect the same two points, and a function is holomorphic everywhere between them, then the two path integrals of the function are equal.Complex Analysis
There are exactly n^(n-2) distinct trees on a set of n labeled vertices.Combinatorics
Given events A and B, and a probability measure P, then: P(A | B) P(B) = P(B | A) P(A).Probability
(cos(x) + i sin(x) )^n = cos(nx) + i sin(nx)Complex Analysis
Given an integer n, if n is even divide it by 2. If it is odd, multiply by 3 and then add 1. Continuing in this way, you always eventually reach 1.Number Theory
No consistent system of axioms whose theorems can be listed by an 'effective procedure' is capable of proving all facts about the natural numbers.Logic
Given a sequence of independent identically distributed random variables, then a tail event determined by this sequence either surely happens, or surely does not happen.Probability
Given sets A, B then if |A| â‰¤ |B|, and |B| â‰¤ |A|, then: |A| = |B|.Set Theory

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