ABC Conjecture

The abc conjecture is a conjecture in number theory, first proposed by Joseph OesterlĂ© and David Masser. It is stated in terms of three positive integers, a, b and c that are relatively prime and satisfy a + b = c. 
Unsolved

0 
Collatz Conjecture

Does the Collatz sequence eventually reach 1 for all positive integer initial values? Also known as the 3n + 1 problem. 
Unsolved

0 
Goldbach's Conjecture

Goldbach's conjecture is one of the oldest and bestknown unsolved problems in number theory and all of mathematics. It states: Every even integer greater than 2 is the sum of two primes. The conjecture remains unproven despite considerable effort. 
Unsolved

0 
HadwigerNelson Problem

The Chromatic Number of the Plane (CNP) is the chromatic number of the graph whose vertices are elements of the plane, and two points are connected by an edge if they are a unit distance apart. The HadwigerNelson problem asks to compute CNP. 
Unsolved
Polymath Project

4 
Kalai's 3^d conjecture

Does every ddimensional centrally symmetric polytope have at least 3^d nonempty faces? 
Unsolved

2 
P versus NP

The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified can also be solved quickly. 
Millennium Problem
Unsolved

2 
Riemann Hypothesis

The Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. 
Millennium Problem
Unsolved

1 
Twin Prime Conjecture

A twin prime is a prime number that is either 2 less or 2 more than another prime number. The Twin Prime Conjecture asks if there are infinitely many twin primes. 
Unsolved
Polymath Project

0 