A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis (hence theory, axiom, principle), which is a testable statement based on accepted grounds. In mathematics, a conjecture is an unproven proposition or theorem that appears correct.

The Langlands program is a far-reaching web of these ideas of 'unifying conjectures' that link different subfields of mathematics, e.g. number theory and representation theory of Lie groups; some of these conjectures have since been proved.

Formal mathematics is based on provable truth. In mathematics, any number of cases supporting a conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample would immediately bring down the conjecture. Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf. Pólya conjecture).

D. Andrew "Andy" Beal (born November 11, 1952) is a Dallas, Texas-based billionaire businessman who was born and raised in Lansing, Michigan. He made his fortune in banking and real estate and is the founder and chairman of Beal Bank and Beal Aerospace Technologies. Beal is also known for his high-stakes poker games and his interest in mathematics. Beal has an estimated worth of US$6.6 billion as of 2011.

Beal wanted to be a businessman since he was a teenager in Lansing. During his years in high school (Lansing Sexton) he began to earn money by fixing televisions with the help of his uncle Denny (Dennis Rogozinski), later installing apartment security systems and eventually with the help of some friends, he began to relocate dislodged houses. Beal would link hydraulic jacks and raise homes at night and then move or level them. At the age of 18, Andy purchased Spartan and Jackson Speedway, one of very few business ventures that haven't worked out for Beal.

Beal, who had excelled on his high school debate team, enrolled at Michigan State University and subsequently attended Baylor University in Texas. At age 19, Beal bought a house in Lansing for $6,500 (USD) and started renting it for $119 per month, which eventually led to his first net gain as a businessman.

Peter Clive Sarnak (born 18 December 1953) is a South African-born mathematician. He has been Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Andrew Wiles, and is an editor of the Annals of Mathematics. Sarnak is also on the permanent faculty at the School of Mathematics of the Institute for Advanced Study.

Sarnak graduated University of the Witwatersrand (B.Sc. 1975) and Stanford University (Ph.D. 1980), under the direction of Paul Cohen.

Sarnak was awarded the Polya Prize of Society of Industrial & Applied Mathematics in 1998, the Ostrowski Prize in 2001, the Levi L. Conant Prize in 2003 and the Frank Nelson Cole Prize in Number Theory in 2005. He was also elected as member of the National Academy of Sciences (USA) and Fellow of the Royal Society (UK) in 2002. He was awarded an honorary doctorate by the Hebrew University of Jerusalem in 2010.