**Horizon - A Mathematical Mystery Tour - [1984-12-10]**

**Horizon** programme from 1984 looking at the greatest unsolved problems in mathematics including Fermat's Last Therom (since solved), The Goldback Conjecture, The Riemann hypothesis, the P=NP Problem, and more. Featuring interviews with many modern mathematicians, this documentary also looks at the history of maths and some of if it's major players from Euclid to Bertrand Russell. In discussing the fact that proof requires more than calculated verification reference is made to the Merten Conjecture. A conjecture which was disproved in 1984, despite holding firm for 99 years and having been verified on computer up to the first 10 billion numbers. Afact that makes us think about the things in our own lives which, with far less evidence, we consider to be certainties. Documentary about pure mathematics, featuring the Japanese mathematicians who had just broken their own world record calculating pi to 16 million decimal points; a 000 prize for the first person to prove there are an infinite number of 'twin primes' and why it took Bertrand Russell 362 pages to prove that one plus one equals two.

From Wikipedia

**The study of mathematics** as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek Î¼Î¬Î¸Î·Î¼Î± (mathema), meaning "subject of instruction". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. Chinese mathematics made early contributions, including a place value system. The Hindu-Arabic numeral system and the rules for the use of its operations, in use throughout the world today, likely evolved over the course of the first millennium AD in India and was transmitted to the west via Islamic mathematics. Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. Many Greek and Arabic texts on mathematics were then translated into Latin, which led to further development of mathematics in medieval Europe.

From ancient times through the Middle Ages, bursts of mathematical creativity were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day.