In the context of The Story of Maths, explain the Hilbert's tenth problem of the "To Infinity and Beyond".
Hilbert's tenth problem asked if there was some universal method that could tell whether any equation had whole number solutions or not. The growing belief was that no so such method was possible yet the question remained, how could you prove that, no matter how ingenious you were, you would never come up with such a method. He mentions Paul Cohen. To answer this Julia Robinson, who created the Robinson Hypothesis which stated that to show that there was no such method all you had to do was cook up one equation whose solutions were a very specific set of numbers: The set of numbers needed to grow exponentially yet still be captured by the equations at the heart of Hilbert's problem. Robinson was unable to find this set. This part of the solution fell to Yuri Matiyasevich who saw how to capture the Fibonacci sequence using the equations at the heart of Hilbert's tenth.
Fibonacci sequence Yuri Matiyasevich Hilbert's tenth problem Fibonacci Julia Robinson Robinson Hypothesis Paul Cohen