Prime Numbers
Zeta function and riemann hypothesis
Gauss 25 primes in 100, 1 in 4, 1in 6 to 1000, and so on getting smaller each time "prime number conjecture" now proven.
Gauss was instrumental in the development of large areas of mathematics such as primes and complex numbers at the turn of the nineteenth century.
zeta function formed by the use of primes
complex numbers fed into zeta function by riemann, zeros seem to fall on the real = half line. Riemann hypothesis that all zeros fall on real = half. Riemann discovered connection between zeros and the distribution of primes - if all zeros on line then prime distribution "fair"
Princeton - Hugh Montgomery chatting Freeman Dyson. Montgomery showed Dyson pattern of zeros, Dyson recognised it as pattern of energy levels in large atoms like Erbium. (online article)
original source BBC Radio 4 In Our Time "Prime Numbers" 2006