Timeline of number theory
A timeline of number theory. Before 1000 BCE ca. 20,000 BCE — Nile Valley, Ishango Bone: possibly the earliest reference to prime numbers and Egyptian multiplication although this is disputed. About 300 BCE 300 BCE — Euclid proves the number of prime numbers is infinite. 1st millennium AD 250 — Diophantus writes Arithmetica, one of the earliest treatises on algebra. 500 — Aryabhata solves the general linear diophantine equation. 628 - Brahmagupta gives Brahmagupta's identity and solves the so called Pell's equation using his composition method. ca. 650 — Mathematicians in India create the Hindu–Arabic numeral system we use, including the zero, the decimals and negative numbers. 1000–1500 ca. 1000 — Abu-Mahmud al-Khujandi first states a special case of Fermat's Last Theorem. 895 — Thabit ibn Qurra gives a theorem by which pairs of amicable numbers can be found, (i.e., two numbers such that each is the sum of the proper divisors of the other). 975 — The earliest triangle of binomial coefficients (Pascal triangle) occur in the 10th century in commentaries on the Chandas Shastra. 1150 — Bhaskara II gives first general method for solving Pell's equation 1260 — Al-Farisi gave a new proof of Thābit ibn Qurra's theorem, introducing important new ideas concerning factorization and combinatorial methods. He also gave the pair of amicable numbers 17296 and 18416 which have also been jointly attributed to Fermat as well as Thabit ibn Qurra. 17th century 1637 — Pierre de Fermat claims to have proven Fermat's Last Theorem in his copy of Diophantus' Arithmetica. 18th century 1742 — Christian Goldbach conjectures that every even number greater than two can be expressed as the sum of two primes, now known as Goldbach's conjecture. 1770 — Joseph Louis Lagrange proves the four-square theorem, that every positive integer is the sum of four squares of integers. In the same year, Edward Waring conjectures Waring's problem, that for any positive integer k, every positive integer is the sum of a fixed number of kth powers. 1796 — Adrien-Marie Legendre conjectures the prime number theorem. 19th century 1801 — Disquisitiones Arithmeticae, Carl Friedrich Gauss's number theory treatise, is published in Latin. 1825 — Peter Gustav Lejeune Dirichlet and Adrien-Marie Legendre prove Fermat's Last Theorem for n = 5. 1832 — Lejeune Dirichlet proves Fermat's Last Theorem for n = 14. 1835 — Lejeune Dirichlet proves Dirichlet's theorem about prime numbers in arithmetic progressions. 1859 — Bernhard Riemann formulates the Riemann hypothesis which has strong implications about the distribution of prime numbers. 1896 — Jacques Hadamard and Charles Jean de la Vallée-Poussin independently prove the prime number theorem. 1896 — Hermann Minkowski presents Geometry of numbers. 20th century 1903 — Edmund Georg Hermann Landau gives considerably simpler proof of the prime number theorem. 1909 — David Hilbert proves Waring's problem. 1912 — Josip Plemelj publishes simplified proof for the Fermat's Last Theorem for exponent n = 5. 1913 — Srinivasa Aaiyangar Ramanujan sends a long list of complex theorems without proofs to G. H. Hardy. 1914