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t. e. Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [1]
1937 — I. M. Vinogradov proves Vinogradov's theorem that every sufficiently large odd integer is the sum of three primes, a close approach to proving Goldbach's weak conjecture. 1949 — Atle Selberg and Paul Erdős give the first elementary proof of the prime number theorem. 1966 — Chen Jingrun proves Chen's theorem, a close approach to ...
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields.
A number x is called an A*-number if the ω*(x, n) converge to 0. If the ω*( x , n ) are all finite but unbounded, x is called a T*-number , Koksma's and Mahler's classifications are equivalent in that they divide the transcendental numbers into the same classes. [ 32 ]
Euler also made contributions to the understanding of planar graphs. He introduced a formula governing the relationship between the number of edges, vertices, and faces of a convex polyhedron. Given such a polyhedron, the alternating sum of vertices, edges and faces equals a constant: V − E + F = 2.
Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər; [b] German: [ˈleːɔnhaʁt ˈʔɔʏlɐ] ⓘ, Swiss Standard German: [ˈleːɔnhart ˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of ...
Terence Chi-Shen Tao FAA FRS (Chinese: 陶哲軒; born 17 July 1975) is an Australian and American mathematician who is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences.
Georg Ferdinand Ludwig Philipp Cantor (/ ˈkæntɔːr / KAN-tor; German: [ˈɡeːɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfiːlɪp ˈkantoːɐ̯]; 3 March [O.S. 19 February] 1845 – 6 January 1918 [1]) was a mathematician who played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established ...