1. The rough subdivision of number theory into its modern subfields—in particular, analytic and algebraic number theory.

2. We've created a number theory problem.

3. Algebra and Number Theory; Linear Algebra

4. The Disquisitiones covers both elementary number theory and parts of the area of mathematics now called algebraic number theory.

5. She is known for her research in number theory.

6. Number theory, field theory, algebraic geometry, algebra, group theory

7. A separate inspiration for F1 came from algebraic number theory.

8. He works in algebraic geometry, representation theory, and number theory.

9. Alhazen's contributions to number theory include his work on perfect numbers.

10. Further branches crucially applying groups include algebraic geometry and number theory.

11. He also wrote on algebraic geometry, number theory, and integral equations.

12. Analytic number theory uses mathematical analysis to solve problems about integers.

13. Étienne Fouvry is a French mathematician working primarily in analytic number theory.

14. Using tools of algebraic number theory, Andrew Wiles proved Fermat's Last Theorem.

15. He has contributed to number theory and related parts of algebraic geometry.

16. This is one of the main results of classical algebraic number theory.

17. First published in 1941, it discusses number theory, geometry, topology and calculus.

18. U+0305 ̅ COMBINING OVERLINE, used as abbreviation for standard numerals (Typographical Number Theory).

19. Algebraic number theory studies various number rings that generalize the set of integers.

20. Ask him what's the reason and he states his "fondness for number theory" .

21. He worked mainly in abstract algebra, but made important contributions to number theory.

22. Beyond probability theory, they are applied in domains ranging from number theory to physics.

23. One of the main results in additive number theory is the solution to Waring's problem.

24. Alongside his teaching responsibilities, Bunyakovsky made significant scientific contributions in number theory and probability theory.

25. With Hans Zassenhaus he also worked on computer algebra and its applications in number theory.

26. János Pintz (December 20, 1950, Budapest) is a Hungarian mathematician working in analytic number theory.

27. In mathematics, the analytic subgroup theorem is a significant result in modern transcendental number theory.

28. Hejhal works on analytic number theory, automorphic forms, the Selberg trace formula and quantum chaos.

29. We discuss here some basic problems of algebraic number theory under a computational point of view.

30. Before the Disquisitiones was published, number theory consisted of a collection of isolated theorems and conjectures.

31. In number theory, he introduced the sieve of Eratosthenes, an efficient method of identifying prime numbers.

32. This could have huge implications for understanding of algebra, geometry, number theory, quantum gravity and chemistry.

33. PARI/GP is a computer algebra system with the main aim of facilitating number theory computations.

34. In addition to the inclusion of research lines in Number Theory, Group Theory and Combinatorics in 2011.

35. Narlikar's core fields of interest are Real and Complex Analysis, Analytic Geometry, Number Theory, Algebra and Topology.

36. Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry

37. They focused on research in pure mathematics related to problems in analytic number theory and harmonic analysis.

38. In number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space.

39. The centre houses strong research teams in computational algebra and number theory, mathematical physics, and actuarial mathematics.

40. The first one (chronologically) is used in analytic number theory, and the other one in computational complexity theory.

41. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra.

42. In this way, Gauss arguably made a first foray towards both Évariste Galois's work and algebraic number theory.

43. Andrew James Granville (born 7 September 1962) is a British mathematician, working in the field of number theory.

44. In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers.

45. Bryna Kra works in ergodic theory and dynamical systems, particularly on problems motivated by combinatorics and number theory.

46. Public-key algorithms are most often based on the computational complexity of "hard" problems, often from number theory.

47. Samuel James Patterson (September 7, 1948 in Belfast) is a Northern Irish mathematician specializing in analytic number theory.

48. Martin Neil Huxley (born in 1944) is a British mathematician, working in the field of analytic number theory.

49. Solving Congruences, 3 introductory examples,Number Theory, Modular Arithmetic, blackpenredpen, math for fun, https://blackpenredpen.com/bprplive, https://tw

50. Another example, playing a key role in algebraic number theory, is the field Qp of p-adic numbers.

51. Pila has been the Editor of Proceedings of the Edinburgh Mathematical Society, and of Algebra and Number Theory.

52. Jean-Marc Deshouillers (born on September 12, 1946 in Paris) is a French mathematician, specializing in analytic number theory.

53. In 2000, Jean Bourgain connected the Kakeya problem to arithmetic combinatorics which involves harmonic analysis and additive number theory.

54. In recent years, he has been working mainly on C*-algebras that are related to structures from number theory.

55. Borho does research on representation theory, Lie algebras, ring theory and also on number theory (amicable numbers) and tilings.

56. Today, one of the most important branches of pure mathematics is algebraic number theory, which studies rational numbers (fractions).

57. Aside from his work in algebraic number theory he wrote a great number of Japanese textbooks on mathematics and geometry.

58. His research interests are Algebraic Geometry and Number Theory (in particular Diophantine Approximation and Transcendence Theory) and Hodge Theory (Periods).

59. Marc Krasner (1912 – 13 May 1985, in Paris) was a Russian-born French mathematician, who worked on algebraic number theory.

60. Working with Hasse, he dealt with algebraic number theory and produced a script of Hassen's lecture on class-field theory.

61. The fascinating story of cryptography requires us to understand two very old ideas related to number theory and probability theory.

62. These texts deal with solving algebraic equations, and have led, in number theory to the modern notion of Diophantine equation.

63. In algebraic number theory, the rings of algebraic integers are Dedekind rings, which constitute therefore an important class of Commutative rings.

64. So he sent a letter back to John saying, "It turns out you can generate these patterns using prime number theory."

65. In 2018, he was awarded the Fields Medal for his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory.

66. ‘Fermat preferred the Algebraic techniques that he used to such devastating effect in number theory.’ ‘His work in Algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.’ ‘This gave powerful results such as a purely Algebraic proof of the Riemann Roch theorem.’

67. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870.

68. As Murty's survey paper notes, Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory, representation theory, and algebraic geometry".

69. Tom Sanders is an English mathematician, working on problems in additive combinatorics at the interface of harmonic analysis and analytic number theory.

70. David Rodney "Roger" Heath-Brown FRS (born 12 October 1952), is a British mathematician working in the field of analytic number theory.

71. In addition, he published important results and elegant proofs of known results in almost all branches of classical algebra and number theory.

72. He read some of Joseph-Louis Lagrange's writings on the solution of numerical equations and Carl Friedrich Gauss's publications on number theory.

73. In 1966, with Vinogradov, he was a Plenary Speaker of the ICM in Moscow with talk Recent developments in analytic number theory.

74. Kronecker wrote his 1845 dissertation, at the University of Berlin, on number theory , giving special formulation to units in certain algebraic number fields .

75. He also makes major breakthroughs and discoveries in the areas of gamma functions, modular forms, divergent series, hypergeometric series and prime number theory.

76. Rosen is known for his textbooks, especially for the book with co-author Kenneth Ireland on number theory, which was inspired by ideas of André Weil; this book, A Classical Introduction to Modern Number Theory gives an introduction to zeta functions of algebraic curves, the Weil conjectures, and the arithmetic of elliptic curves.

77. Within the PROBCOMB (Sparse discrete structures) project, mathematicians found applications in areas ranging from extremal graph theory to additive and combinatorial number theory.

78. Susan Howson (born in 1973) is a former British mathematician whose research was in the fields of algebraic number theory and arithmetic geometry.

79. Godfrey Harold Hardy FRS (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis.

80. In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n-gonal numbers.