Number theory · Group theory · Cryptography
Babylonian scribes compiled Plimpton 322, a table of Pythagorean triples demonstrating sophisticated understanding of number-theoretic relationships in a base-60 system. · Wikipedia: https://en.wikipedia.org/wiki/Plimpton_322
Ancient Egyptian scribe Ahmes copied the Rhind papyrus, containing arithmetic, algebraic problems, and fraction methods used in Egyptian mathematics. · Wikipedia: https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus
This foundational Chinese mathematical text compiled methods for solving linear equations, computing areas, and arithmetic with negative numbers, influencing East Asian mathematics for centuries. #ancient #science
Mathematician Liu Hui completed his commentary on the Nine Chapters, providing rigorous proofs and calculating π ≈ 3.1416 using polygonal approximation methods. Source — Wikipedia:
Indian mathematician Aryabhata composed the Aryabhatiya, covering arithmetic, algebra, and trigonometry, including methods for solving quadratic equations and computing π. Source — Wikipedia:
Brahmagupta's Brahmasphutasiddhanta introduced rules for arithmetic with zero and negative numbers, and methods for solving quadratic equations, foundational to algebra. Source — Wikipedia:
Al-Khwarizmi wrote Al-Jabr, systematically solving linear and quadratic equations, giving algebra its name and introducing the word 'algorithm' into European mathematics. Source — Wikipedia:
Persian polymath Omar Khayyam classified cubic equations and provided geometric solutions using intersections of conic sections, advancing algebraic technique. Source — Wikipedia:
Bhaskara II wrote the Lilavati and Bijaganita, covering arithmetic and algebra including solutions to indeterminate equations and early forms of the Pell equation. Source — Wikipedia:
Chinese mathematician Qin Jiushao published Shushu Jiuzhang, containing the earliest known method for solving simultaneous congruences, now called the Chinese Remainder Theorem. Source — Wikipedia:
Chinese mathematician Yang Hui documented the binomial coefficient triangle (Pascal's triangle) in his mathematical works, predating Pascal's publication by nearly 400 years. Source — Wikipedia:
Madhava of the Kerala school discovered infinite series expansions for π and trigonometric functions, predating Newton and Leibniz by over three centuries. Source — Wikipedia:
Italian mathematician Gerolamo Cardano published Ars Magna, presenting general solutions to cubic and quartic equations, marking a major advance in European algebra. Source — Wikipedia: )
Joseph-Louis Lagrange published Réflexions sur la résolution algébrique des équations, analyzing permutations of roots and laying groundwork for group theory. Source — Wikipedia:
Carl Friedrich Gauss published Disquisitiones Arithmeticae, systematizing number theory and introducing modular arithmetic, foundational to modern algebra and cryptography. Source — Wikipedia:
Évariste Galois developed the theory of groups to characterize solvability of polynomial equations, founding Galois theory and modern abstract algebra before his death at 20. Source — Wikipedia:
Arthur Cayley published 'On the theory of groups,' giving the first abstract definition of a finite group, independent of any specific permutation context. Source — Wikipedia:
Leopold Kronecker gave an abstract definition of fields and rings, helping shift algebra from operations on numbers to the study of abstract algebraic structures. Source — Wikipedia:
Emmy Noether published 'Idealtheorie in Ringbereichen,' establishing the abstract theory of ideals in commutative rings, foundational to modern algebraic structures. · Wikipedia: https://en.wikipedia.org/wiki/Emmy_Noether
Kurt Gödel published his incompleteness theorems, proving that any consistent formal system containing arithmetic has undecidable statements, profoundly impacting number theory and logic. · Wikipedia: https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems
Whitfield Diffie and Martin Hellman published the first practical public-key cryptosystem, using the discrete logarithm problem in finite cyclic groups. · Wikipedia: https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange
Ron Rivest, Adi Shamir, and Leonard Adleman published the RSA cryptosystem, whose security relies on the difficulty of factoring large integers, linking number theory to cryptography. · Wikipedia: https://en.wikipedia.org/wiki/RSA_(cryptosystem)
Neal Koblitz and Victor Miller independently proposed elliptic curve cryptography, using the group structure of elliptic curves over finite fields for cryptographic applications. · Wikipedia: https://en.wikipedia.org/wiki/Elliptic-curve_cryptography
Peter Shor published a quantum algorithm for integer factorization, demonstrating that sufficiently powerful quantum computers could break RSA and reshaping cryptographic research. · Wikipedia: https://en.wikipedia.org/wiki/Shor's_algorithm
NIST launched a process to standardize post-quantum cryptographic algorithms resistant to quantum attacks, evaluating lattice-based and other algebraic-structure-based schemes. · Wikipedia: https://en.wikipedia.org/wiki/Post-quantum_cryptography