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History of Mathematics

Key developments, mathematicians, and ideas throughout mathematical history

M
mathesis_mx 23 terms May 5, 2025
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Terms 23

1
Babylonian Mathematics
Base-60 number system; solving quadratic equations; Pythagorean triples; ~2000 BCE
2
Euclid's Elements
~300 BCE; axiomatic geometry; 13 books; foundation of mathematics for 2000 years
3
Axiomatic Method
Starting from self-evident axioms and deriving theorems by logical deduction; Euclid's approach
4
Eratosthenes
~240 BCE; calculated Earth's circumference; Sieve of Eratosthenes for primes
5
Archimedes
~250 BCE; method of exhaustion (proto-calculus); pi estimate; lever and buoyancy
6
Brahmagupta
628 CE; Indian mathematician; rules for zero and negative numbers; Brahmagupta's theorem
7
Al-Khwarizmi
9th century; father of algebra; 'Kitab al-mukhtasar fi hisab al-jabr' → 'algebra'
8
Fibonacci
1202 CE; Liber Abaci introduced Hindu-Arabic numerals to Europe; Fibonacci sequence
9
René Descartes
1637; Cartesian coordinate system; united algebra and geometry; analytic geometry
10
Newton and Leibniz
1660s–70s; independently invented calculus; priority dispute; different notation systems
11
Euler
18th century; prolific mathematician; e^(iπ)+1=0; graph theory; notation f(x), e, i, Σ
12
Gauss
'Prince of Mathematics'; number theory, differential geometry, statistics, electromagnetism
13
Non-Euclidean Geometry
Lobachevsky, Bolyai, Riemann (1820s–1850s); parallel postulate not necessary; curved spaces
14
Cantor's Set Theory
1870s; infinite sets; different sizes of infinity; aleph numbers; controversial in his time
15
Cantor's Diagonalization
Proves real numbers uncountable; no bijection with naturals; revolutionary
16
Hilbert's Program
Formalize all mathematics; complete and consistent axiom system; Gödel proved impossible
17
Gödel's Incompleteness Theorems
1931: any sufficiently powerful formal system contains true but unprovable statements; not completable
18
Church-Turing Thesis
Any effectively computable function is Turing-computable; formalizes notion of algorithm
19
Halting Problem
Turing 1936: no algorithm can determine if arbitrary program halts; undecidable
20
Riemann Hypothesis
Nontrivial zeros of zeta function on critical line Re(s)=½; unproven; Millennium Problem
21
Fermat's Last Theorem
x^n + y^n = z^n has no integer solutions for n>2; stated 1637; proved by Wiles 1995
22
Four Color Theorem
Any planar map needs at most 4 colors; proved 1976 with computer assistance; first major computer proof
23
Poincaré Conjecture
Every simply connected 3-manifold is homeomorphic to 3-sphere; proved by Perelman 2003