In mathematics, computer science, and related subjects, an algorithm is an effective method for solving a problem using a finite sequence of instructions. Algorithms are used for calculation, data processing, and many other fields.


3000BC-1000BC: Ancient mathematics
 - Babylonian, Egyptian, Chines, Mayan, Greek, Arabic, Indian
 - Algorithms for calculation
   - long multiplication, division
   - extracting square and cubic roots

300BC: Euclid
 - geometric constructions
 - axiomatic treatment of geometry
 - Euclidean algorithm (gcd)
  - gcd(x,0) = x
  - for x > y, gcd(x,y) = gcd(x-y,y)
  - running time is O(log max{x,y})

200BC: Eratosthenes
 - algorithm to find all primes < N

10-70: Hero of Alexandria
 - complicated gears and lever devices, steam driven

85-185: Ptolemaios (Ptolemy)
 - approximations of pi
 - 3.1415926535897932384626433832795028841971693993751058209749445923

780: al-Khowarizmi
 - The word algorism originally referred only to the rules of performing arithmetic using Arabic numerals but evolved via European Latin translation of al-Khwarizmi's name into algorithm by the 18th century. The word evolved to include all definite procedures for solving problems or performing tasks.
 - The word "algebra" comes from the title of one of his books

1643-1747: Newton 
 - Newton's Method of finding zeros of equations

1800: Gauss
 - Gaussian elimination
 - probably the greatest mathematician ever

1840: Charles Babbage and Ada Lovelace
 - 1841 First computer Babbage's difference engine
 - 1842 First computer program (algorithm), computed Bernoulli numbers
 - Programming language Ada named after her

1926: Otakar Boruvka's minimum spanning tree algorithm
 - O((m+n)log n) time algorithm

1931: Kurt Goedel's incompleteness theorem
 - Later proved the theoretical possibility of time-travel and teleportation
 - Friend of Einstein

1932: Alonzo Church
 - Undecideability of first-order logic 1932
 
1912-1954: Alan Turing
  - Student of Alonzo Church
  - Defined the Turing machine
  - Discovered non-computable functions, the halting problem
  - Instrumental if cracking the Enigma and the Lorenz 40/42 (Turing's Bombe)
  - Involved with the creation of the Mark I
  - His lover helped someone break in, he reported this to police,
    police arrested him
  - Committed suicide by half-eating a poison apple after being 
    "treated" for homosexuality
  - Rainbow Apple logo does is not a reference to Turing (but a nice story)
  - First digital programmable computer - Colossus
  - Contributions to war effort only made public in 1970
  - September 10, 2009 - official apology from British Prime Minister

1903-1957: John von Neumann 
  - described the von Neumann architecture - ENIAC
  - game theory - minimax theorem of 2-person zero sum games
  - inventor (in 1945) of the merge-sort algorithm
  - cellular automata - self-replicating automata
  - proposed the use of self-replication in interstellar large 
    scale-mining operations

1906-1992: Grace Hopper
  - 1944: first functional computer program for the Mark I
  - Instrumental in development of COBOL
  - First compiler
  - Coined the term bug & debugging (maybe)
  - Was strongly discouraged from computer programming
  - Promoted to rear-admiral

1947: George Dantzig
  - simplex method for linear programming

1951: Alston Householder
  - Decomposition approach to matrix problems (LU, LUP, etc)

1953: Hans Peter Luhn
  - Described hashing with chaining in an IBM technical memo

1953: Richard Bellman
  - Dynamic programming

1959: Dijkstra's
  - Dijkstra's shortest path algorithm (also, Moore 1957)

1960: Kolmogorov complexity
  - Measuring the randomness of a string in terms of the length 
    of the shortest algorithm that generates it

1960: A. H. Land and A. G. Doig in 1960
  - Branch-and-bound for integer linear programming

1962: C. A. R. Hoare
  - Quicksort

1965 James Cooley and John Tukey 
  - The Fast Fourier transform algorithm

1971: Stephen Cook and Leonid Levin
  - Cook-Levin Theorem: there exists NP-complete problems
  - Limits on what computers can do efficiently

1972: Richard Karp
  - 21 NP-Complete problems.

1973: Donald Knuth
  - Published The Art of Computer Programming
  - Fundamental rigorous theoretical study of algorithms

1974: Hopcroft and Tarjan
  - O(n) time planarity testing algorithm
    "This paper describes an efficient algorithm to determine whether an
    arbitrary graph G can be embedded in the plane. The algorithm may
    be viewed as an iterative version of a method originally proposed
    by Auslander and Parter and correctly formulated by Goldstein. The
    algorithm uses depth-first search and has O(V) time and space bounds,
    where V is the number of vertices in G. An ALGOL implementation of
    the algorithm successfully tested graphs with as many as 900 vertices
    in less than 12 seconds."

1976: Michael Rabin
   - O(n) time closest pair algorithm 
   - First ever randomized algorithm!
   - sample sqrt(n) points
   - compute closest-pair among sample points (d)
   - use a d*d grid to find closest pair among all points

1977: Ferguson and Forcade
   - integer relation detection algorithm
   - generalization of gcd to real numbers

1978: Ron Rivest, Adi Shamir, and Leonard Adleman
  - Workable public key crytography

1979: Michael Garey and David Johnson
  - Book: Computers and Intractability
    A Guide to the theory of NP-completeness

1980: Gary Miller and Michael Rabin
  - Randomized primality testing algorithm

1985: Daniel Sleator and Robert Tarjan
  - Amortized analysis 

1987 Michael Rabin and Richard Karp
  - Karp-Rabin string matching algorithm

  
2000: Craig Ventner
  - Shotgun sequencing algorithm for the human genome project

2000: Larry Page, Sergey Brin
  - Pagerank
  - Search algorithms
  - Adsense