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1970

Alan Baker is awarded a Fields Medal for his work on Diophantine equations.

1970

Matiyasevich shows that "Hilbert's tenth problem" is unsolvable, namely that there is no general method for determining when polynomial equations have a solution in whole numbers.

1971

Stephen Cook formulates the *P* versus *NP* problem regarding polynomial time algorithms.

1972

Thom publishes *Structural Stability and Morphogenesis* which explains catastrophe theory. The theory examines situations in which gradually changing forces lead to so-called catastrophes, or abrupt changes, and has important applications in biology and optics.

1972

Quillen formulates higher algebraic *K*-theory, a new tool that uses geometric and topological methods and ideas to formulate and solve major problems in algebra, particularly ring theory and module theory.

1973

Deligne proves the three "Weil conjectures".

1973

Chen Jingrun shows that every sufficiently large even integer is the sum of a prime and a number with at most two prime factors. It makes a major contribution to the Goldbach Conjecture.

1974

Mumford is awarded a Fields Medal for his work on algebraic varieties.

1975

Feigenbaum discovers a new constant, approximately 4.669201609102..., which is related to period-doubling bifurcations and plays an important part in chaos theory.

1975

Mandelbrot publishes *Les objets fractals, forme, hasard et dimension* which describes the theory of fractals.

1976

Lakatos work *Proofs and Refutations* is published as a book two years after his death. First published in four parts in 1963-64 the work gives Lakatos's account of how mathematics develops.

1976

Thurston is awarded the Oswald Veblen Geometry Prize of the American Mathematical Society for his work on foliations.

1976

Appel and Haken show that the Four Colour Conjecture is true using 1200 hours of computer time to examine around 1500 configurations. (See this History Topic.)

1977

Adleman, Rivest, and Shamir introduce public-key codes, a system for passing secret messages using large primes and a key which can be published.

1978

Fefferman is awarded a Fields Medal for his work on partial differential equations, Fourier analysis, in particular convergence, multipliers, divergence, singular integrals and "Hardy spaces".

1978

Mori proves the "Hartshorne conjecture", that projective spaces are the only smooth complete algebraic varieties with ample tangent bundles.

1979

Connes publishes work on non-commutative integration theory.

1980

The classification of finite simple groups is complete.

List of mathematicians alive in 1970.

List of mathematicians alive in 1980.

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