Loading in 5 sec....

A Brief History of the Computability ProblemPowerPoint Presentation

A Brief History of the Computability Problem

- 68 Views
- Updated On :

A Brief History of the Computability Problem. Gottfried Wilhelm Leibniz (1646 - 1716). Leibniz's computer. Georg Cantor (1845 - 1918). 1886. 1900. David Hilbert (1862 - 1943). 1886. 1900. David Hilbert (1862 - 1943). Hilbert's List (1900). Foundations (general)

Related searches for A Brief History of the Computability Problem

Download Presentation
## PowerPoint Slideshow about 'A Brief History of the Computability Problem' - jeroen

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Computability Problem

- Foundations (general)
- cardinal number of the continuum
- compatibility of arithmetic axioms

- Foundations (specific areas)
- tetrahedra with equal bases and altitudes (geometry)
- straight line as shortest distance between points (alternative geometries)
- Lie group without differentiability (analysis)
- axiomatization of Physics

- Number theory
- irrationality and transcendence of certain numbers
- prime numbers
- most general law of reciprocity in number field
- algorithm for solvability of a diophantine equation
- quadratic form with algebraic coefficients
- extend Kronecker's Abelian field result to algebraic realms

- Algebra and Geometry
- .....

- Analysis
- .....

Jacques Herbrand (1908 - 1931)

Alonzo Church (1903 - 1995)

Emil Post (1897 - 1954)

Emil Post (1897 - 1954)

Emil Post (1897 - 1954)

Martin Davis (1928 - ), Julia Robinson (1919 - 1985),

Yuri Matiyasevich (1947 - )

e.g., perfect squares are diophantine

Davis Normal Form (1949): each r.e. set admits definition in terms of a

Diophantine equation

What set associated with this family of equations?

Davis "daring" conjecture (1953):

The recursively enumerable sets are precisely the diophantine sets.

Clay Mathematics Institute: 7 prize problems ($1 million each)

P = NP ?

Riemann hypothesis

Poincare conjecture: 3-sphere simply connected?

- Landau's problems (1912):
- Goldbach conjecture integer > 4 is sum of three primes even integer > 3 is sum of two primes
- Twin prime conjecture
- A prime between every pair of adjacent squares?

- Smale's list (2000):
- Goldbach conjecture
- Riemann hypothesis
- Poincare conjecture
- Twin prime conjecture
- P = NP ?
- Theoretical limits of intelligence, human and artificial
- .....

- References:
- The Honors Class: Hilbert's Problems and Their Solvers by Benjamin Yandell (2002)
- The Unknowable by Gregory Chaitin (1999)
- Conversations with a Mathematician by Gregory Chaitin (1999)
- The Universal Computer: The Road from Leibniz to Turing by Martin Davis (2000)

Download Presentation

Connecting to Server..