Monday January 7, 2002 2:20 p.m

MAA Session on History of Mathematics in the Second Millennium, III

.

Martin E Flashman

flashman@humboldt.edu

Department of Mathematics,

Humboldt State University,

Arcata, CA 955521

The Continuum Hypothesis:

A Look at the History of the Real Numbers in The Second
Millennium.

After Cantor first demonstrated that the real numbers
(continuum) were uncountable, the hypothesis arose that the set of the
real numbers was "the smallest" uncountable set. In 1900 David Hilbert
made settling the continuum hypothesis the first problem on his now famous
list of problems for this century. The author will discuss some of the
historical, philosophical, and mathematical developments connected
to this problem proceeding from issues of definition of the real numbers
and proofs of uncountability to issues of consistency and models and proofs
of the independence of this hypothesis and possibly some comments on its
current status. (Received September 14, 2001)

Outline of possible
Discussion (depending on time allowed).

I. "Greek" Views
- Control early Second Millenium.

II. Pre-Calculus and Early Calculus Views

III. The Age of Development
and Conventions

Euler:1707-1783

Bolzano 1781- 1848
(1817 paper)

Cauchy:1789-1857

Dirichlet: 1805-1859

IV. The Age of Critical
Awareness and Foundations

Weierstrass: 1815-
1897

Dedekind: 1831-1916

Frege: 1848-1925

Peano: 1858-1932

V. Cantor 1845-1918: Investigation of discontinuities with Fourier series and Set Theory Beginnings.

VI. The XXth Century:
An Age of Exploration and Discovery.

Hilbert: (1862-1943)

Brouwer: (1881-1966)

Godel: (1906-1978)

Cohen: (1934- )

Dana Scott/ Solovay

VII.? The XXIst Century: The Hypothesis is False?