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Paul Cohen Quotes

1934–2007 United States

Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician and logician, best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was awarded a Fields Medal.

United States
Academics
Logicians
Mathematicians

Random Paul Cohen quote

4 quotes

The object of mathematics is to discover "true" theorems. We shall use the term "valid" to describe statements formed according to certain rules and then shall discuss how this notion compares with the intuitive idea of "true".

Set Theory and the Continuum Hypothesis (1966)

To the average mathematician who merely wants to know that his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency.

In the Realist philosophy, one wholeheartedly accepts traditional mathematics at face value. All questions such as the Continuum Hypothesis are either true or false in the real world despite their independence from the various axiom systems. The Realist position is probably the one that most mathematicians would prefer to take.

A recurring concern has been whether set theory, which speaks of infinite sets, refers to an existing reality, and if so how does one ‘know’ which axioms to accept. It is here that the greatest disparity of opinion exists (and the greatest possibility of using different consistent axiom systems).

Attribution

Quotes and notes from Wikiquote: Paul Cohen (page history), available under CC BY-SA 4.0.