“Formal proofs, where there is deliberately no meaning, can convince only formalists, and of the results they themselves seem to deny any meaning. Is that to be the mathematics we are to use to understand the world we live in?”

— Richard Hamming

Source: Mathematics on a Distant Planet (1998), p. 645

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Richard Hamming 90

American mathematician and information theorist 1915–1998

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“The formalists neglected the content altogether and made mathematics meaningless, the logicians neglected the form and made mathematics consist of any true generalizations; only by taking account of both sides and regarding it as composed of tautologous generalizations can we obtain an adequate theory.”

Frank P. Ramsey (1903–1930) British mathematician, philosopher

The Foundations of Mathematics (1925)

“There are so many clues and feelings in the world that it makes a mystery and a mystery means there's a puzzle to be solved. Once you think like that you're hooked on probably finding a meaning, and there' many avenues in life where we're given little indications that the mystery can one day be solved. we get little proofs, — not the big proof — but the little proofs that keep us searching.”

David Lynch (1946) American filmmaker, television director, visual artist, musician and occasional actor

McKenna interview (1992)

“The theory of the nature of mathematics is extremely reactionary. We do not subscribe to the fairly recent notion that mathematics is an abstract language based, say, on set theory. In many ways, it is unfortunate that philosophers and mathematicians like Russell and Hilbert were able to tell such a convincing story about the meaning-free formalism of mathematics. In Greek, mathematics simply meant learning, and we have adapted this... to define the term as "learing to decide."”

C. West Churchman (1913–2004) American philosopher and systems scientist

Mathematics is a way of preparing for decisions through thinking. Sets and classes provide one way to subdivide a problem for decision preparation; a set derives its meaning from decision making, and not vice versa.

C. West Churchman, Leonard Auerbach, Simcha Sadan, Thinking for Decisions: Deductive Quantitative Methods (1975) Preface.
1960s - 1970s

“We live in a world where there is more and more information, and less and less meaning.”

Jean Baudrillard book Simulacra and Simulation

Source: Simulacra and Simulation

“Reality contains not only evidence, but also the means (such as our minds, and our artefacts) of understanding it. There are mathematical symbols in physical reality. The fact that it is we who put them there does not make them any less physical.”

David Deutsch book The Fabric of Reality

Source: The Fabric of Reality (1997), Ch.3

“However, in all honesty, I must say that one must essentially forget that all proofs are transcribed in this formal language. In order to think productively, one must use all the intuitive and informal methods of reasoning at one's disposal. At the very end one must check that no errors have been committed; but in practice set theory is treated as any other branch of mathematics. The reason that we can do this is that we will never speak about proofs but only about models.”

Paul Cohen (1934–2007) American mathematician

p. 1078 of "The discovery of forcing." http://www.logic.univie.ac.at/~ykhomski/ST2013/The%20Discovery%20of%20Forcing.pdf Rocky Mountain Journal of Mathematics 32, no. 4 (2002): 1071–1100.

“Experts can explain anything in the objective world to us, yet we understand our own lives less and less. In short, we live in the postmodern world, where everything is possible and almost nothing is certain.”

Václav Havel (1936–2011) playwright, essayist, poet, dissident and 1st President of the Czech Republic

The Need for Transcendence in the Postmodern World (1994)
Context: There appear to be no integrating forces, no unified meaning, no true inner understanding of phenomena in our experience of the world. Experts can explain anything in the objective world to us, yet we understand our own lives less and less. In short, we live in the postmodern world, where everything is possible and almost nothing is certain.

“We live in a world where people don't all have the same scruples, where all blows can be given, and where, in order to down somebody, all means can be used. Nothing will lead me astray from the path that I have chosen.”

Nicolas Sarkozy (1955) 23rd President of the French Republic

Le Monde, 2005

“Suggesting evil is human doesn't mean we can always understand it, or doesn't mean there's only one way of understanding it. It's sort of like a great work of art. You can never fully absorb it. It's got many dimensions. It lives on through time, in different ways.”

Kanan Makiya (1949) American orientalist

"Faith and Doubt at Ground Zero" http://www.pbs.org/wgbh/pages/frontline/shows/faith/interviews/makiya.html, PBS Frontline (2002)

“Formal proofs, where there is deliberately no meaning, can convince only formalists, and of the results they themselves seem to deny any meaning. Is that to be the mathematics we are to use to understand the world we live in?”

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