“The idea that theorems follow from the postulates does not correspond to simple observation.”

— Richard Hamming

The Unreasonable Effectiveness of Mathematics (1980)
Context: The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.

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Richard Hamming 90

American mathematician and information theorist 1915–1998

Richard Stone (1913–1991) British economist, Nobel Memorial Prize winner

Source: The Role of Measurement in Economics. 1951, p. 12

“The good is the everlasting, the pinnacle of our life. … life is striving towards the good, toward God. The good is the most basic idea … an idea not definable by reason … yet is the postulate from which all else follows.”

Leo Tolstoy (1828–1910) Russian writer

What is Art? (1897)
Context: The good is the everlasting, the pinnacle of our life. … life is striving towards the good, toward God. The good is the most basic idea … an idea not definable by reason … yet is the postulate from which all else follows. But the beautiful … is just that which is pleasing. The idea of beauty is not an alignment to the good, but is its opposite, because for most part, the good aids in our victory over our predilections, while beauty is the motive of our predilections. The more we succumb to beauty, the further we are displaced from the good.... the usual response is that there exists a moral and spiritual beauty … we mean simply the good. Spiritual beauty or the good, generally not only does not coincide with the typical meaning of beauty, it is its opposite.

“H. A. Lorentz has found out the Relativity theorem and has created the Relativity postulate as a hypothesis that electrons and matter suffer contractions in consequence of their motion according to a certain law. A. Einstein has brought out the point very clearly, that this postulate is not an artificial hypothesis but is rather a new way of comprehending the time-concept, which is forced upon us by observation of natural phenomena.”

Hermann Minkowski The Fundamental Equations for Electromagnetic Processes in Moving Bodies

The Fundamental Equations for Electromagnetic Processes in Moving Bodies (1907)

“Galaxies are observed to be simple systems following laws that result from scale-invariant dynamics which do not emanate from the haphazard merging history of halos of exotic dark matter.”

Pavel Kroupa (1963) Australian astrophysicist

Do astronomical data contradict the existence of dynamically relevant cold or dark matter? (seminar talk at Columbia U. Astronomy Department), Pavel Kroupa, 16 Oct. 2014 http://www.astro.columbia.edu/event?eid=185,

“The goys have proven the following theorem…”

John Von Neumann (1903–1957) Hungarian-American mathematician and polymath

Statement at the start of a classroom lecture, as quoted in 1,911 Best Things Anyone Ever Said (1988) by Robert Byrne.

“How close men, despite all their knowledge, usually live to madness? What is truth but to live for an idea? When all is said and done, everything is based on a postulate; but not until it no longer stands on the outside, not until one lives in it, does it cease to be a postulate. (Dialectic - Dispute)”

Sören Kierkegaard (1813–1855) Danish philosopher and theologian, founder of Existentialism

Journals of Søren Kierkegaard 1A75, 1835
1830s, The Journals of Søren Kierkegaard, 1830s

“Seeing therefore they are both [heat and pain] immediately perceived at the same time, and the fire affects you only with one simple, or uncompounded idea, it follows that this same simple idea is both the intense heat immediately perceived, and the pain; and consequently, that the intense heat immediately perceived, is nothing distinct from a particular sort of pain.”

George Berkeley book Three Dialogues between Hylas and Philonous

Philonous to Hylas.
Three Dialogues between Hylas and Philonous (1713)

“A simple calculation shows that from the classical theory follows that we should find a broadening of the beam with the maximum intensity on the place of the beam without field. However, from the quantum theory follows that we should find there no intensity at all, and deflected molecules on both sides. The beam should split up in two beams corresponding to the two orientations of the magnet. The experiment decided in favor of the quantum theory.”

Otto Stern (1888–1969) German physicist

the conclusion of the historical Stern-Gerlach experiment, in The Method of Molecular Rays http://nobelprize.org/nobel_prizes/physics/laureates/1943/stern-lecture.html, Nobel Lecture, December 12, 1946.

“Knowledge of God is obedience to God. Observe that we do not say that knowledge of God may also be obedience, or that of necessity it has obedience attached to it, or that it is followed by obedience. No; knowledge of God as knowledge of faith is in itself and of essential necessity obedience. It is an act of human decision corresponding to the act of divine decision; corresponding to the act of the divine being as the living Lord; corresponding to the act of grace in which faith is grounded and continually grounded again in God. In this act God posits Himself as our object and ourselves as those who know Him. But the fact that He does so means that our knowing God can consist only in our following this act, in ourselves becoming a correspondence of this act, in ourselves and our whole existence and therefore our considering and conceiving becoming the human act corresponding to the divine act. This is obedience, the obedience of faith.”

Karl Barth book Church Dogmatics

2:1
Church Dogmatics (1932–1968)

“On the account (or for the reason that, or… from the fact that… "Du fait que", Fr.) that one person advocate and want something, it does not follow that others have to want it too; only the postulates of reason and certitude are identicals, invariables, and can always be of use to everyone as a fulcrum ("point d'appui", Fr.) with a view to a free agreement”

African Spir (1837–1890) Russian philosopher

"entente libre", Fr
Source: Words of a Sage : Selected thoughts of African Spir (1937), p. 42.

“The idea that theorems follow from the postulates does not correspond to simple observation.”

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Richard Hamming 90

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