Formalism Quotes (5 quotes)

If physics leads us today to a world view which is essentially mystical, it returns, in a way, to its beginning, 2,500 years ago. ... This time, however, it is not only based on intuition, but also on experiments of great precision and sophistication, and on a rigorous and consistent mathematical formalism.

On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.

That ability to impart knowledge
what does it consist of?
a deep belief in the interest and importance of the thing taught, a concern about it amounting to a sort of passion. A man who knows a subject thoroughly, a man so soaked in it that he eats it, sleeps it and dreams itthis man can always teach it with success, no matter how little he knows of technical pedagogy. That is because there is enthusiasm in him, and because enthusiasm is almost as contagious as fear or the barbers itch. An enthusiast is willing to go to any trouble to impart the glad news bubbling within him. He thinks that it is important and valuable for to know; given the slightest glow of interest in a pupil to start with, he will fan that glow to a flame. No hollow formalism cripples him and slows him down. He drags his best pupils along as fast as they can go, and he is so full of the thing that he never tires of expounding its elements to the dullest.

This passion, so unordered and yet so potent, explains the capacity for teaching that one frequently observes in scientific men of high attainments in their specialtiesfor example, Huxley, Ostwald, Karl Ludwig, Virchow, Billroth, Jowett, William G. Sumner, Halsted and Oslermen who knew nothing whatever about the so-called science of pedagogy, and would have derided its alleged principles if they had heard them stated.

This passion, so unordered and yet so potent, explains the capacity for teaching that one frequently observes in scientific men of high attainments in their specialtiesfor example, Huxley, Ostwald, Karl Ludwig, Virchow, Billroth, Jowett, William G. Sumner, Halsted and Oslermen who knew nothing whatever about the so-called science of pedagogy, and would have derided its alleged principles if they had heard them stated.

The computational formalism of mathematics is a thought process that is externalised to such a degree that for a time it becomes alien and is turned into a technological process. A mathematical concept is formed when this thought process, temporarily removed from its human vessel, is transplanted back into a human mold. To think ... means to calculate with critical awareness.

To the average mathematician who merely wants to know 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 ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.