I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.
Interpretation
Dirac emphasizes the importance of mathematics in understanding physical theories over relying solely on physical concepts.
In this quote, Paul Dirac expresses his belief that the foundation of theoretical physics should be rooted in mathematics rather than purely physical ideas. He argues that even if a mathematical framework seems initially disconnected from physical phenomena, it has the potential to lead to deeper insights and advancements in understanding the universe. This reflects the critical role innovative mathematical concepts play in the development of scientific theories.
In practice
During a lecture on theoretical physics, one might use this quote to emphasize the importance of mathematical foundations in developing scientific theories.
The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence.
The methods of theoretical physics should be applicable to all those branches of thought in which the essential features are expressible with numbers.
One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.
The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.
It is quite clear that beauty does depend on one's culture and upbringing for certain kinds of beauty, pictures, literature, poetry and so on...But mathematical beauty is of a rather different kind. I should say perhaps it is of a completely different kind and transcends these personal factors. It is the same in all countries and at all periods of time.
It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.
In science, 'fact' can only mean 'confirmed to such a degree that it would be perverse to withhold provisional assent.' I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms.
The real accomplishment of modern science and technology consists in taking ordinary men, informing them narrowly and deeply and then, through appropriate organization, arranging to have their knowledge combined with that of other specialized but equally ordinary men. This dispenses with the need for genius. The resulting performance, though less inspiring, is far more predictable.
In the midst of all dwells the Sun. For who could set this luminary in another or better place in this most glorious temple, than whence he can at one and the same time brighten the whole.
Every mode of transport that we use - whether it's planes, trains, automobiles, bikes, horses - is reusable, but not rockets. So we must solve this problem in order to become a space-faring civilization.
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
People think if you have deciphered the genome of humans that you can change everything. But you cannot change everything, because you do not know what the genes mean, and you have no methods for changing them, and you can't do experiments with humans like you can with animals.
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