God used beautiful mathematics in creating the world.
Interpretation
Mathematics is fundamental to the structure and beauty of the universe.
In this quote, Paul Dirac emphasizes the idea that the universe is inherently mathematical and that the laws of nature can be expressed through mathematical principles. It suggests that the beauty of the world around us is not just aesthetic but deeply rooted in mathematical relationships, reflecting the harmony between science and art in the natural world.
In practice
In a lecture about the relationship between science and art, one might quote Dirac to illustrate the elegance of mathematical principles in understanding nature.
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.
Spacewalking trumps everything. Viscerally, it is a phenomenal place to be; to be able to glance right and see the world, glance left and see the universe, and realise for a moment that you're holding on to your known existence with one hand. That's the thing.
Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.
Ideas which have been developed simultaneously or in immediate succession in the same mind mutually reproduce each other, and do this with greater ease in the direction of the original succession and with a certainty proportional to the frequency with which they were together
Our minds work in real time, which begins at the Big Bang and will end, if there is a Big Crunch - which seems unlikely, now, from the latest data showing accelerating expansion. Consciousness would come to an end at a singularity.
The real achievement in discoveries... is seeing an analogy where no one saw one before... The essence of discovery is that unlikely marriage of cabbages and kings β of previously unrelated frames of reference or universes of discourse β whose union will solve the previously insoluble problem.
Evolution works by selection, not by instruction. There is no final cause, no teleology, no purpose guiding the overall process
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