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.
If African farmers can use improved seeds and better practices to grow more crops and get them to market, then millions of families can earn themselves a better living and a better life.
The fact that you can remember yesterday but not tomorrow is because of entropy. The fact that you're always born young and then you grow older, and not the other way around like Benjamin Button - it's all because of entropy. So I think that entropy is underappreciated as something that has a crucial role in how we go through life.
I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.
Only 20 percent of our longevity is genetically determined. The rest is what we do, how we live our lives and increasingly the molecules that we take. It's not the loss of our DNA that causes aging, it's the problems in reading the information, the epigenetic noise.
Life ... is a relationship between molecules.
Politicians, real-estate agents, used-car salesmen, and advertising copy-writers are expected to stretch facts in self-serving directions, but scientists who falsify their results are regarded by their peers as committing an inexcusable crime. Yet the sad fact is that the history of science swarms with cases of outright fakery and instances of scientists who unconsciously distorted their work by seeing it through lenses of passionately held beliefs.
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