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.
Interpretation
Understanding physical laws is essential, but their complexity often makes direct application difficult.
This quote by Paul Dirac emphasizes that while the fundamental laws governing physics and chemistry are well-established, the challenge lies in the application of these laws to complex systems. Dirac advocates for the development of approximate methods in quantum mechanics, which would enable scientists to simplify and understand intricate atomic behaviors without the burden of excessive calculations, thus bridging the gap between theory and practical application.
In practice
This quote can be used in a scientific presentation to highlight the challenges faced in applying complex 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.
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.
There is in my opinion a great similarity between the problems provided by the mysterious behavior of the atom and those provided by the present economic paradoxes confronting the world.
Mathematics is the language with which God has written the universe.
If we could look through the skull into the brain of a consciously thinking person, and if the place of optimal excitability were luminous, then we should see playing over the cerebral surface, a bright spot with fantastic, waving borders constantly fluctuating in size and form, surrounded by a darkness more or less deep, covering the rest of the hemisphere.
Science has always been my preoccupation and when you think a breakthrough is possible, it is terribly exciting.
In future, children won't perceive the stars as mere twinkling points of light: they'll learn that each is a 'Sun', orbited by planets fully as interesting as those in our Solar system.
We should've asked China to be a portion of the space station. We should've worked out ways that we can... just give away the technology that we have that puts things up into space, with cooperation up above the atmosphere that's needed to help each other.
To stop short in any research that bids fair to widen the gates of knowledge, to recoil from fear of difficulty or adverse criticism, is to bring reproach on science. There is nothing for the investigator to do but go straight on, 'to explore up and down, inch by inch, with the taper his reason;' to follow the light wherever it may lead, even should it at times resemble a will-o'-the-wisp.
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