A great deal of my work is just playing with equations and seeing what they give.
Interpretation
The exploration of equations can lead to significant discoveries in science.
Paul Dirac expresses the importance of experimentation and play in scientific work. He suggests that engaging with mathematical equations, even in a playful manner, can yield unexpected and valuable insights, highlighting how creativity and curiosity are essential in the pursuit of knowledge.
In practice
In a lecture on scientific methodology, you might say, 'As Paul Dirac wisely noted, much of scientific discovery comes from just playing with equations.'
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.
When the wrong question is being asked, it usually turns out to be because the right question is too difficult. Scientists ask questions they can answer. That is, it is often the case that the operations of a science are not a consequence of the problematic of that science, but that the problematic is induced by the available means.
I could never have gone far in any science because on the path of every science the lion Mathematics lies in wait for you.
I enjoy science, and I'm a very curious person. I always want to know the reason behind everything, big or small.
The sheer quantity of brain power that hurled itself voluntarily and quixotically into the search for new baseball knowledge was either exhilarating or depressing, depending on how you felt about baseball. The same intellectual resources might have cured the common cold, or put a man on Pluto.
In space there are countless constellations, suns and planets; we see only the suns because they give light; the planets remain invisible, for they are small and dark. There are also numberless earths circling around their suns.
As someone who flew two space capsules and twice landed in the ocean, I can attest from personal experience how much logistics work is needed to get you home.
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