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.
Autoimmunity is probably the next frontier. The majority of cases of autoimmune disease result from a complex genetic problem that has environmental influences. It is a colossal task for the immune system to maintain tolerance to self and yet be ready to react to everything in the world around us.
Any important disease whose causality is murky, and for which treatment is ineffectual, tends to be awash in significance.
There's branches of science which I don't understand; for example, physics. It could be said, I suppose, that I have faith that physicists understand it better than I do.
What is mathematics? It is only a systematic effort of solving puzzles posed by nature.
What I want to do is demonstrate that biology can learn how to make a vast array of molecules that people thought were outside the realm of biology.
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