Pure mathematicians do not think about the equations of physics in the same way as a physicist does. They are concerned only with the structure of the equations and the formal rules for manipulating them. But physicists regard the equations as representations of real things or processes; they are only partial representations of the physicists’ knowledge, so to improve a representation they may alter the equations in ways that violate mathematical rules. Both Einstein and Heisenberg were masters at this. Neither was a mathematical virtuoso. Indeed, in the period when Einstein was developing his general relativity theory, the mathematician Hilbert expressed the opinion that Einstein was mathematically naive. I have heard a similar opinion about Heisenberg expressed by one of his students in later years. Mathematics played an essential role in Einstein’s thinking, but, as mathematical physics goes, the mathematics in all his great papers is comparatively simple. His forte was in analyzing the physical meaning of the mathematics. Indeed, such analysis is generally characteristic of the best work in theoretical physics. I have heard the Nobel laureate Richard Feynman, himself a true mathematical virtuoso, express this opinion forcefully, asserting that the value of a paper on theoretical physics is inversely proportional to the density of mathematics in it.
From the paper, the four prominent characteristics of Einstein’s thinking are:
- Skepticism and objectivity
- Search for general principles
- Symmetry arguments
- Gedanken experiments
According to the paper, the characteristics of Einstein’s thinking involve cognitive skills that develop only with concentrated practice. Is it wrong then, to dismiss the creative process in science as nothing more than glorified problem solving?
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