Mathematics and Physics
Until the end of the nineteenth century, the people who studied mathematics and those who studied physics would probably not have separated themselves out professionally. Both would have called themselves "natural philosophers," and many of them did research work in both fields. The Greeks who did much original work in geometry also formulated many theorems about the physical world around them, most memorably in Archimedes' bathtub revelation about the calculation of volume. The Arabic scholars who invented algebra also preserved what texts remained of Greek physics. However, it was in the person of Isaac Newton that mathematics and physics were most completely united. Newton's physics informed his mathematics. The study of the rate of change in calculus was necessary for the Newtonian theory of mechanics. While it is still not yet well-determined whether Newton or Leibniz originally formulated calculus, Newton was the one who applied that type of mathematics extensively to the physical universe.
This application allowed physics to make a transition from a largely observational science, as it was when astronomy was the viable component of it, to a science with considerable predictive and explanatory power.
Though most of the great nineteenth-century physicists were also mathematicians, mathematics and physics were already separating themselves into separate disciplines. Distinguished mathematicians such as Helmholtz and the great Gauss made contributions in the then-new science of electromagnetics as well as formulating much of the theory of differential equations, non-Euclidean geometries, and diverse other mathematical fields of interest. By the dawn of the twentieth century, physicists considered mathematics the language in which physics is expressed. It had its own validity, of course, and there were vast fields of arcane mathematics that seemed to have no physical applications. For its part, physics was making fewer contributions to mathematics, although every once in awhile a physicist would find some theorem or property useful and would prove it or ask a mathematician to do so. The contributions physics makes to mathematics are subtler, because physics allows for some concrete examples and visualizations of mathematics as it is taught. However, as quantum mechanics grows more arcane by the decade, the evolving relationship between mathematics and physics continues to change. The arcane theories of yesterday (group theory, for example) are essential to explaining the concrete physical data of tomorrow. While the two disciplines have both grown too large to allow for many people who do work in both, they continue to inform each other and contribute problems and explanations back and forth across the subject boundaries.
This is the complete article, containing 418 words
(approx. 1 page at 300 words per page).
