The seventeenth century English physicist and mathematician, Isaac Newton [1642–1727], developed a wealth of new mathematics (for example, calculus and several numerical methods [e.g. Newton's method ]) to solve problems inphysics. Other important mathematical physicists of the seventeenth century included the Dutchman Christiaan Huygens [1629–1695] (famous for suggesting the wave theory of light), and the German Johannes Kepler [1571–1630] (Tycho Brahe's assistant, and discoverer of the equations for planetary motion/orbit).
In the eighteenth century, two of the innovators of mathematical physics were Swiss: Daniel Bernoulli [1700–1782] (for contributions to fluid dynamics, and vibrating strings), and, more especially, Leonhard Euler [1707–1783], (for his work in variational calculus, dynamics, fluid dynamics, and many other things). Another notable contributor was the Italian-born Frenchman, Joseph-Louis Lagrange [1736–1813] (for his work in mechanics and variational methods).
In the late eighteenth and early nineteenth centuries, important French figures were Pierre-Simon Laplace [1749–1827] (in mathematical astronomy, potential theory, and mechanics) and Siméon Denis Poisson [1781–1840] (who also worked in mechanics and potential theory). In Germany, both Carl Friedrich Gauss [1777–1855] (in magnetism) and Carl Gustav Jacobi [1804–1851] (in the areas of dynamics and canonical transformations) made key contributions to the theoretical foundations of electricity, magnetism, mechanics, and fluid dynamics.
Gauss's contributions to non-Euclidean geometry laid the groundwork for the subsequent development of Riemannian geometry by Bernhard Riemann [1826–1866]. As we shall see later, this work is at the heart of general relativity.
The nineteenth century also saw the Scot, James Clerk Maxwell [1831–1879], win renown for his four equations of electromagnetism, and his countryman, Lord Kelvin [1824–1907] make substantial discoveries in thermodynamics. Among the English physics community, Lord Rayleigh [1842–1919] worked on sound; and George Gabriel Stokes [1819–1903] was a leader in optics and fluid dynamics; while the Irishman William Rowan Hamilton [1805–1865] was noted for his work in dynamics.
The German Hermann von Helmholtz [1821–1894] is best remembered for his work in the areas of electromagnetism, waves, fluids, and sound. In the U.S.A., the pioneering work of Josiah Willard Gibbs[1839–1903] became the basis for statistical mechanics. Together, these men laid the foundations of electromagnetic theory, fluid dynamics and statistical mechanics.
The late nineteenth and the early twentieth centuries saw the birth of special relativity. This had been anticipated in the works of the Dutchman, Hendrik Lorentz [1853–1928], with important insights from Jules-Henri Poincaré [1854–1912], but which were brought to full clarity by Albert Einstein [1879–1955]. Einstein then developed the invariant approach further to arrive at the remarkable geometrical approach to gravitational physics embodied in general relativity. This was based on the non-Euclidean geometry created by Gauss and Riemann in the previous century.
Einstein's special relativity replaced the Galilean transformations of space and time with Lorentz transformations in four dimensional Minkowski space-time. His general theory of relativity replaced the flat Euclidean geometry with that of a Riemannian manifold, whose curvature is determined by the distribution of gravitational matter. This replaced Newton's vector gravitational force by the Riemann curvature tensor.
Another revolutionary development of the twentieth century has been quantum theory, which emerged from the seminal contributions of Max Planck [1856–1947] (on black body radiation) and Einstein's work on the photoelectric effect.
This was, at first, followed by a heuristic framework devised by Arnold Sommerfeld [1868–1951] and Niels Bohr [1885–1962], but this was soon replaced by the quantum mechanics developed by Max Born [1882–1970], Werner Heisenberg [1901–1976], Paul Dirac [1902–1984], Erwin Schrödinger [1887–1961], and Wolfgang Pauli [1900–1958]. This revolutionary theoretical framework is based on a probabilistic interpretation of states, and evolution and measurements in terms of self-adjoint operators on an infinite dimensional vector space (Hilbert space, introduced by David Hilbert [1862–1943]).
Paul Dirac, for example, used algebraic constructions to produce a relativistic model for the electron, predicting its magnetic moment and the existence of its antiparticle, the positron.
Later important contributors to twentieth century mathematical physics include Satyendra Nath Bose [1894–1974], Julian Schwinger [1918–1994], Sin-Itiro Tomonaga [1906–1979], Richard Feynman [1918–1988], Freeman Dyson [1923– ], Hideki Yukawa [1907–1981], Roger Penrose [1931– ], Stephen Hawking [1942– ], Edward Witten [1951– ] and Rudolf Haag [1922– ]