Of billions living and dead perhaps a few thousand have been gifted with mathematical intuition; a few hundred have lived in circumstances permitting use of it; a smaller fraction have been mathematical physicists. Of these a few dozen have left permanent marks on physics.
But without these few we would not have science. Mathematical physics is basic to all sciences. No exceptions. None.
Mathematical physicists sometimes hint that experimentalists are frustrated pipe fitters; experimentalists mutter that theoreticians are so lost in fog they need guardians. But they are indispensable to each other. Piling up facts is not science - science is facts and - theories. Facts alone have limited use and lack meaning; a valid theory organizes them into far greater usefulness. To be valid a theory must be confirmed by all relevant facts. A "natural law" is theory repeatedly confirmed and drops back to "approximation" when one fact contradicts it. Then search resumes for better theory to embrace old facts plus this stubborn new one.
No "natural law" of 500 years ago is "law" today; all our present laws are probably approximations, useful but not perfect. Some scientists, notably Paul Dirac, suspect that perfection is unattainable.
A powerful theory not only embraces old facts and new but also discloses unsuspected facts. These are landmarks of science: Nicolas Copernicus' heliocentric theory, Johannes Kepler's refining it into conic sections ballistics, Isaac Newton's laws of motion and theory of universal gravitation, James C. Maxwell's equations linking electricity with magnetism, Planck's quantum theory, Einstein's relativity, Dirac's synthesis of quantum theory and special relativity - a few more, not many.
Mathematical physicists strive to create a mathematical structure interrelating all space - time events, past and future, from infinitesimally small to inconceivably huge and remote in space and time, a "unified field theory" embracing 10 or 20 billion years and light - years, more likely 80 billion or so - or possibly eternity in an infinity of multiple universes.
Some order!
They try. Newton made great strides. So did Einstein. Nearly 50 years ago Dirac brought it closer, has steadily added to it, is working on it today.
Paul Dirac may be and probably is the greatest living theoretical scientist. Dirac, Newton, and Einstein are equals. Paul A. M. Dirac
The experimentalists' slur about theoretical physicists holds a grain of truth. Newton apparently never noticed the lovely sex in all his years. Einstein ignored such trivialities as socks. One mathematical physicist who swayed World War II could not be trusted with a screwdriver.
Dirac is not that sort of man.
Other than genius, his only unusual trait is strong dislike for idle talk. (His Cambridge students coined a unit the Dirac - one word per light - year.) But he lectures and writes with admirable clarity. Taciturn, he is not unsocial; in 1937 he married a most charming Hungarian lady. They have two daughters and a son.
He can be trusted with tools; he sometimes builds instruments and performs his own experiments. He graduated in engineering before he became a mathematical physicist; this influenced his life. Engineers find working solutions from incomplete data; approximations are close enough if they do the job - too fussy wastes man - hours. But when a job needs it, a true engineer gives his utmost to achieve as near perfection as possible.
Dirac brought this attitude to theoretical physics; his successes justify his approach.
He was born in Bristol, England, Aug. 8, 1902, and named Paul Adrien Maurice Dirac. His precocity in mathematics showed early; his father supplied books and encouraged him to study on his own. Solitary walks and study were the boy's notion of fun - and are of the man today. Dirac works (and plays) hardest by doing and saying nothing ... while his mind roams the universe.
When barely 16 years old, he entered the University of Bristol. At 18 he graduated, bachelor of science in electrical engineering. In 1923 a grant enabled him to return to school at the foremost institution for mathematics, Cambridge University. In three years of study for a doctorate Dirac published 12 papers in mathematical physics, 5 in The Proceedings of the Royal Society. A cub with only an engineering degree from a minor university has trouble getting published in any journal of science; to appear at the age of 22 in the most highly respected of them all is amazing.
Dirac received his doctorate in May 1926, his dissertation being "Quantum Mechanics" - the stickiest subject in physical science. He tackled it his first year at Cambridge and has continued to unravel its paradoxes throughout his career; out of 123 publications over the last 50 years the word quantum can be found 45 times in his titles.
Dirac remained at Cambridge - taught, thought, published. In 1932, the year before his Nobel prize, he received an honor rarer than that prize, one formerly held by Newton: Lucasian professor of mathematics. Dirac kept it 37 years, until he resigned from Cambridge. He accepted other posts during his Cantabrigian years: member of the Institute for Advanced Study at Princeton, N.J., professor of the Dublin Institute for Advanced Studies, visiting professorships here and there.
Intuitive mathematicians often burn out young. Not Dirac! - he is a Michelangelo who started very young, never stopped, is still going strong. Antimatter is not necessarily his contribution most esteemed by colleagues, but his other major ones are so abstruse as to defy putting them into common words:
A mathematical attribute of particles dubbed "spin"; co invention of the Fermi - Dirac statistics; an abstract mathematical replacement for the "pellucid ether" of classical mechanics. For centuries, ether was used and its "physical reality" generally accepted either as "axiomatic" or "proved" through various negative proofs. Both "axiom" and "negative proof" are treacherous; the 1887 Michelson - Morley experiment showed no physical reality behind the concept of ether, and many variations of that experiment over many years gave the same null results.
So Einstein omitted ether from his treatments of relativity - while less brilliant men ignored the observed facts and clung to classical ether for at least 40 years.
Dirac's ether (circa 1950) is solely abstract mathematics, more useful thereby than classical ether as it avoids the paradoxes of the earlier concepts. Dirac has consistently warned against treating mathematical equations as if they were pictures of something that could be visualized in the way one may visualize the Taj Mahal or a loaf of bread; his equations are rules concerning space - time events - not pictures.
(This may be the key to his extraordinary successes.) One more example must represent a long list:
Dirac's work on Georges Lemaltre's "primeval egg" - later popularized as the "big bang."
Honors also are too many to list in fulclass="underline" fellow of the Royal Society, its Royal Medal, its Copley Medal, honorary degrees (always refused), foreign associate of the American Academy of Sciences, Oppenheimer Memorial Prize, and (most valued by Dirac) Great Britain's Order of Merit.
Dirac "retired" by accepting a research professorship at Florida State University, where he is now working on gravitation theory. In 1937 he had theorized that Newton's "constant of gravitation" was in fact a decreasing variable ... but the amount of decrease he predicted was so small that it could not be verified in 1937.
Today the decrease can be measured. In July 1974 Thomas C. Van Flandern of the U.S. Naval Observatory reported measurements showing a decrease in gravitation of about a ten - billionth each year (1 per 1010 per annum). This amount seems trivial, but it j very large in astronomical and geological time. If these findings are confirmed and if they continue to support Dirac's mathematical theory, he will have upset physical science even more than he did in 1928 and 1930.
Here is an incomplete list of the sciences that would undergo radical revision: physics from micro - through astro - , astronomy, geology, paleontology, meteorology, chemistry, cosmology, cosmogony, geogony, ballistics. It is too early to speculate about effects on the life sciences, but we exist inside this physical world and gravitation is the most pervasive feature of our world.