I think it’s really hard to say who made the “biggest paradigm shift”. For most people, it is tempting to say Einstein, because his name and legacy is so huge in 20th Century physics; even people who barely know who Newton and Archimedes are can immediately recognize Einstein. However, it’s worthwhile to note that, while Einstein developed his theories outside the academic medium and essentially without reference to other work being done in the field, much of the details that went into Special Relativity were already developed by others (Lorentz, Poincaré), and there are some who contend that Einstein’s first wife, mathematician Mileva Marić, was responsible for much of the formalism, and possibly some of the ideas behind Special Relativity. This is entirely speculative–there are no notes or publications that substantiate this, but many of her contemporaries felt that she was materially responsible for some or much of the concepts behind SR based upon statements or relative competency, and Einstein ceeded his Nobel Prize money (won for his work on the Photoelectric Effect 'cause the Nobel Prize Committiee felt that Henri Poincaré deserved equal credit) to Marić due to a divorce agreement under which she was prohibited from making any further claim against the fruits of Einstein’s intellectual property.
The case for General Relativity is even more precarious; I daresay mathematicians who’ve studied the history would argue that David Hilbert and his students materially aided in the development and should be credited again for the formalism. GR is really “just” an extension of SR onto a topologically curved space (Chronos is probably going to have a stroke when he sees that statement) and not quite as fundamental a discovery as SR, nor one Einstein could have developed without the mathematical tools and methods devised by Hilbert, et al. In any case, Einstein’s work capped off about thirty years of anxiety, alternate theorizing, and argumentation about the obviously flawed notion of an objective spacetime plenum. He tied things together, but the individual components were all out there in the community.
To dismiss Newton’s observations and subsequent laws as “obvious” is at its least unfair to an extreme. Before Newton, explainations for the physical behavior of objects in motion was ad hoc and disjointed. Newton formulated all of classical mechanics as three simple laws that could readily be expressed mathematically. This was a masterstroke of deconstruction, but it would be unfair to say that Newton did it all on his own. He certainly drew from those around and before him. And should be be inclined to award too much foresight to Newton, it should be remembered that Newton’s nemisis and competitor for title of the inventor of differential calculus, Gottfried Leibniz, proposed (correctly, as it turns out) that action is space is relative to an inertial reference frame rather than against a static (objective) background as Newton contended, though it took a couple of centuries for this to be validated. He also foresaw, in a very general way, the indeterminacy of quantum mechanics and the ultimate unpredictability of complex systems in action as ergodic/chaos theory now asserts. In general, he was far more broadly accomplished than Newton, though most historians feel that Newton was the “better” physicist (again, possibly displaying a cultural and educational bias). Newton’s frequent crackpotism, most notably with respect to alchemy, is widely derided, but largely unfair, as alchemy was then the respected precursor to chemistry, and was no reflection on his work in mechanics and mathematics.
Archimedes was mostly wrong about a vast number of things, having been born long before modern mathematical and algebraic formalism, much less four-color textbooks and Mathematica, but he (and his students) are primarily responsible for the foundations of plane geometry, basic algebraic theory, and what we now refer to as “the scientific method” of making a hypothesis or model and correlating it to or falsifying by observation and experiment. Given the derth of information on Archimedes actual life and teachings its difficult to say how much of what is attributed to him is uniquely his work and how much is derivative or in conjunction with others, but more than any other natural philosopher the big Arch is responsible for modern scientific thinking and process.
Somebody mentioned James Clark Maxwell, who on the basis of applicability and uniqueness of his work may well be advanced to the head of the class. Although Maxwell’s most famous achievement–the equations of electromagnetism that bear his name (even though he didn’t actually formalize them as such)–is certainly paradigm-shifting–he did much other work in areas from thermodynamics to complex physical mechanisms to color photography. Maxwell was also one of the first to touch on aspects of special relativity (specifically, the invariance of spacetime with respect to electromagnetic waves), though he lacked both the mathematical tools and the body of evidence that overturned his lovely, but totally wrong regarding his “luminiferous aether” as a medium for conduction, at least in the form that he thought it worked.
If we can take an excursion from physics and into the more general realm of natural science, I’d nominate Charles Darwin as the crown prince of paradigm shifts in natural science. While people had been discussing for a couple of decades before the general notion of evolution (as opposed to static Biblical or otherwise Creationism, which was rapidly becoming more stinky than Limberger cheese left out on a hot day), Darwin proposed an alternate, surprisingly comprehensive, and largely unmodified-in-the-present-day theory of Natural Selection (or “Descent by Modification” as he referred to it), and put it on a secure, virtually unshakable foundation via his famous research on the Beagle and his more mundane, but highly critical research at home with barnacles, snails, and other mundane creatures of everyday life. The one piece that he was missing–the transmission of inherited characteristics via the genome–was integrated into selection theory shortly after his death, although the clincher had to wait until the technique of x-ray defraction came about and the discover by Crick and Watson (and the underrecognized Maurice Wilkins and Rosalind Franklin). It represented a shift away from the blind, totally inevidenced, dogmatic superstition of Christian (or otherwise) creationism to a rigorous, testable, falsifiable theory for how biology works, rather than a post hoc explaination of it.
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