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List: Top Ten Greatest Equations Ever

Date: October 2004

Source: Critical Point: Physics World magazine readers poll

Base: From a total of 120 responses to Robert P Crease who asked readers of Physics World magazine to send him their shortlists of great equations. He also asked them to explain why their nominations belonged on the list and why, if at all, the topic matters.

Notes: Readers proposed about 50 different equations, ranging from obvious classics to "overlooked" candidates, personal favourites and equations invented by the respondents themselves. For a discussion of the equations and results for the top twenty please click on the link above. Robert P Crease works in the Department of Philosophy, State University of New York at Stony Brook, and is an historian at the Brookhaven National Laboratory.




Maxwell's four equations describing how an electromagnetic field varies in space and time.


Euler's equation of momentum-flow and force-density in fluid dynamics.


Newton's Second Law (F=ma) - 'The rate of change of momentum of a body is equal to the resultant force acting on the body and is in the same direction'.


Pythagoras's Theorum (a²+b²=c²) - In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.


Schrödinger's equation describing the time-dependence of quantum mechanical systems.


Boltzmann equation describing the statistical distribution of particles in a fluid.


Principle of Least Action (or Principle of stationary action)


De Broglie's equation - showing that the wavelength is inversely proportional to the momentum of a particle and that the frequency is directly proportional to the particle's kinetic energy


Fourier Transformation - an integral transform that re-expresses a function in terms of sinusoidal basis functions.


Einstein's field equations for General Relativity

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