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Hall of Equations
Curated Collection of Nature's Laws
All
210
Quantum
33
Relativity
11
Classical
69
Thermodynamics
15
Pure Math
54
Cosmology
11
Chaos
8
Particle Physics
9
No. qm-1
Quantum
Time-Dependent Schrödinger Equation
1925
Erwin Schrödinger
No. qm-2
Quantum
Heisenberg Uncertainty Principle
1927
Werner Heisenberg
No. gr-1
Relativity
Einstein Field Equations
1915
Albert Einstein
No. gr-2
Relativity
Mass-Energy Equivalence
1905
Albert Einstein
No. cl-1
Classical
Navier-Stokes Equations
1822
Claude-Louis Navier & George Gabriel Stokes
No. cl-2
Classical
Maxwell's Equations
1865
James Clerk Maxwell
No. th-1
Thermodynamics
Boltzmann Entropy Formula
1875
Ludwig Boltzmann
No. pm-1
Pure Math
Euler's Identity
1748
Leonhard Euler
No. cos-1
Cosmology
Friedmann Equations
1922
Alexander Friedmann
No. ch-1
Chaos
Lorenz Attractor
1963
Edward Lorenz
No. qm-3
Quantum
Dirac Equation
1928
Paul Dirac
No. qm-4
Quantum
Planck's Law
1900
Max Planck
No. qm-5
Quantum
Born Rule
1926
Max Born
No. pp-1
Particle Physics
Standard Model Lagrangian
1970s
Various (Weinberg, Salam, Glashow)
No. gr-3
Relativity
Schwarzschild Radius
1916
Karl Schwarzschild
No. gr-4
Relativity
Lorentz Factor
1904
Hendrik Lorentz
No. cl-3
Classical
Newton's Law of Universal Gravitation
1687
Isaac Newton
No. cl-4
Classical
Bernoulli's Principle
1738
Daniel Bernoulli
No. cl-5
Classical
Hooke's Law
1660
Robert Hooke
No. cl-6
Classical
Lagrangian Mechanics
1788
Joseph-Louis Lagrange
No. th-2
Thermodynamics
Ideal Gas Law
1834
Benoît Paul Émile Clapeyron
No. th-3
Thermodynamics
First Law of Thermodynamics
1850
Rudolf Clausius
No. pm-2
Pure Math
Fourier Transform
1822
Joseph Fourier
No. pm-3
Pure Math
Riemann Zeta Function
1859
Bernhard Riemann
No. pm-4
Pure Math
Bayes' Theorem
1763
Thomas Bayes
No. pm-5
Pure Math
Normal Distribution (Gaussian)
1809
Carl Friedrich Gauss
No. cos-2
Cosmology
Hubble's Law
1929
Edwin Hubble
No. cos-3
Cosmology
Drake Equation
1961
Frank Drake
No. ch-2
Chaos
Logistic Map
1976
Robert May
No. ch-3
Chaos
Mandelbrot Set
1980
Benoit Mandelbrot
No. qm-6
Quantum
De Broglie Wavelength
1924
Louis de Broglie
No. qm-7
Quantum
Bell's Inequality
1964
John Stewart Bell
No. qm-8
Quantum
Pauli Exclusion Principle
1925
Wolfgang Pauli
No. cl-7
Classical
Lorentz Force Law
1895
Hendrik Lorentz
No. cl-8
Classical
Coulomb's Law
1785
Charles-Augustin de Coulomb
No. cl-9
Classical
Snell's Law
1621
Willebrord Snellius
No. cl-10
Classical
Wave Equation
1746
Jean le Rond d'Alembert
No. th-4
Thermodynamics
Stefan-Boltzmann Law
1879
Josef Stefan & Ludwig Boltzmann
No. th-5
Thermodynamics
Carnot Efficiency
1824
Nicolas Léonard Sadi Carnot
No. th-6
Thermodynamics
Gibbs Free Energy
1873
Josiah Willard Gibbs
No. gr-5
Relativity
Geodesic Equation
1915
Albert Einstein
No. gr-6
Relativity
Gravitational Time Dilation
1907
Albert Einstein
No. pp-2
Particle Physics
Radioactive Decay Law
1902
Ernest Rutherford & Frederick Soddy
No. pm-6
Pure Math
Fundamental Theorem of Calculus
1660s
Newton & Leibniz
No. pm-7
Pure Math
Quadratic Formula
2000 BC (Babylonians) / 628 AD (Brahmagupta)
Brahmagupta
No. pm-8
Pure Math
Pythagorean Theorem
500 BC
Pythagoras
No. cl-11
Classical
Reynolds Number
1851
George Gabriel Stokes
No. el-1
Classical
Ohm's Law
1827
Georg Ohm
No. el-2
Classical
Kirchhoff's Current Law
1845
Gustav Kirchhoff
No. el-3
Classical
Poynting Vector
1884
John Henry Poynting
No. qm-9
Quantum
Rydberg Formula
1888
Johannes Rydberg
No. qm-10
Quantum
Fine Structure Constant
1916
Arnold Sommerfeld
No. qm-11
Quantum
Compton Shift
1923
Arthur Compton
No. opt-1
Classical
Rayleigh Criterion
1879
Lord Rayleigh
No. opt-2
Classical
Lens Maker's Equation
1600s
Various (Descartes/Halley)
No. cos-4
Cosmology
Cosmological Redshift
1929
Edwin Hubble
No. cos-5
Classical
Kepler's Third Law
1619
Johannes Kepler
No. cos-6
Classical
Escape Velocity
1687
Isaac Newton
No. pm-9
Pure Math
Taylor Series
1715
Brook Taylor
No. pm-10
Pure Math
Golden Ratio
300 BC
Euclid
No. pm-11
Pure Math
Stirling's Approximation
1730
James Stirling
No. pm-12
Pure Math
Cauchy-Schwarz Inequality
1821
Augustin-Louis Cauchy
No. th-7
Thermodynamics
Van der Waals Equation
1873
Johannes Diderik van der Waals
No. cl-12
Classical
Newton's Second Law
1687
Isaac Newton
No. cl-13
Classical
Kinetic Energy
1720s
Willem 's Gravesande / Émilie du Châtelet
No. cl-14
Classical
Centripetal Force
1659
Christiaan Huygens
No. cl-15
Classical
Torque
Antiquity (Archimedes)
Archimedes (Concept)
No. cl-16
Classical
Angular Momentum
1700s
Euler / Bernoulli
No. em-1
Classical
Gauss's Law
1813
Carl Friedrich Gauss
No. em-2
Classical
Faraday's Law of Induction
1831
Michael Faraday
No. em-3
Classical
Ampère's Law
1826
André-Marie Ampère
No. qm-12
Quantum
Time-Independent Schrödinger Equation
1925
Erwin Schrödinger
No. qm-13
Quantum
Wien's Displacement Law
1893
Wilhelm Wien
No. cos-7
Cosmology
Chandrasekhar Limit
1930
Subrahmanyan Chandrasekhar
No. cos-8
Cosmology
Luminosity Formula
19th Century
Various
No. fl-2
Classical
Drag Equation
19th Century
Lord Rayleigh
No. wav-1
Classical
Doppler Effect
1842
Christian Doppler
No. opt-3
Classical
Malus's Law
1809
Étienne-Louis Malus
No. opt-4
Classical
Brewster's Angle
1811
David Brewster
No. pm-13
Pure Math
Divergence Theorem
1826
Gauss / Ostrogradsky
No. pm-14
Pure Math
Stokes' Theorem
1854
George Stokes (Popularized by)
No. pm-15
Pure Math
Binomial Theorem
1665
Isaac Newton
No. pm-16
Pure Math
Green's Theorem
1828
George Green
No. ss-1
Quantum
Bragg's Law
1913
William Lawrence Bragg
No. ss-2
Quantum
Fermi-Dirac Distribution
1926
Enrico Fermi & Paul Dirac
No. fl-3
Classical
Archimedes' Principle
250 BC
Archimedes
No. fl-4
Classical
Continuity Equation
1700s
Leonhard Euler
No. th-8
Thermodynamics
Heat Equation
1822
Joseph Fourier
No. th-9
Thermodynamics
Partition Function
19th Century
Boltzmann / Gibbs
No. nuc-1
Particle Physics
Nuclear Binding Energy
1930s
Various
No. nuc-2
Particle Physics
Cyclotron Frequency
1932
Ernest Lawrence
No. pm-17
Pure Math
Laplace Transform
1785
Pierre-Simon Laplace
No. pm-18
Pure Math
Jacobian Matrix
1800s
Carl Gustav Jacob Jacobi
No. pm-19
Pure Math
Fibonacci Sequence
1202
Leonardo of Pisa (Fibonacci)
No. gr-7
Relativity
Minkowski Metric
1908
Hermann Minkowski
No. cos-9
Cosmology
Roche Limit
1848
Édouard Roche
No. pde-1
Pure Math
Laplace Equation
1780s
Pierre-Simon Laplace
No. pde-2
Classical
Poisson Equation
1813
Siméon Denis Poisson
No. pde-3
Classical
Helmholtz Equation
1860
Hermann von Helmholtz
No. qm-17
Quantum
Expectation Value
1926
Max Born
No. qm-18
Quantum
Commutator (Heisenberg Algebra)
1927
Werner Heisenberg
No. qm-19
Quantum
Bose-Einstein Distribution
1924
Satyendra Nath Bose & Albert Einstein
No. qm-20
Quantum
Quantum Tunneling Probability (WKB)
1920s
Wentzel, Kramers, Brillouin (WKB)
No. qm-21
Quantum
Zero-Point Energy (ZPE)
1913
Max Planck / Otto Stern
No. gr-11
Relativity
Relativistic Doppler Effect
1905
Albert Einstein
No. gr-12
Relativity
Gravitational Lensing Angle
1915
Albert Einstein
No. gr-13
Relativity
Relativistic Momentum
1905
Albert Einstein
No. gr-14
Relativity
Kerr Metric (Conceptual)
1963
Roy Kerr
No. cl-20
Classical
Work-Energy Theorem
1829
Gaspard-Gustave Coriolis
No. cl-21
Classical
Simple Pendulum Period
1602
Galileo Galilei (Discovery)
No. cl-22
Classical
Potential Energy (Gravitational)
19th Century
William Rankine (Term coined)
No. cl-23
Classical
Fick's Law of Diffusion (First)
1855
Adolf Eugen Fick
No. cl-24
Classical
Damping Ratio (ζ)
Early 20th Century
Various (Control Theory)
No. cl-25
Classical
Biot-Savart Law (Magnetic Field)
1820
Jean-Baptiste Biot and Félix Savart
No. cl-26
Classical
Piston Work (Thermodynamic)
18th Century
Various
No. cl-27
Classical
Capacitance
1780s
Alessandro Volta
No. cl-28
Classical
Inductance
1834
Heinrich Lenz (Coefficient defined by Neumann)
No. cl-29
Classical
Wave Speed on a String
18th Century
Jean le Rond d'Alembert
No. cl-30
Classical
Focal Length of a Mirror
Antiquity
Known since antiquity, formalized later.
No. cl-31
Classical
Pressure in a Fluid at Depth
1648
Blaise Pascal
No. cl-32
Classical
Ohm's Law (Heat Flow)
1822
Joseph Fourier
No. cl-33
Classical
Thin Lens Equation
17th Century
Known to many, popularized by Gauss
No. cl-34
Classical
Kinetic Theory RMS Speed
1859
James Clerk Maxwell
No. cl-35
Classical
Larmor Radius (Gyroradius)
1897
Joseph Larmor
No. th-13
Thermodynamics
Second Law of Thermodynamics (Clausius)
1850
Rudolf Clausius
No. th-14
Thermodynamics
Heat Capacity (Specific)
18th Century
Joseph Black
No. th-15
Thermodynamics
Helmholtz Free Energy
1882
Hermann von Helmholtz
No. th-16
Thermodynamics
Third Law of Thermodynamics
1912
Walther Nernst
No. th-17
Classical
Thermal Expansion (Linear)
18th Century
Various
No. cos-10
Cosmology
Critical Density
1920s
Friedmann / Lemaître
No. cos-11
Cosmology
Jeans Instability
1902
Sir James Jeans
No. cos-12
Cosmology
Tully–Fisher Relation
1977
Brent Tully and Richard Fisher
No. cos-13
Cosmology
Virial Mass Estimation (Conceptual)
1930s
Fritz Zwicky
No. pp-5
Particle Physics
Weak Interaction Range (W/Z Bosons)
1935
Hideki Yukawa
No. pp-6
Particle Physics
Bethe-Bloch Formula (Stopping Power)
1930s
Hans Bethe, Felix Bloch
No. pp-7
Particle Physics
Higgs Mechanism (Conceptual)
1964
Peter Higgs, et al.
No. pp-8
Particle Physics
C-P-T Theorem (Conceptual)
1954
Gerhard Lüders and Wolfgang Pauli
No. pm-27
Pure Math
Wave Number
18th Century
Various
No. pm-28
Pure Math
The Heat Kernel (Fundamental Solution)
1822
Joseph Fourier
No. pm-29
Pure Math
Möbius Strip (Parametric)
1858
August Ferdinand Möbius and Johann Benedict Listing
No. pm-30
Pure Math
Chebyshev Polynomials (Recurrence)
1853
Pafnuty Chebyshev
No. pm-31
Pure Math
Cauchy–Riemann Equations
1814
Augustin-Louis Cauchy and Bernhard Riemann
No. pm-32
Pure Math
Green's Function (Conceptual)
1828
George Green
No. pm-33
Pure Math
Cramer's Rule
1750
Gabriel Cramer
No. pm-34
Pure Math
Central Limit Theorem (Conceptual)
1901
Aleksandr Lyapunov (Formal proof)
No. pm-35
Pure Math
Law of Large Numbers
1713
Jacob Bernoulli
No. pm-36
Pure Math
Euler–Lagrange Equation (Conceptual)
1755
Leonhard Euler and Joseph-Louis Lagrange
No. pm-37
Pure Math
Dirichlet Problem (Conceptual)
1840s
Johann Peter Gustav Lejeune Dirichlet
No. pm-38
Pure Math
Fibonacci Ratio (Binet's Formula)
1843
Jacques Philippe Marie Binet
No. ch-4
Chaos
Lyapunov Exponent (Conceptual)
1892
Aleksandr Lyapunov
No. ch-5
Chaos
Mandelbrot Boundary Condition (Conceptual)
1980
Benoit Mandelbrot
No. ch-6
Chaos
Feigenbaum Constant ($delta$)
1975
Mitchell Feigenbaum
No. it-1
Pure Math
Shannon Entropy
1948
Claude Shannon
No. it-2
Pure Math
Noisy Channel Coding Theorem (Conceptual)
1948
Claude Shannon
No. wav-2
Classical
Index of Refraction
18th Century
Various
No. wav-3
Classical
Thin Film Interference (Constructive)
1665
Robert Hooke and Isaac Newton
No. wav-4
Classical
Single-Slit Diffraction
1818
Augustin-Jean Fresnel
No. wav-5
Classical
Group Velocity
1839
Sir George Stokes
No. fl-5
Classical
Shear Stress (Newtonian Fluid)
1687
Isaac Newton
No. fl-6
Classical
Lift Coefficient (Conceptual)
19th/20th Century
Lord Rayleigh (Basis) / Ludwig Prandtl (Airfoil Theory)
No. fl-7
Classical
Stokes' Drag Law (Spheres)
1851
George Gabriel Stokes
No. pm-46
Pure Math
Law of Sines
10th Century (Al-Battani)
Abu-Mahmud Khojandi
No. pm-47
Pure Math
Eigenvalue Equation
19th Century
Cauchy and Fourier
No. pm-48
Pure Math
Wronskian (Differential Equations)
1812
Józef Hoene-Wroński
No. pm-49
Pure Math
Erlang C Formula (Queue Theory)
1917
A.K. Erlang
No. pm-50
Pure Math
Jensen's Inequality
1906
Johan Jensen
No. pm-61
Pure Math
Cauchy Integral Formula
1831
Augustin-Louis Cauchy
No. pm-62
Pure Math
Determinant of a Matrix
1683
Gottfried Leibniz (Concept) / Gabriel Cramer (Rule)
No. pm-63
Pure Math
Jordan Normal Form (Conceptual)
1870
Camille Jordan
No. pm-64
Pure Math
Divergence (Vector Calculus)
19th Century
George Green
No. pm-65
Pure Math
Curl (Vector Calculus)
19th Century
James Clerk Maxwell
No. geo-1
Classical
Mohorovičić Discontinuity (Conceptual)
1909
Andrija Mohorovičić
No. geo-2
Classical
Richter Scale (Magnitude)
1935
Charles Richter
No. geo-3
Classical
Gaia Hypothesis (Conceptual)
1972
James Lovelock and Lynn Margulis
No. qm-22
Quantum
Fine Structure Constant (Alternative)
1916 (Conceptual)
Arnold Sommerfeld
No. qm-23
Quantum
Energy-Time Uncertainty
1927
Werner Heisenberg
No. qm-24
Quantum
Landauer's Principle
1961
Rolf Landauer
No. qm-25
Quantum
Quantum Hall Effect (Conductivity)
1980
Klaus von Klitzing
No. qm-26
Particle Physics
Uncertainty in Energy (Lorentzian Width)
1930s
Werner Heisenberg
No. qm-27
Quantum
London Penetration Depth
1935
Fritz and Heinz London
No. qm-28
Quantum
Mott Insulator Condition (Conceptual)
1949
Sir Nevill Mott
No. qm-29
Quantum
Bloch's Theorem
1928
Felix Bloch
No. qm-30
Quantum
Quantum Computing (Qubit State)
1995
Various (QIT)
No. qm-31
Quantum
Quantum Entanglement (Bell State)
1964
John Bell
No. ss-3
Quantum
BCS Theory Gap Equation
1957
Bardeen, Cooper, Schrieffer (BCS)
No. ss-4
Classical
Drude Model Conductivity
1900
Paul Drude
No. pm-69
Pure Math
Euler-Mascheroni Constant
1734
Leonhard Euler
No. pm-70
Pure Math
Cauchy-Schwartz Inequality (Continuous)
1888
Hermann Schwarz
No. pm-71
Pure Math
L'Hôpital's Rule
1696
Guillaume de l'Hôpital (discovered by Johann Bernoulli)
No. cl-36
Classical
Hamiltonian Mechanics (Energy)
1833
William Rowan Hamilton
No. cl-37
Classical
Coriolis Force
1835
Gaspard-Gustave Coriolis
No. cl-38
Classical
Rocket Equation (Tsiolkovsky)
1903
Konstantin Tsiolkovsky
No. ch-7
Chaos
Period-Doubling Bifurcation (Conceptual)
1975
Mitchell Feigenbaum
No. ch-8
Chaos
Poincaré Recurrence Theorem (Conceptual)
1890
Henri Poincaré
No. it-3
Pure Math
Kullback-Leibler Divergence (Conceptual)
1951
Solomon Kullback and Richard Leibler
No. pm-74
Pure Math
Euler Characteristic
1758
Leonhard Euler
No. pm-75
Pure Math
Fundamental Theorem of Algebra
1799
Carl Friedrich Gauss (First full proof)
No. pm-76
Pure Math
Gromov's Theorem (Conceptual)
1983
Mikhail Gromov
No. cl-40
Quantum
Wave-Particle Duality (Energy)
1900
Max Planck
No. cl-41
Classical
Young's Modulus (Elasticity)
1807
Thomas Young
No. cl-42
Classical
Pohl's Law (Flow Resistance)
1851
George Gabriel Stokes
No. th-10
Thermodynamics
Zeroth Law of Thermodynamics
1931
Ralph H. Fowler
No. th-11
Classical
Joule's First Law (Heat Generation)
1840
James Prescott Joule
No. th-12
Thermodynamics
Efficiency of a Heat Pump/Refrigerator
1824
Sadi Carnot (Principle)
No. pm-77
Pure Math
Stirling's Formula (Accurate)
1730
James Stirling
No. pm-78
Pure Math
Gamma Function
1729
Leonhard Euler
No. pm-79
Pure Math
Chebyshev's Inequality
1867
Pafnuty Chebyshev
No. qm-33
Quantum
Zeeman Effect (Conceptual)
1896
Pieter Zeeman
No. cl-43
Quantum
Bohr Magneton (Constant)
1911
Niels Bohr
No. cl-44
Classical
Capacitor Energy Storage
19th Century
Various (Generalized from Leyden Jars)
Quantum & Relativity Club