1807 
After serving as a member of the Revolutionary
Committee that terrorized France, sent Coulomb into hiding, arrested Lagrange
and guillotined Lavoisier, a repentant Jean Baptiste Joseph Fourier causes
controversy with his memoir On the Propagation
of Heat in Solid Bodies. His former teachers Laplace and Lagrange
object to his use of infinite trigonometric series, which we now call
Fourier series. Fourier later wins the Paris Institute Mathematics Prize
for solving the problem of heat propagation, over the repeated objections
of Laplace and Lagrange. 
1817 
Johann Karl Friedrich Gauss begins
working on nonEuclidean geometry, and lays the foundations of differential
geometry, but doesn't publish because he is afraid of the controversy
that would result. 
1820 
Danish physicist Hans Christian Oersted
studied the way an electric current in a wire could move the magnetic
needle of a compass, which strongly suggested that electricity and magnetism
were related somehow. 
1823 
Transylvanian mathematician János
Bolyai, despite being warned against it by his father, tosses out Euclid's
Fifth Axiom and shows that nonEuclidean geometry is possible. Gauss calls
him a genius of the first order, but then crushes the young man by telling
him he discovered it years ago but failed to publish due to his own fear
of controversy. 
1826 
Elliptic functions are developed by
Gauss, Jacobi and Abel. 
1826 
In his book Memoir
on the Mathematical Theory of Electrodynamic Phenomena, Uniquely Deduced
from Experience. André Marie Ampère gave a mathematical derivation
of the magnetic force between two parallel wires with electric current,
what we now call Ampère's Law. 
1827 
Ohm's Law of electrical resistance
is published in his book Die galvanische Kette,
mathematisch bearbeitet. 
1827 
AugustinLouis Cauchy develops the
calculus of residues, beginning his work in mathematics that made complex
analysis one of the most important analytical tools of modern theoretical
physics, including string theory. 
1828 
Selfeducated English mill worker
George Green publishes his work on the use of potential theory to solve
partial differential equations, and develops one of the most powerful
mathematical technologies in theoretical physics  the Green
function. 
1829 
Russian mathematician Nikolai Ivanovich
Lobachevsky publishes his independent discovery of nonEuclidean geometry
in the Kazan Messenger. Years later, one
of his physics students will become known to history as Lenin's father.

1831 
Evariste Galois develops the nascent
group theory with his work on the permutation group. 
1831 
Michael Faraday discovers magnetic
induction, now known as Faraday's Law, where moving magnetism creates
electricity, and this result increases support for the idea of a unified
theory of electricity and magnetism. 
1829 
French mathematician Joseph Liouville
begins to work on boundary value problems in partial differential equations,
leading to SturmLiouville theory. He then develops the study of conformal
transformations, and later proves the Liouville Theorem regarding the
invariance of the measure of phase space under what will later be called
Hamiltonian flow. 
1834 
William Rowan Hamilton applies his
mathematical development of characteristic functions in optics to mechanics
and the enormous and potent mathematical technology of Hamiltonian dynamics
is born. 
1840 
Karl Weierstrass begins his work on
elliptic functions. 
1843 
After a period of emotional distress
and alcohol abuse, Hamilton finally deduces the noncommutative multiplication
rule for quaternions. His first publication on the subject is to carve
the quaternion formula into a bridge. 
1844 
Hermann Grassmann develops exterior
algebra and the Grassmannian. 
1851 
Bernhard Riemann submits his Ph.D.
thesis to his supervisor Gauss. In his thesis he describes what is now
called a Riemann surface, an essential element in understanding string
theory. 
1854 
George Boole develops Boolean logic
in Laws of Thought. 
1871 
Norwegian mathematician Marius Sophus
Lie publishes work on Lie algebras, opening up the field of differential
topology and paving the way for gauge field theory 100 years later. 
1873 
James Clerk Maxwell publishes a set of equations from which all of
the observed laws of electromagnetism could be derived through mathematics.
These equations turn out to have solutions that describe waves traveling
through space with a speed that agrees with the measured speed of light.
Maxwell makes the bold conclusion that light therefore must consist
of electromagnetic waves, writing that he could "scarcely
avoid the inference that light consists in the transverse undulations
of the same medium which is the cause of electric and magnetic phenomena."

1874 
Cantor invents set theory. 
1878 
William Clifford develops Clifford
algebras from the work of Grassmann and Hamilton. 
1878 
Arthur Cayley writes The
theory of groups, where he proved that every finite group can be
represented as a group of permutations. 
1883 
Wilhelm Killing works on ndimensional
nonEuclidean geometry and Lie algebras, work that later results in the
concept of a Killing vector, a powerful tool in differential geometry,
quantum gauge field theory, supergravity and and string theory. 
1884 
Heinrich Hertz rewrites Maxwell's
Equations in a more elegant notation where the symmetry between
electricity and magnetism was obvious. Hertz then creats the first radio
waves and microwaves in his laboratory and shows that these electromagnetic
waves behaved just as observable optical light behaved, proving that light
was electromagnetic radiation, as Maxwell had predicted. 
1884 
Ludwig Boltzmann makes a theoretical
derivation of black body radiation using Maxwell's equations and thermodynamics,
confirming the 1879 result measured experimentally by Josef Stefan. Their
result, the StefanBoltzmann Law, is not quite right, and the correct
solution in the next century will mark the beginning of quantum theory. 
1887 
Michelson and Morley measure the Earth's
velocity through the ether to be zero, strongly suggesting that there
is no ether, and that the velocity of light is the same for all observers,
a result whose full implications have changed the world forever. 
1894 
Elie Cartan classifies simple Lie
algebras 
1895 
Henri Poincaré publishes Analysis
Situs, and gives birth to the field of algebraic topology. 
1897 
Electron discovered by J.J. Thompson. 
1899 
Hendrik Lorentz becomes the third
person, after Voigt and FitzGerald, to write down the relativistic coordinate
transformations that will bear his name. The Lorentz transformations leave
the speed of light invariant, as suggested by the MichelsonMorley experiment.

1899 
David Hilbert's Grundlagen
der Geometrie (Foundations of Geometry)
is published, putting modern geometry on a solid rigorous foundation.

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