||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.
||Johann Karl Friedrich Gauss begins
working on non-Euclidean geometry, and lays the foundations of differential
geometry, but doesn't publish because he is afraid of the controversy
that would result.
||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.
||Transylvanian mathematician János
Bolyai, despite being warned against it by his father, tosses out Euclid's
Fifth Axiom and shows that non-Euclidean 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
||Elliptic functions are developed by
Gauss, Jacobi and Abel.
|| 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.
||Ohm's Law of electrical resistance
is published in his book Die galvanische Kette,
||Augustin-Louis 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.
||Self-educated 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
||Russian mathematician Nikolai Ivanovich
Lobachevsky publishes his independent discovery of non-Euclidean geometry
in the Kazan Messenger. Years later, one
of his physics students will become known to history as Lenin's father.
||Evariste Galois develops the nascent
group theory with his work on the permutation group.
||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.
||French mathematician Joseph Liouville
begins to work on boundary value problems in partial differential equations,
leading to Sturm-Liouville 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
||William Rowan Hamilton applies his
mathematical development of characteristic functions in optics to mechanics
and the enormous and potent mathematical technology of Hamiltonian dynamics
||Karl Weierstrass begins his work on
|| 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.
||Hermann Grassmann develops exterior
algebra and the Grassmannian.
||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
||George Boole develops Boolean logic
in Laws of Thought.
||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.
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."
||Cantor invents set theory.
||William Clifford develops Clifford
algebras from the work of Grassmann and Hamilton.
||Arthur Cayley writes The
theory of groups, where he proved that every finite group can be
represented as a group of permutations.
||Wilhelm Killing works on n-dimensional
non-Euclidean 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.
||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.
||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 Stefan-Boltzmann Law, is not quite right, and the correct
solution in the next century will mark the beginning of quantum theory.
||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.
||Elie Cartan classifies simple Lie
||Henri Poincaré publishes Analysis
Situs, and gives birth to the field of algebraic topology.
||Electron discovered by J.J. Thompson.
||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 Michelson-Morley experiment.
||David Hilbert's Grundlagen
der Geometrie (Foundations of Geometry)
is published, putting modern geometry on a solid rigorous foundation.
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