Max Planck makes his quantum
hypothesis -- that energy is carried by indistinguishable units
called quanta, rather than flowing in a
pure continuum. This hypothesis leads to a successful derivation of the
black body radiation law, now called Planck's Law, although in 1901 the
quantum hypothesis as yet had no experimental support. The unit of quantum
action is now called Planck's constant.

1905

Swiss patent clerk Albert Einstein
proposes Planck's quantum hypothesis as the physics underlying the photoelectric
effect. Planck wins the Nobel Prize in 1918, and Einstein in 1921, for
developing quantum theory, one of the two most important developments
in 20th century physics.

1905

Einstein publishes his simple, elegant
Special Theory of Relativity, making mincemeat of his competition by relying
on only two ideas: 1. The laws of physics are the same in all inertial
frames, and 2. The speed of light is the same for all inertial observers.

1905

Poincaré shows that Lorentz
transformations in space and time plus rotations in space form a group,
which comes to be known as the Lorentz group. The Lorentz group plus translations
in space form a group called the Poincaré group.

1907

Minkowski publishes Raum und Zeit
(Space and Time), and establishes the idea of a spacetime continuum

1909

Hilbert's work on integral equations
later leads to the concept of a Hilbert space
in quantum mechanics

1915

Emmy Noether publishes Noether's
Theorem, discovering the relationship between symmetries and conserved
currents that was crucial to the later development of quantum gauge field
theory and string theory

1915

Einstein, with Hilbert in stiff competition,
publishes his stunning General Theory of Relativity, and is lucky enough
to be able to find observational support for his theory right away, in
the perihelial advance of Mercury, and the deflection of starlight by
the Sun.

1916

German astrophysicist Karl Schwarzschild,
serving on the Russian front in WWI, mails Einstein his paper on the Schwarzschild
metric and Einstein presents it at a meeting of the Prussian Academy of
Sciences. Six months and another major paper later, Schwarzschild dies
of illness on the front.

1921

Theodor Kaluza follows Einstein's
advice and publishes his highly unorthodox ideas about unifying gravity
with electromagnetism by adding an extra dimension of space that is compactified
into a small circle. Kaluza-Klein compactification will become a rich
subject of exploration in particle theory 60 years later.

1925

Werner Heisenberg shows that his quantized
probability operators form a non-commutative algebra. Born and Jordan
point out to him that this is a matrix algebra, and the matrix formulation
of quantum mechanics is born. He gets the Nobel Prize in 1932.

1924

Louis duc de Broglie proposes the
particle-wave duality of the electron in his doctoral thesis at the Sorbonne.
He gets the Nobel Prize in 1929.

1926

After learning of the work of de Broglie,
Erwin SchrÃ¶dinger develops his wave equation version of quantum mechanics,
and unravels its relationship to the matrix formulation of quantum mechanics
by Heisenberg. He shares the Nobel Prize with Dirac in 1933.

1926

Young Cambridge math student Paul
Dirac discovers the operator algebra behind Heisenberg's Uncertainty Principle
for his doctoral thesis.

1927

Heisenberg discovers the Uncertainty
Principle that bears his name.

1928

Dirac introduces a relativistic quantum
equation for the electron, an equation now known as the Dirac
equation. His equation predicts the discovery of the positron,
and he shares the Nobel Prize with Schrodinger in 1933.

1928

Werner Heisenberg, Hermann Weyl and
Eugene Wigner begin an exploration of symmetry groups in quantum mechanics
that has far-reaching consequences.

1929

Edwin Hubble, with the help of his
mule driver Humason, observes the redshift of distant galaxies and concludes
that the Universe is expanding.

1931

Einstein stops using the cosmological
constant to keep the Universe from expanding.

1931

Dirac shows that the existence of
magnetic monopoles would lead to electric charge quantization.

1931

Georges De Rham goes to work on his
famous theorem in cohomology and characteristic classes, results that
would become very important in string theory.

1935

Young physicist Subramahnyan Chandrasekhar
is attacked by famous astronomer Arthur Eddington for his report that
there is a stellar mass limit beyond which collapse to what we now call
a black hole is inevitable. Chandrasekhar wins the Nobel Prize in 1983
for his work on stellar evolution.

1938

Wigner constructs a class of irreducible
unitary representations of the Lorentz group

1939

Elements de
Mathematique, by Nicholas Bourbaki, pseudonym for a group of young
mathematicians at the Ecole Normale in Paris, is begun. This extended
set of works aims to set down in writing what is no longer in doubt, but
rather on a boring and rigorous footing, in modern mathematics.

1943

Chinese mathematician Shiing-Shen
Chern begins his work on characteristic classes and fiber bundles that
will become an important tool for understanding quantum gauge theories
and string theory.

1948

Richard Feynman, Julian Schwinger
and Tomonaga Shin'ichiro report that the divergent integrals that plague
the quantum gauge field theory of electrodynamics (QED) can be sensibly
dealt with through the process of renormalization.

1953

Based on particle scattering data,
Murray Gell-Mann suggests that there is a new quantum number, called hypercharge,
which we now call stangeness and recognize as a part of the quark model
coming from the strange quark. Gell-Mann receives the Nobel Prize in 1969
for his work on the quark model.

1954

Gell-Mann and Francis Low develop
the idea that the physical content of a quantum theory should be invariant
under a change of scale in the theory. This is called renormalization
group, and it turns out to constrain quantum field theories enough to
make it a very powerful tool for analyzing asymptotic behavior of quantum
theories.

1954

C.N. Yang and R. Mills develop non-Abelian
gauge invariance, an idea that takes 17 years to gain acceptance, and
then revolutionizes particle physics.

1954

Eugenio Calabi conjectures the existence of a Kähler manifold
with a Ricci-flat metric with a vanishing first Chern class, and a given
complex structure and Kähler class. This funny-sounding stuff will
eventually become of major importance in understanding superstring theory.

1964

Cambridge mathematician Roger Penrose
proves that a black hole spacetime must contain behind the black hole
event horizon a singularity where spacetime physics ceases to make good
sense.

1964

Gell-Mann and George Zweig independently
propose fundamental particles that Gell-Mann succeeds in naming "quarks".

1964

Peter Higgs, Francois Englert and
R. Brout suggest a method of breaking quantum gauge symmetry that is later
called the Higgs mechanism.

1967

In his paper A
Model of Leptons, Steven Weinberg relies on Lie group theory combined
with quantum field theory to explain the weak nuclear and electromagnetic
forces in a single theory, using the Higgs mechanism to give mass to the
weak bosons. Adbus Salam and Sheldon Glashow share the Nobel Prize with
Weinberg in 1979 for Electroweak Theory.

1967

Sidney
Coleman and Jeffrey Mandula prove that well-behaved particle scattering
theories can't have symmetry algebras that relate particles of different
spin. But the strict consequences of the Coleman-Mandula Theorem were
avoided by the supersymmetry algebras that were discovered a few years
later.

1968

Michael Atiyah and Isadore Singer
begin their work on The Index of Elliptic Operators.
They prove the Atiyah-Singer index theorem, a powerful mathematical result
that will later be used extensively in theoretical physics.

1968

Gabriele Veneziano begins modern string
theory with his paper on the dual resonance model of the strong interactions.

1970

Yoichiro Nambu, Leonard Susskind,
and Holger Nielsen independently discover that the dual resonance model
devised by Veneziano is based on the quantum mechanics of relativistic
vibrating strings, and string theory begins.

1971

Gerard 't Hooft publishes his proof
that the electroweak gauge theory of Weinberg is renormalizable and a
new chapter in theoretical physics begins -- the age of quantum gauge
field theory.

1971

Pierre Ramond, André Neveu
and John Schwarz develop a string theory with fermions and bosons. Gervais
and Sakita show that this theory obeys what turns out to be a supersymmetry
algebra in two dimensions.

1971

Ken Wilson publishes work using the
renormalization group to understand the quantum behavior of systems undergoing
phase transitions, this opens up the study of critical phenomena in particle
physics and leads to greater understading of quark confinement. Wilson
wins the Nobel Prize in 1981.

1971

Soviet physicists Yuri Gol'fand and
E. Likhtman extend the Poincaré algebra into a superalgebra and
discover supersymmetry in four spacetime dimensions.

1973

David Gross, David Politzer, Frank
Wilczek and Gerard 't Hooft arrive at the conclusion that the coupling
constant in non-abelian quantum gauge theories vanishes at high energy.
This is called asymptotic freedom and is one of the major results in the
history of quantum gauge field theory.

1973

Quantum field theories with spacetime
supersymmetry in four spacetime dimensions are discovered by Julius Wess
and Bruno Zumino.

1974

Stephen Hawking combines quantum field
theory with classical general relativity and predicts that black holes
radiate through particle emission, behave as thermodynamic objects, and
decay with a finite lifetime into objects that we don't yet understand.

1974

Magnetic monopole solutions of non-Abelian
gauge field theories are found separately by 't Hooft and Moscow physicist
Alexander Polyakov.

1974

Joel Scherk and John Schwarz propose
string theory as a theory of quantum gravity, an idea that takes ten years
to be widely appreciated.

1974

Howard Georgi and Sheldon Glashow
propose SU(5) for a "Grand Unified Theory" (GUT) of all forces
except gravity, the theory predicts that protons could decay.

1975

Instanton solutions of Yang-Mills
equations are discovered by Belavin, Polyakov, A. Schwarz and Tyupkin.
This is exciting because instantons can tell us about non-perturbative
physics that is not approachable by other means of calculation.

1976

Shing-Tung Yau proves the Calabi conjecture
and discovers the Calabi-Yau space, an important development for later
progress in string theory.

1980

Alan Guth puts forward the idea of
an inflationary phase of the early Universe, before the Big Bang.

1981

Michael Green and John Schwarz develop
superstring theory.

1981

After Schoen and Yau do it in a more
traditional manner, Ed Witten uses supersymmetry to prove the positive
mass conjecture.

1982

Mathematician Karen Uhlenbeck shows
that Yang-Mills instantons discovered by physicists can be used as a powerful
analytical tool in abstract mathematics.

1983

Witten and Luis Alvarez-Gaumé
derive general formulas for gauge and gravitational anomalies in quantum
field theories in any dimension. They show that the gravitational anomalies
cancel in type IIB superstring theory.

1983

Mathematics graduate student Simon
Donaldson discovers exotic 4-manifolds, using instanton techniques learned
in part from Uhlenbeck.

1984

Michael Green and John Schwarz show
that superstring theory is free from quantum anomalies if the spacetime
dimension is 10 and the quantum gauge symmetry is SO(32) or E8 times E8.

1984

Gross, Harvey, Martinec and Rohm find
another class of anomaly-free superstring theories, and call it the heterotic
string theory.

1985

Candelas, Strominger, Horowitz and
Witten propose the use of Calabi-Yau spaces for the extra dimensions in
heterotic string theory.

1991

Connes and Lott develop non-commutative
geometry, which will find its way into the heart of string theorists at
the turn of the millennium.

1993

In search of an understanding of black
hole entropy, 't Hooft
suggests the idea that the information in a 3+1-dimensional system cannot
be greater than what is need to store it as an image in 2+1 dimensions.
Susskind generalizes this idea and applies it to string theory in his
paper The
World as a Hologram, and the Holographic Principle is born.

1994

Nathan
Seiberg and Ed Witten discover electric-magnetic duality in
N=2 supersymmetric gauge theory in four spacetime dimensions, with very
important applications in both mathematics and string theory.

1995

Witten
and Townsend
introduce the idea of Type IIA superstring theory as a special limit of
11-dimensional supergravity theory with quantized membranes. This begins
the M-theory revolution in superstring theory, and leads people to ponder
the role of spacetime in string theory.

1995

Andrew Wiles, with help from Richard
Taylor, completes a rigorous proof of Fermat's Last Theorem.

1995

Joseph
Polchinski ignites the D-brane revolution in string theory
with his paper describing extended objects in string theory formed by
dual open strings with Dirichlet boundary conditions.

1996

In their paper Microscopic
Origin of Black Hole Entropy, Andy Strominger and Cumrun
Vafa use D-branes to count the quantum states of an extreme black hole
and their result matches the Bekenstein-Hawking value. This stimulates
new respect for string theory from the relativity community.

1997

Juan
Maldacena finds that string theory in a background of five-dimensional
anti-de Sitter space times a five-sphere obeys a duality relationship
with superconformal field theory in four spacetime dimensions. The result,
called AdS-CFT duality, opens up a new era of exploration in string theory.