|Lists of unsolved problems|
|Science magazine 125 big questions|
|MATHEMATICS (PHYSICIST'S PERSPECTIVE)|
Sir Michael Atiyah's Fields Lecture (.ps)
|Unified theory: Langlands Program, Witten on Langlands,|
Theory of "motives"
|Lists of unsolved problems|
Long standing open problems PRICE
P versus NP
The Hodge Conjecture
The Poincaré Conjecture (solved)
The Riemann Hypothesis
Yang-Mills Existence and Mass Gap
Navier-Stokes Existence and Smoothness
The Birch and Swinnerton-Dyer Conjecture
Mathematical challenges of the 21st centuryincluding moduli spacesand borderland physics
Normality of pi digits in an integer base
Unsolved problems and difficult to understand areas
Fields Medal and Rolf Nevanlinna Prize
|Important unsolved problems in physics|
Explaining high-Tc superconductors
Complete theory of the nucleus
Realizing the potential of fusion energy
Solar magnetic field
Complexity, catastrophe and physics
|Peter Woit's list|
More general geometry of principal and vector bundles: connection, curvature, etc.
Lie groups and representation theory
|Another list from the European Journal of Physics|
|Learn it all in one fell swoop|
|Physics Today (NRC)|
|Learn it all on the web|
|John Baez's list|
|David Gross list|
|Nature's greatest puzzles at SLAC|
Nobel Prize for physics
|COSMOLOGY AND ASTROPHYSICS|
|Eleven key questions about the universe|
|Survey Of The Universe|
Linde-Vilenkin, inflation (horizon, flatness, density-fluctuation) Photons, ordinary visible matter, ordinary nonluminous matter, MACHOs, exotic dark matter WIMPs, dark energy, Standard model, supersymmetry, technicolor, string theory, M-theory, Multiverses (eternal inflation, Smolin, ekpyrosis)
|Black holes and nonlocality|
|What they look like:|
Connes-Chamseddine spectral action
|Survey of quantum gravity|
|Problem of continuous approaches: parametrization of the dynamical degrees of freedom in a diffeomorphism invariant way|
|Problem of infinity of vacua|
|Top questions in M-theory|
|Top ten string theory questions|
|Ten physics problems for the next millenium from the Strings 2000 Conference|
Are all the (measurable) dimensionless paramters that characterize the physical universe calculable in principle or are some merely determined by historical or quantum mechanical accident and uncalculable?
How can quantum gravity help explain the origin of the universe?
What is the lifetime of the proton and how do we understand it?
Is nature supersymmetric and if so, how is supersymmetry broken?
Why does the universe appear to have one time and three space dimensions?
Why does the cosmological constant have the value that it has, is it zero and is it really constant?
What are the fundamental degrees of freedom of M-theory (the theory whose low-energy limit is eleven-dimensional supergravity and which subsumes the five consistent superstring theories) and does the theory describe nature?
What is the resolution of the black hole information paradox?
What physics explains the disparity between the gravitational scale and the typical mass scale of the elementary particles?
Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap?
|What are twistors?|
|Problems: construct a quantum theory of gravity from some basic principles assuming noncommutative geometry (John Madore, ...) or express some sector or limit of an underlying theory in terms of the language of noncommutative geometry|
|Euclidean quantum gravity|
|Problem: show the classical limit of smooth space-time can be recovered|
|a variant: causal dynamical calculations|
|Causal sets (Rafael Sorkin, ...)|
|Problem: cannot mimic general relativity at large scales||Loop quantum gravity|
|Hamiltonian or spin networkapproach|
|Lagrgangian approach or spin foam models|
|Emerging properties (Sakharov induced gravity, ...)|
|List of open questions including condensed matter problems|
|Standard model open questions|
|Areas of research|
|Technicolour: the unifying symmetry is a scaled-up version of the strong force|
|Unnaturalness problem: original calculation in which the introduction of the Higgs boson in the standard model gives it and the Z and two W infinite mass|
|Supersymmetry: for every fermion in the standard model, there is a corresponding supersymmetric boson, and vice versa|
|Failure to account for gravity|
|Theories of extra dimensions: there are at least five dimensions and a single new particle, a gravitational boson called a graviton|
|Flavour problem: why are they three and only three generations of fermions and why do the particles in each generation have the masses that they do?|
|Hierarchy problem: why do the different forces operate at such different energies, are they all manifestations of the same underlying phenomenon, and if they are, can they be united mathematically?|
|COMPLEX AND CHAOTIC SYSTEMS|
|Monty Hall, Gamow-Stern, Kruskal, Cantor, Banach-Tarski|
List of paradoxes
|PHYSICS OF FINANCE|
|Future of econometrics|
|Open questions in financial econometrics||Evolutionary finance|
|Forecasting Economic and Financial Time Series Using Nonlinear Methods|
|Scientific study of financial data|
|UNSOLVED PROBLEMS IN BIOLOGY|
|SEVENTY OPEN QUESTIONS IN ARCHEOLOGY|
|NINE UNDECIPHERED LANGUAGES|