Open Problems In Mathematics And Physics (original) (raw)
OPEN QUESTIONS
GENERAL
Science magazine 125 big questions
MATHEMATICS (PHYSICIST'S PERSPECTIVE)
Unified theory: Langlands Program, Witten on Langlands,
Theory of "motives"
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
Mathworld list Mathematical challenges of the 21st centuryincluding moduli spacesand borderland physics
Goldbach conjecture
Normality of pi digits in an integer base Unsolved problems and difficult to understand areas
PRICES Fields Medal and Rolf Nevanlinna Prize Abel Prize
PHYSICS
Important unsolved problems in physics Quantum gravity
Explaining high-Tc superconductors
Complete theory of the nucleus
Realizing the potential of fusion energy
Climate prediction
Turbulence
Glass physics
Solar magnetic field
Complexity, catastrophe and physics
Consciousness
Peter Woit's list
Riemannian geometry
More general geometry of principal and vector bundles: connection, curvature, etc.
Spinor geometry
Lie groups and representation theory
deRham cohomology
Another list from the European Journal of Physics
Learn it all in one fell swoop
Nature's greatest puzzles at SLAC
PRICES Nobel Prize for physics Wolff
COSMOLOGY AND ASTROPHYSICS
Eleven key questions about the universe
Inflation
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)
Brane cosmology
QUANTUM GRAVITY
Problem of continuous approaches: parametrization of the dynamical degrees of freedom in a diffeomorphism invariant way
Problem of infinity of vacua
Top ten string theory questions
String theory
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?
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
Stephen Hawking
Problem: show the classical limit of smooth space-time can be recovered
Discrete approaches
a variant: causal dynamical calculations
Causal sets (Rafael Sorkin, ...)
Problem: cannot mimic general relativity at large scales
Hamiltonian or spin networkapproach
Lagrgangian approach or spin foam models
Emerging properties (Sakharov induced gravity, ...)
CONDENSED MATTER
List of open questions including condensed matter problems
PARTICLE PHYSICS
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
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
Non-linear dynamics
Evolutionary dynamics
Cellular automata
Self-organising systems
Networks
PARADOXES
Monty Hall, Gamow-Stern, Kruskal, Cantor, Banach-Tarski List of paradoxes
Open questions in financial econometrics
Forecasting Economic and Financial Time Series Using Nonlinear Methods
Scientific study of financial data