fields in the mathematical sciences are mature enough

researchers know the capabilities and limitations of the tools provided by their field, and they are seeking other tools from other areas

researchers know the capabilities of the tools provided by their field

there is greater interest in combinatorial methods

took up the modeling of the reentry dynamics of space flight through the upper atmosphere

gave rise to 20 years of remarkable development

showed the existence of solutions

took the equation as part of the need for the modeling of the reentry dynamics of space flight through the upper atmosphere

stability of solutions

the phenomenon of shock formation

some properties of solutions

existence, regularity, stability of solutions, as well as possible shock formation

a more flexible understanding of the process

kinetic theory

the equation involving the spatial interaction of probability densities of particles

no correct answer

 a reason

a result

a condition

an effect

the most important and surprising recent developments

swathes of geometry, representation theory, and topology

theoretical high-energy physics

no correct answer

There is no information about solving the problem

A vast theory relating complex manifolds and symplectic manifolds

The Jones polynomial

A mirror symmetry, discovered by physicists

the cross-fertilization between mathematics and physics

the practical problem of computing backgrounds for the Large Hadron Collider

the reformulation of the geometric Langlands program in terms of quantum field theory

using  the tools of algebraic geometry and some methods from geometric number theory

the sorts of connections are powerful

mathematical concepts may be explored

the mathematical sciences have benefited in recent years from valuable connections within the discipline itself

Lie theory, and representation groups have more recently been linked to physics

the idea of modeling of particles interacting at a rarefied scale underlies phenomena involving decision making in social behaviour

decision making involves social behaviour

the idea of modeling of particles interacting at a rarefied scale appeared in some fields

no correct answer