In the mathematical theory of knots, the Kontsevich invariant, also known as the Kontsevich integral of an oriented framed link, is a universal Vassiliev invariant in the sense that any coefficient of the Kontsevich invariant is of a finite type, and conversely any finite type invariant can be presented as a linear combination of such coefficients.
 It was defined by Maxim Kontsevich.
In mathematics, specifically in symplectic topology and algebraic geometry, one can construct the moduli space of stable maps, satisfying specified conditions, from Riemann surfaces into a given symplectic manifold.
 This moduli space is the essence of the Gromov–Witten invariants, which find application in enumerative geometry and type IIA string theory.
 The idea of stable map was proposed by Maxim Kontsevich around 1992 and published in .
Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich.
 It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory.
Mark Grigorievich Krein (Ukrainian: Марко Григорович Крейн , Russian: Марк Григо́рьевич Крейн ; 3 April 1907 – 17 October 1989) was a Soviet Jewish mathematician, one of the major figures of the Soviet school of functional analysis.
 He is known for works in operator theory (in close connection with concrete problems coming from mathematical physics), the problem of moments, classical analysis and representation theory.
Motivic integration is a notion in algebraic geometry that was introduced by Maxim Kontsevich in 1995 and was developed by Jan Denef and François Loeser.
 Since its introduction it has proved to be quite useful in various branches of algebraic geometry, most notably birational geometry and singularity theory.
 Roughly speaking, motivic integration assigns to subsets of the arc space of an algebraic geometry, a volume living in the Grothendieck ring of algebraic varieties.
 The naming 'motivic' mirrors the fact that unlike ordinary integration, for which the values are real numbers, in motivic integration the values are geometric in nature.
In probability theory, the Markov–Krein theorem gives the best upper and lower bounds on the expected values of certain functions of a random variable where only the first moments of the random variable are known.
 The result is named after Andrey Markov and Mark Krein.
In mathematics, the Kontsevich quantization formula describes how to construct a generalized ★-product operator algebra from a given arbitrary Poisson manifold.
 This operator algebra amounts to the deformation quantization of the corresponding Poisson algebra.
 It is due to Maxim Kontsevich.
Operad theory is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity.
 Operads generalize the various associativity properties already observed in algebras and coalgebras such as Lie algebras or Poisson algebras by modeling computational trees within the algebra.
 Algebras are to operads as group representations are to groups. Originating from work in algebraic topology by Boardman and Vogt, and J. Peter May, it has more recently found many applications, drawing for example on work by Maxim Kontsevich and Thomas Willwacher on graph homology.
Letters in Mathematical Physics is a peer-reviewed scientific journal in mathematical physics published by Springer Science+Business Media.
 It publishes letters and longer research articles, occasionally also articles containing topical reviews.
 It is essentially a platform for the rapid dissemination of short contributions in the field of mathematical physics.
 In addition, the journal publishes contributions to modern mathematics in fields which have a potential physical application, and developments in theoretical physics which have potential mathematical impact.
 The editors are Volker Bach, Edward Frenkel, Maxim Kontsevich, Dirk Kreimer, Nikita Nekrasov, Massimo Porrati, and Daniel Sternheimer.
Maxim Lvovich Kontsevich (Russian: Макси́м Льво́вич Конце́вич ;   ; born 25 August 1964) is a Russian and French mathematician.
 He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami.
 He received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Fundamental Physics Prize in 2012, and the Breakthrough Prize in Mathematics in 2014.

Question: Which mathematician received the Breakthrough Prize in Mathematics in 2014, Maxim Kontsevich or Mark Krein?
Answer: Maxim Lvovich Kontsevich