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Nash's major contributions, as far as I know, are the following:

1. His work on game theory. EDIT: This is viewed by many mathematicians as being more important to economics than mathematics. However, see the answer by Gil Kalai (someone else whose views should be taken much more seriously than mine).

2. His famous work on the existence of smooth isometric embeddings of Riemannian manifolds into Euclidean space. As Denis Serre mentions, he developed in this paper what is now known as the Nash-Moser implicit function theorem, which has been used in other applications.

3. His work on regularity of solutions to elliptic and parabolic PDE's, which were also obtained, I believe independently by Moser and DiGorgi. This is perhaps his most cited work.

4. His theorem about how any Riemannian manifold has a $C^1$ isometric embedding as a codimension 2 submanfold of Euclidean space. Kuiper showed that the embedding could be actually a hypersurface (codimension 1). This is perhaps his most spectacular theorem. Recently, De Lellis, László Székelyhidi, and their collaborators have used Nash's original "twist" construction to obtain new results on Onsager's conjecture, which is about the apparently totally unrelated topic of fluid dynamics.

Nash's influence on mathematics (and on my own work) is enormous.

Nash's major contributions, as far as I know, are the following:

1. His work on game theory. EDIT: This is viewed by many mathematicians as being more important to economics than mathematics. However, see the answer by Gil Kalai (someone else whose views should be taken much more seriously than mine).

2. His famous work on the existence of smooth isometric embeddings of Riemannian manifolds into Euclidean space. As Denis Serre mentions, he developed in this paper what is now known as the Nash-Moser implicit function theorem, which has been used in other applications.

3. His work on regularity of solutions to elliptic and parabolic PDE's, which were also obtained, I believe independently by Moser and DiGorgi. This is perhaps his most cited work.

4. His theorem about how any Riemannian manifold has a $C^1$ isometric embedding as a codimension 2 submanfold of Euclidean space. Kuiper showed that the embedding could be actually a hypersurface (codimension 1). This is perhaps his most spectacular theorem. Recently, De Lellis, László Székelyhidi, and their collaborators have used Nash's original "twist" construction to obtain new results on Onsager's conjecture, which is about the apparently totally unrelated topic of fluid dynamics.

Nash's influence on mathematics (and on my own work) is enormous.

Nash's major contributions, as far as I know, are the following:

1. His work on game theory. EDIT: This is viewed by many mathematics as being more important to economics than mathematics. However, see the answer by Gil Kalai (someone else whose views should be taken much more seriously than mine).

2. His famous work on the existence of smooth isometric embeddings of Riemannian manifolds into Euclidean space. As Denis Serre mentions, he developed in this paper what is now known as the Nash-Moser implicit function theorem, which has been used in other applications.

3. His work on regularity of solutions to elliptic and parabolic PDE's, which were also obtained, I believe independently by Moser and DiGorgi. This is perhaps his most cited work.

4. His theorem about how any Riemannian manifold has a $C^1$ isometric embedding as a codimension 2 submanfold of Euclidean space. Kuiper showed that the embedding could be actually a hypersurface (codimension 1). This is perhaps his most spectacular theorem. Recently, De Lellis, László Székelyhidi, and their collaborators have used Nash's original "twist" construction to obtain new results on Onsager's conjecture, which is about the apparently totally unrelated topic of fluid dynamics.

Nash's influence on mathematics (and on my own work) is enormous.

Nash's major contributions, as far as I know, are the following:

1. His work on game theory. EDIT: This is viewed by many mathematicians as being more important to economics than mathematics. However, see the answer by Gil Kalai (someone else whose views should be taken much more seriously than mine).

2. His famous work on the existence of smooth isometric embeddings of Riemannian manifolds into Euclidean space. As Denis Serre mentions, he developed in this paper what is now known as the Nash-Moser implicit function theorem, which has been used in other applications.

3. His work on regularity of solutions to elliptic and parabolic PDE's, which were also obtained, I believe independently by Moser and DiGorgi. This is perhaps his most cited work.

4. His theorem about how any Riemannian manifold has a $C^1$ isometric embedding as a codimension 2 submanfold of Euclidean space. Kuiper showed that the embedding could be actually a hypersurface (codimension 1). This is perhaps his most spectacular theorem. Recently, De Lellis, László Székelyhidi, and their collaborators have used Nash's original "twist" construction to obtain new results on Onsager's conjecture, which is about the apparently totally unrelated topic of fluid dynamics.

Nash's influence on mathematics (and on my own work) is enormous.

Nash's major contributions, as far as I know, are the following:

1. His work on game theory. This was more important to economics than mathematics.

2. His famous work on the existence of smooth isometric embeddings of Riemannian manifolds into Euclidean space. As Denis Serre mentions, he developed in this paper what is now known as the Nash-Moser implicit function theorem, which has been used in other applications.

3. His work on regularity of solutions to elliptic and parabolic PDE's, which were also obtained, I believe independently by Moser and DiGorgi. This is perhaps his most cited work.

4. His theorem about how any Riemannian manifold has a $C^1$ isometric embedding as a codimension 2 submanfold of Euclidean space. Kuiper showed that the embedding could be actually a hypersurface (codimension 1). This is perhaps his most spectacular theorem. Recently, De Lellis, László Székelyhidi, and their collaborators have used Nash's original "twist" construction to obtain new results on Onsager's conjecture, which is about the apparently totally unrelated topic of fluid dynamics.

Nash's influence on mathematics (and on my own work) is enormous.

Nash's major contributions, as far as I know, are the following:

1. His work on game theory. EDIT: This is viewed by many mathematics as being more important to economics than mathematics. However, see the answer by Gil Kalai (someone else whose views should be taken much more seriously than mine).

2. His famous work on the existence of smooth isometric embeddings of Riemannian manifolds into Euclidean space. As Denis Serre mentions, he developed in this paper what is now known as the Nash-Moser implicit function theorem, which has been used in other applications.

3. His work on regularity of solutions to elliptic and parabolic PDE's, which were also obtained, I believe independently by Moser and DiGorgi. This is perhaps his most cited work.

4. His theorem about how any Riemannian manifold has a $C^1$ isometric embedding as a codimension 2 submanfold of Euclidean space. Kuiper showed that the embedding could be actually a hypersurface (codimension 1). This is perhaps his most spectacular theorem. Recently, De Lellis, László Székelyhidi, and their collaborators have used Nash's original "twist" construction to obtain new results on Onsager's conjecture, which is about the apparently totally unrelated topic of fluid dynamics.

Nash's influence on mathematics (and on my own work) is enormous.