Weinstein was born in New York City.^[1] After attending Roslyn High School,^[2] Weinstein obtained a bachelor's degree at the Massachusetts Institute of Technology in 1964. His teachers included, among others, James Munkres, Gian-Carlo Rota, Irving Segal, and, for the first senior course of differential geometry, Sigurður Helgason.^[2] He received a PhD at University of California, Berkeley in 1967 under the direction of Shiing-Shen Chern. His dissertation was entitled "The cut locus and conjugate locus of a Riemannian manifold".^[3]

Weinstein worked then at MIT on 1967 (as Moore instructor) and at Bonn University in 1968/69. In 1969 he returned to Berkeley as assistant professor and from 1976 he is full professor. During 1975/76 he visited IHES in Paris^[2] and during 1978/79 he was visiting professor at Rice University. Weinstein was awarded in 1971 a Sloan Research Fellowship^[4] and in 1985 a Guggenheim Fellowship.^[5] In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki.^[6] In 1992 he was elected Fellow of the American Academy of Arts and Sciences^[7] and in 2012 Fellow of the American Mathematical Society.^[8] In 2003 he was awarded an honorary doctorate from Universiteit Utrecht.^[9][10]

Weinstein's works cover many areas in differential geometry and mathematical physics, including Riemannian geometry, symplectic geometry, Lie groupoids, geometric mechanics and deformation quantization.^[2][11]

Among his most important contributions, in 1971 he proved a tubular neighbourhood theorem for Lagrangians in symplectic manifolds.^[12]

In 1974 he worked with Jerrold Marsden on the theory of reduction for mechanical systems with symmetries, introducing the famous Marsden–Weinstein quotient.^[13]

In 1978 he formulated a celebrated conjecture on the existence of periodic orbits,^[14] which has been later proved in several particular cases and has led to many new developments in symplectic and contact geometry.^[15]

In 1981 he formulated a general principle, called symplectic creed, stating that "everything is a Lagrangian submanifold".^[16] Such insight has been constantly quoted as the source of inspiration for many results in symplectic geometry.^[2][11]

Building on the work of André Lichnerowicz, in a 1983 foundational paper^[17] Weinstein proved many results which laid the ground for the development of modern Poisson geometry. A further influential idea in this field was its introduction of symplectic groupoids.^[18][19]

He is author of more than 50 research papers in peer-reviewed journals and he has supervised 35 PhD students.^[3]

• Geometric Models for Noncommutative Algebras (with A. Cannas da Silva), Berkeley Mathematics Lecture Notes series, American Mathematical Society (1999)^[20]
• Lectures on the Geometry of Quantization (with S. Bates), Berkeley Mathematics Lecture Notes series, American Mathematical Society (1997)^[21]
• Basic Multivariable Calculus (with J.E. Marsden and A.J. Tromba), W.A. Freeman and Company, Springer-Verlag (1993), ISBN 978-0-387-97976-2
• Calculus, I, II, III (with J.E. Marsden), 2nd ed., Springer-Verlag (1985), now out of print and free at CaltechAUTHORS.^[22][23][24]
• Calculus Unlimited (with J.E. Marsden), Benjamin/Cummings (1981), now out of print and free at CaltechAUTHORS.^[25]