Israel Gelfand

Israel Gelfand (1913-2009) was one of the most influential mathematicians of the 20th century, making fundamental contributions across multiple areas of mathematics including functional analysis, algebra, and representation theory. His work spanned over six decades and resulted in more than 800 papers and 30 books. Gelfand's mathematical innovations include the Gelfand representation in Banach algebras, the Gelfand-Naimark theorem in operator theory, and the Gelfand-Fuks cohomology theory. He founded the Moscow school of mathematics and led one of the most significant mathematical seminars, which ran for nearly 50 years and shaped generations of mathematicians. Beyond pure mathematics, Gelfand made important contributions to applied mathematics and mathematical physics, particularly in the areas of generalized functions and integral geometry. He also worked on mathematical biology later in his career, applying mathematical methods to cell biology and protein folding. His dedication to mathematics education led him to create the Gelfand Correspondence Program in Mathematics, which provided distance learning opportunities for students in remote areas of the Soviet Union. After emigrating to the United States in 1989, he continued his research and teaching at Rutgers University until his death.

Readers consistently note Gelfand's dense, terse writing style in his mathematics texts. His books feature minimal exposition and explanations, requiring readers to work through proofs independently. On Goodreads, students appreciate the rigor and elegance of texts like "Linear Algebra" and "Calculus of Variations," but note they are best used as supplements rather than primary textbooks. Multiple reviewers mention needing to spend hours unpacking single paragraphs. Common complaints include: - Too few worked examples - Assumes high level of mathematical maturity - Can be frustratingly concise From Amazon reviews of "Method of Coordinates": "Forces you to think deeply but provides little guidance" "Not for self-study" "Rewards careful study but requires persistence" Average ratings: Goodreads: 4.2/5 (127 ratings) Amazon: 3.8/5 (43 ratings) Most readers recommend working through Gelfand's books with guidance from an instructor or after gaining foundation from more accessible texts.

Lectures on Linear Algebra - A comprehensive textbook covering vector spaces, linear transformations, and inner product spaces, originally published in Russian in 1948.

The Method of Coordinates - An introductory mathematics text explaining coordinate systems and their applications to geometry and algebra.

Functions and Graphs - A foundational text examining mathematical functions, their properties, and graphical representations.

Calculus of Variations - A detailed examination of variational principles and their applications in mathematics and physics.

Generalized Functions, Volume 1: Properties and Operations - First volume in a series covering the theory of distributions and generalized functions.

Representation Theory and Automorphic Functions - An advanced text connecting group representations with automorphic forms and complex analysis.

Commutative Normed Rings - A mathematical treatise on the theory of Banach algebras and normed rings.

Mathematics as an Education - A collection of essays discussing mathematical pedagogy and educational approaches.

Trigonometry - A systematic introduction to trigonometric functions and their applications, co-authored with E. G. Glagoleva and E. E. Schnol.

The Elementary Mathematics Library Series - A collection of accessible mathematics books covering various topics for students and teachers.