The letter I sent on March 7, 2022 to the office of the Rector of the Moscow State University, mathematician V. A. Sadovnichiy, in connection with his endorsement of Russia's invasion of Ukraine

Did you know: In one's afterlife, one is condemned to finding counter-examples to all false statements made in life?
Hence the advice: Start early!

From W. H. Aumer:

Two millenniums back / Euclid founded the science of Data.
Two Wikipedia lines / are all it merits to date.

Alexander GIVENTAL Here is a photo of mine (and here is of yours)

Office: 701 Evans Hall
Phone Number: 510-642-3660
Email address:
Postal Address:
Department of Mathematics
University of California Berkeley
Berkeley, California, 94720

  Vladimir   Arnold   (my teacher)
June 12, 1937 -- June 3, 2010
As a Matter of Thought   (English)   (Russian)
Links (at MCCME)   Photos (courtesy of S. Tretyakova)
A duck with ducklings


Math 140. Metric Differential Geometry. Spring'05.

Math 214. Differential Manifolds. Fall'07.

Math 104. Introduction to Analysis. Fall'11.

Math 123. Ordinary Differential Equations. Fall'11.

Math277. Riemann-Roch Formulas in Gromov-Witten Theory. Spring'13. CANCELLED

Math 104. Introduction to Analysis. Spring'15

Math 53. Mutivariable Calculus, Fall'15.

Math H110. Honors Linear Algebra. Fall'16.

Math 185. Introduction to Complex Analysis. Spring'17.

Math 115. Introduction to Number Theory. Spring'18

Math 141. Elementary Differential Topology. Fall'18

Math39A (Freshman/Sophomore Seminar). Onegin in English. Spring'19

Math 215A. Algebraic topology. Fall'19

Math 215B. Algebraic topology. Spring'20

Math 189. Math Methods of Classical and Quantum Mechanics. Fall'20

Math 191. Putnam workshop. Fall'20

Math H185. Complex Analysis. Spring'21

Math 242. Symplectic Geometry. Fall'21

Math H110. Honors Linear Algebra. Fall'22

Math H113, Honors Intro to Abstract Algebra. Fall'22

Math 191: Putnam workshop. Fall'22

Verse Translations from Russian


Laurent Lafforgue's "Why the Public Schools?"


Three points on the plane

The Pythagorean theorem: what is it about?

Singapore vs. California math textbooks

Is There Math on Mars? (for Tehiyah Day School Newsletter)

Ignorance at its best

The University of Chelm

Why Johnny won't be able to count

The incompetent enlightens the ignorant

Fourth grade science: Sharp and vibrant

Geometry of Surfaces

Linear Algebra

Linear Algebra

After using several iterations of this text in Math H110,
I have finally produced it as an e-book available at Sumizdat
together with about 100 sample pages.

Lectures on Groups, Rings, and Fields

Lectures on Groups, Rings, and Fields

This is my new e-textbook intended for Math H113.
It is available at Sumizdat . Here are sample lectures ,
which include the entire material on groups.

Introduction to Quantum Mechanics

Introduction to Quantum Mechanincs

Here are several sample chapters in PDF format.
Now complete with exercises and some solutions,
this book is not a work in progress anymore,
and is available in its entirety as an e-book.

Kiselev's Geometry. Book I. Planimetry Kiselev's Geometry. Book II. Stereometry


Kiselev's Geometry. Book I: Planimetry. Book II Stereometry Published by SUMIZDAT - a publisher that promotes nonsense-free mathematics and science curricula.

This is an English adaptation of a classical textbook in plane geometry which has served well several generations of middle- and high-school students in Russia. Available from Sumizdat , (Book I) and (Book II)

Please visit Sumizdat Home Page , examine the book, and if you like it, make a link from your website to in order to bring the book closer to students and their teachers.

Arithmetic for Parents

Ron Aharoni. Arithmetic for Parents.
A book for grownups about children's mathematics

Several years ago Ron Aharoni, Technion, accepted his friend's invitation to teach mathematics in elementary school. Since then he devoted much of his time to primary mathematics education.
Aharoni played a major role in a successful fight against "fuzzy math" in his country, and in the implementation of a competent, no-frills curriculum (based on Primary Math from Singapore).
In this book, he shares with the reader -- a parent, or a teacher -- the insights he gained concerning elementary mathematics and mathematical education.
Available from Sumizdat , and

Marina Tsvetaeva. To You -- in 10 Decades
Selected Russian Poetry Rendered in English

This new arrival (available at and ) is a joint work of Alexander Givental and Elysee Wilson-Egolf. It includes poetry by Marina Tsvetaeva, with contributions by Bella Akhmadulina and Arseny Tarkovsky, and commentaries in English.

Her poetry's the fruit of passion. So is this book of side-by-side translations from the pliant Russian into the English tongue. We tried not simply to preserve the music, rhyme, rhythm, meter, gist, or gems, but all of the above, refusing to compromise - a stance that stems from love for the expressions of that fascinating act of Nature called M. Tsvetaeva. This love, together with the sense of grandeur of the phenomenon in view, are what we hope to spark in you.

Math Circle by the Bay. Topics for Grades 1--5
by Laura Givental, Maria Nemirovskaya, and Ilya Zakharevich
Based on years of teaching math circles at UC Berkeley and Stanford
Available at the AMS Bookstore and Amazon,com

Math Circles for Elementary School Students
A book by
Natasha Rozhkovskaya (KSU)
based on her teaching in 2009
at the Berkeley Math Circle
Available in Russian at
and in English translation
at the AMS bookstore and

Lecture notes

Linear algebra and differential equations   Published by AMS

Topics in enumerative algebraic geometry   Accessed here (ps and pdf)

Discrete Mathematics   A 40-page-short comprehensive textbook for the sophomore-level college course, by Alexander Borisovich

BTW, the author asked us to thank E. Wilson-Egolf for editing his manuscipt.

Research papers available online (pdf)

Quantum K-theory of grassmannians and non-abelian localization (with Xiaohan Yan)
Permutation-equivariant quantum K-theory I--XI
Virasoro constraints for toric bundles (with Tom Coates and Hsian-Hua Tseng)
Kepler's laws and conic sections. Irina Boyadzhiev from Ohio State U provided the following visualization for this paper.
Explicit reconstruction in quantum cohomology and K-theory
The Hirzebruch-Riemann-Roch theorem in true genus-0 quantum K-theory (with Valentin Tonita)
Soliton equations, vertex operators, and simple singularities (with Edward Frenkel and Todor Milanov)
Quantum cobordisms and formal group laws (with Tom Coates)
PhD thesis (2003) of Tom Coates (without A.G.): Riemann-Roch theorems in Gromov-Witten theory"
Symplectic geometry of Frobenius structures
Simple singularities and integrable hierarchies (with Todor Milanov)
A_{n-1}-singularities and nKdV hierarchies
Quantum Riemann-Roch, Lefschetz and Serre (with Tom Coates)
Gromov-Witten invariants and quantization of quadratic hamiltonians
Semisimple Frobenius structures at higher genus
Introduction to symplectic field theory (with Yakov Eliashberg and Helmut Hofer)
Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups (with Yuan-Pin Lee)
On the WDVV-equation in quantum K-theory
Singularity theory and symplectic topology
A tutorial on quantum cohomology
Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture
The mirror formula for quintic threefolds
Elliptic Gromov-Witten invariants and the generalized mirror conjecture
A mirror theorem for toric complete intersections
Equivariant Gromov-Witten invariants
Homological geometry and mirror symmetry
Homological geometry I. Projective hypersurfaces
Quantum cohomology of flag manifolds and Toda lattices (with Bumsig Kim)
A symplectic fixed point theorem for toric manifolds
Whitney singularities of solutions of partial differential equations
Singular Lagrangian varieties and their Lagrangian mappings (based on my PhD thesis)