''Arnold's Problems'' is a book edited by Soviet mathematician

Vladimir Arnold Vladimir Igorevich Arnold (or Arnol'd; , ; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to s ...

, containing 861

mathematical problem A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the Solar System, or a problem of a more ...

s from many different

areas of mathematics Mathematics is a broad subject that is commonly divided in many areas or branches that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the u ...

. The book was based on Arnold's seminars at

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

. The problems were created over his decades-long career, and are sorted chronologically (from the period 1956–2003). It was published in Russian as ''Задачи Арнольда'' in 2000, and in a translated and revised English edition in 2004 (printed by

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

). The book is divided into two parts: formulations of the problems, and comments upon them by 59 mathematicians. This is the largest part of the book. There are also long outlines for programs of research.

Notable problems

The problems in ''Arnold's Problems'' are each numbered with a year and a sequence number within the year. They include: *1956–1, the

napkin folding problem The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis na ...

, on whether a paper rectangle can be folded to a shape with larger perimeter than the rectangle *1972–33, the

Arnold conjecture The Arnold conjecture, named after mathematician Vladimir Arnold, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry. Strong Arnold conjecture Let (M, \omega) be a closed (compact without boundary) ...

, on the number of fixed points of a Hamiltonian diffeomorphism *There are many questions related to the

Hilbert–Arnold problem In mathematics, particularly in dynamical systems, the Hilbert–Arnold problem is an list of unsolved problems in mathematics, unsolved problem concerning the estimation of limit cycles. It asks whether in a generic property, generic finite-para ...

: 1978–6, 1979–16, 1980–1, 1983–11, 1989–17, 1990–24, 1990–25, 1994–51 and 1994–52.Bravo, J. L., Mardešić, P., Novikov, D., & Pontigo-Herrera, J. (2025). "Infinitesimal and tangential 16-th Hilbert problem on zero-cycles". ''Bulletin Des Sciences Mathématiques'', 202, 103634. https://doi.org/10.1016/j.bulsci.2025.103634 https://arxiv.org/abs/2312.03081

References

2000 non-fiction books Mathematics books Translations into English

External link

«Математика в высшем образовании», №10 (2012)
(in Russian) {{Math-book-stub