For most of the twentieth century, if you studied higher mathematics in Russia, you worked from one problem book. This is its first English edition. Günter and Kuzmin's Collection of Problems in Higher Mathematics began in 1912 as a working set of problems compiled by the mathematics department of the Institute of Engineers of Ways of Communication in St Petersburg. It grew to three volumes, ran to a thirteenth edition, and became the standard problem book of the Soviet universities and the higher technical institutes alike. Russian biographical accounts record that its problems supplied the mathematics of the entrance examination Lev Landau set his prospective students — the celebrated "theoretical minimum." Here is the part most people don't know. The two men who assembled it were not textbook compilers. They were working research mathematicians, and it shows on every page. RODION KUZMIN (1891–1949) left two permanent results. In 1928 he settled a question Gauss had raised and left unanswered — the limiting distribution of the partial quotients of a continued fraction — and was the first to prove it with an estimate of the rate of convergence. The theorem and the distribution now carry Gauss's name and his. In 1930 he proved that a^b is transcendental whenever a is a positive algebraic number other than 1 and b is a real quadratic irrational. So 2^√2 is transcendental. That is a case of Hilbert's seventh problem, and he got there four years before Gelfond and Schneider settled it in general. He was expelled from Petersburg University for student politics, finished his degree at Petrograd in 1916, and held the chair of general mathematics at Leningrad University from 1945 until his death. NIKOLAI GÜNTER (1871–1941) was taught by Korkin, Markov and Possé — the direct line of Chebyshev's school. Doctorate in 1915 on the characteristics of systems of partial differential equations. Professor from 1916 until his death. Corresponding member of the USSR Academy of Sciences from 1924. His treatise on potential theory was published in Paris in 1934, in Borel's collection at Gauthier-Villars, and reviewed in the English mathematical press on publication. He led the higher mathematics department at the Institute of Engineers of Ways of Communication from 1906, and for long stretches taught at four institutions at once, across some four decades. Günter died in 1941. Kuzmin finished the last revision alone and signed its preface from Biysk, in 1944, a long way from Leningrad. WHAT IS IN THE BOOK 6,314 problems, numbered continuously from 1 to 6,314, running from analytic geometry in the plane through to the calculus of variations and the theory of probability. Higher algebra, integration, multiple and surface integrals, ordinary and partial differential equations, special functions, series, approximate computation, complex variables, mathematical physics. The theoretical interludes that make the problems usable sit exactly where a working student needs them — not in an appendix. a.co/d/07jMUsK1

The guy who likes to flaunt trivial math books on Twitter is shocked to learn that Russia doesn’t treat calculus as a separate subject… it just doesn’t exist as a subject. That’s true. What they study instead is mathematical analysis. Much deeper and harder subject. China 🇨🇳 does the same. Calculus is for school kids. See what that looks like on Awesome Math Books. For example Nikolsky trilogy that is used at MIPT. github.com/valeman/Awesome_M… Calculus was a separate subject at Imperial Russian schools. 14 year olds studied it. In modern day USA calculus has become a university level subject and even that half of Berkeley students can’t cope with. russianmathbooks.com/books/k…

The guy who likes to flaunt trivial math books on Twitter is shocked to learn that Russia doesn’t treat calculus as a separate subject… it just doesn’t exist as a subject. That’s true. What they study instead is mathematical analysis. Much deeper and harder subject. China 🇨🇳 does the same. Calculus is for school kids. See what that looks like on Awesome Math Books. For example Nikolsky trilogy that is used at MIPT. github.com/valeman/Awesome_M… Calculus was a separate subject at Imperial Russian schools. 14 year olds studied it. In modern day USA calculus has become a university level subject and even that half of Berkeley students can’t cope with. russianmathbooks.com/books/k…

The guy who likes to flaunt trivial math books on Twitter is shocked to learn that Russia doesn’t treat calculus as a separate subject… it just doesn’t exist as a subject. That’s true. What they study instead is mathematical analysis. Much deeper and harder subject. China 🇨🇳 does the same. Calculus is for school kids. See what that looks like on Awesome Math Books. For example Nikolsky trilogy that is used at MIPT. github.com/valeman/Awesome_M… Calculus was a separate subject at Imperial Russian schools. 14 year olds studied it. In modern day USA calculus has become a university level subject and even that half of Berkeley students can’t cope with. russianmathbooks.com/books/k…

The guy who likes to flaunt trivial math books on Twitter is shocked to learn that Russia doesn’t treat calculus as a separate subject… it just doesn’t exist as a subject. That’s true. What they study instead is mathematical analysis. Much deeper and harder subject. China 🇨🇳 does the same. Calculus is for school kids. See what that looks like on Awesome Math Books. For example Nikolsky trilogy that is used at MIPT. github.com/valeman/Awesome_M… Calculus was a separate subject at Imperial Russian schools. 14 year olds studied it. In modern day USA calculus has become a university level subject and even that half of Berkeley students can’t cope with. russianmathbooks.com/books/k…

This is very cool. 😎 Revolut is piloting a new facial recognition payment system in London that allows customers to pay for items with a “simple glance”. The Pay with Smile feature will be available at participating businesses using Revolut Register terminals, with the pilot launching in London on Thursday. thetimes.com/article/3b522a5…

Absolutely no hate to arxiv, I appreciate everything theyve done. this is just genuine question but why does arxiv need 17.2M$ to maintain its exact same website that didnt change for 20 years? Like surely you just need couple servers? Not like they are using CDNs for this Can someone clue me on this

To those of you who say it’s DNA that makes you English, I would say this: You don’t know what you’re talking about. Our DNA is already mixed up. Have a look at your own DNA. Dare I say, you want to take the beam out of your own eye before you take the mote out of the eye of others. We English are not, and nor should we be seen as, some eugenically pure island race. We are a people who have values and culture and strengths and liberties. People who join that should be incorporated in it and encouraged in it, rather than made to feel foreign. But I would say to those who come here and wish to maintain their culture, that they are making a grave mistake. They have come here because of the strength of Englishness. They should join in with it and not hold themselves out as something separate. The condition for coming is to become English, to be part of this great enterprise, not to remain a foreigner in these lands. ✍️ Jacob Rees-Mogg Article | spectator.com/article/the-en…