Hauy’s theory accounted for crystal shapes and symmetries, and more. Why can crystals of the same species have different geometric forms? Because the stacks of bricks can be completed in different ways! Why is the pentagonal dodecahedral form of pyrite never quite regular? Because the vertices of crystals have rational coordinates!

Contemporary science, the mathematician P. L. Chebyshev told him, was not interested in this subject. Undiscouraged, Fedorov persisted. He knew that Camille Jordan, in his 1868 “Memoire sur les groupes des mouvements,” had generalized lattices to orbits of groups of orientation- preserving motions (rotations, translations, and screw-rotations). http://mathcenter.spb.ru/nikaan/book/fedorov_math.pdf

X-ray diffraction showed that the crystal structure of rocksalt – known to be cubic – is a checkerboard arrangement of Na and Cl atoms. Top Row: Fedorov had expected to see an arrangement of NaCl molecules like this. Bottom Row: A plane in the actual structure. There is no way to group Na and Cl atoms into “molecules” in a pattern with cubic symmetry.

Картинка с пиритом, где видны пятиугольники https://www.ebay.com/itm/Pyritohedron-Pyrite-Crystals-Shiny-Golden-Perfect-Pentagonal-Facets-/123288435360

и я в питерской вышке читаю спецкурс о топологическом анализе данных, слайды тут (и далее там же будут) http://mathcenter.spb.ru/nikaan/2020/topdata.pdf

Владимир Абрамович Рохлин, 1919-1984 http://mathcenter.spb.ru/nikaan/book/rokhlin_bio.pdf Биография настолько богатая, что прям всю статью надо по абзацам сюда скидывать.

V.A. Rokhlin was born in Baku (the capital of Azerbaijan). V.A.’s mother originated from a well-to-do Jewish family of a businessmen who had arrived from Ukraine. She was a physician with a European medical education. She perished when V.A. was 4 years old during the epidemic disorder in Baku in 1923; perhaps it could be a murder by a rioting crowd. V.A.’s father, a Belorussian Jew, was an economist and social- democrat who had irreconcilable differences with Bolsheviks. He was exiled to Kazakhstan in the 1930s and later was arrested and executed in 1942.

During his student years he studied simultaneously set theoretical topology with Pavel Alexandrov; measure theory and dynamics with Andrei Kolmogorov; functional analysis with Israel M. Gelfand and Lazar Lusternik; group theory, algebra and topology with Lev Pontryagin; and operator theory with Abram Plesner. All of them suggested V.A. some problems and he successfully solved some of them; during his undergraduate years, Rokhlin published two research papers. All those mathematicians gave him recommendations for graduate school (“aspirantura”) under their supervision.

Near Vyazma, Rokhlin’s regiment was surrounded by the Germans, he was wounded in both legs and left in a village in the care of locals. Since his wounds did not heal, he was put into a local hospital in the territory occupied by the Germans. After a denunciation, the Germans arrested him and sent to a prisoner-of-war camp; he became ill with typhoid, recovered, was transferred to a camp in Belorussia, then in Poland; several times he attempted to escape.
He was able to conceal his ethnicity; he knew very well German (he spoke it without any Jewish accent) and Azerbaijani. He was liberated as late as 1944 by the Red Army. After a short period of army service as an interpreter, he was again arrested on May 1945, in Berlin, now by NKVD, and spent almost two years in Stalin’s camp on suspicion of being a traitor.

Later he said that he pretended that he did not remember anybody from German camps, because he was heavily wounded, thus he could not be caught on discrepancies and can not slander anybody. Finally he was acquitted.

Rokhlin managed to send a secret letter (a note thrown from the train) to his fianc ́ee Ariadna. She knew A. Kolmogorov and then informed him that V.A. was in prison. Kolmogorov and Pontryagin wrote a letter to the chief of NKVD with a request to free V.A. Rokhlin.

Through war and camps he carried a cahier were he wrote his ideas and plans. During the next one and half years after his liberation he instantly defended both dissertations (candidate and doctoral).

The beginning of 1950 was marked in the Soviet Union by the antisemitic campaign. Rokhlin was fired from Steklov Institute (allegedly being told that he could not stay there even if he would compute all the homotopy groups of all spheres) and thus he was forced to leave Moscow together with his family since they had no apartment and no job.

In Leningrad, he modernised the program of the mathematical department, in particular he introduced an obligatory course of topology, first in the country and may be in the world. He passed to faculty some innovations which became traditions, such as serious seminars on important topics for the freshman bachelor students.

Два текста Вершика о Рохлине http://www.mathsoc.spb.ru/pantheon/rokhlin/vershik1.pdf http://www.mathsoc.spb.ru/pantheon/rokhlin/vershik2.pdf

Относительные гомологии H_k(X,A) не всегда равны H_k(X/A), для этого обычно требуют, чтобы A было окрестностым деформационным ретрактом, но самое общее требование — что (X,A) — пара Борсука или корасслоение. Собрал всё, что надо о них знать http://mathcenter.spb.ru/nikaan/2020/borsuk.pdf А то местами что-то неправильное пишут (и в книгах, и в википедии)

Говорят, так выглядит вселенная. Пустоты (войды, с поэтическими названиями — Супервойд Гончих Псов) и галактические нити. К этому делу можно применять устойчивые гомологии (а как ещё это изучать, видно же, что структура есть, и надо считать её инварианты)

Стопоходящий механизм Чебышева. Размером примерно с большой аквариум. Старое дерево, выглядит очень классно. Музей матмеха.

а вот об этом на этюдах с видео.

А вот, как подсказывает Лев, современная инкарнация этой жажды роботов (красиво, огромный робот ходит от силы ветра — такое можно купить, дуешь, и он двигается)

А вот, как подсказывает Лев, современная инкарнация этой жажды роботов https://www.youtube.com/watch?v=LewVEF2B_pM

Михлин, символ сингулярного оператора, многомерные сингулярные операторы, как это привело к индексу оператора, которое потом привело к теореме Атья-Зингера о индексе http://mathcenter.spb.ru/nikaan/book/mikhlin_math.pdf