Eminent Ukrainian Orientalist, belletrist, linguist, literary scholar, folklorist, and translator; full member of the All-Ukrainian Academy of Sciences (VUAN) (and later Academy of Sciences of the Ukrainian SSR) from 1918 and the Shevchenko Scientific Society from 1903. A graduate of Galagan College in Kyiv (1889), the Lazarev Institute of Oriental Languages in Moscow (1891), and Moscow University (1896), he conducted research in Syria and Lebanon (1896–8) and then taught at the Lazarev Institute, from 1900 as professor of Arabic literature and from 1902 also as professor of Oriental history. He was an active member of Moscow's Ukrainian Hromada. His political views were greatly influenced by Mykhailo Drahomanov, Ivan Franko, and Pavlo Tuchapsky. In July 1918 Krymsky moved to Kyiv. There he helped to found the VUAN and its library and served as the first VUAN permanent secretary and de facto director until the Soviet government brought about his defeat in the VUAN elections of 1929. He edited 20 of the 25 volumes of Zapysky Istorychno-filolohichnoho viddilu VUAN (1920–9) and was a professor at Kyiv University as well as the vice-president of the Ukrainian Scientific Society in Kyiv (from 1918). Krymsky survived the Stalinist terror of the 1930s although for nearly 10 years he was removed from scholarly and pedagogical activity. Apparently rehabilitated in 1939, he was, however, arrested by the NKVD in July 1941, and disappeared.

As an Orientalist (an expert in up to 34 languages) Krymsky contributed several hundred entries to the prerevolutionary Brockhaus and Efron and Granat Russian encyclopedias and wrote many other works on Arabic, Turkish, Turkic, Crimean Tatar, and Iranian history and literature. He wrote, in Russian, pioneering textbook histories of Islam (3 parts, 1904–12); of Turkey and its literature (2 vols, 1910, 1916); of the Arabs and their literature (3 parts, 1911–13); of Persia, its literature, and Dervish theosophy (3 vols, 1901–6, 1909–14); and a study of the Semitic languages and peoples (3 parts, 1903–12). In Ukrainian he also wrote histories of Turkey and its literature (2 vols, 1924, 1927) and of Persia and its literature (1923); monographs on Hafiz and his songs (1924) and on the Turkic peoples, their languages, and literatures (1930); edited a collection of articles on the Crimean Tatars (1930); and wrote, with O. Boholiubsky, a study of Arab higher education and the Arabian Academy of Sciences (1928). During the last years of his life he wrote a six-volume history of the Khazars; it was never published.

As a belletrist Krymsky is known for his three books of lyrical poetry on Oriental themes entitled Pal’move hillia: Ekzotychni poeziï (Palm Branches: Exotic Poems, 1901, 1908, 1922), the novella Andrii Lahovs’kyi (1905, 1972), the collection Povistky i eskizy z ukraïns’koho zhyttia (Narratives and Sketches from Ukrainian Life, 1895), and the collection Beiruts’ki opovidannia (Beirut Stories, 1906).