Born on May 6th, 1936 in Warsaw, Poland. Studied elementary and high school gym until 1953. His early scholar interests were the history, geography, painting and drawing. Planning to study architecture. However, in 1952, under the influence of science fiction
(S. Lem) and popular literature his interests were attracted to cosmic ships and travels, and he decided to study physics.
In the summer of 1953 he begins his own studies of mathematical analysis. In the autumn of 1953 he starts the studies in the Faculty of MathematicalPhysics at the University of Warsaw. Due to his lack of dedication to the laboratories, his plans to specialize in the propulsion vessels evaporated, but the interest in abstract mathematics survived. In 1954, he presents a student contribution to the proof of HahnBanach theorem (published by W. Sikorski). Antagonized by an excess of purely calculational problems and by mandatory courses of "Political Science".
Since 1956 his interest changed to special relativity and quantum mechanics. At the end of 1957, master work undertaken by the direction of Jerzy Plebanski, on soluble cases of quantum evolution. The first encounters with the problem of BakerCampbellHausdorff (BCH). Between september 1958 and november 1962 he collaborates with Jerzy Plebanski and serves as an assistant at the Conference Jablonna Relativity in 1962. Coauthor of popular articles collected in the book: J. Plebanski, S. Bazanski, B Mielnik, J. Ryten, "Znane i Nieznane" Iskry 1963.
In 1962 he is invited to the newly opened Research Center IPN (CINVESTAV), in Mexico, as an assistant of Dr. Jerzy Plebanski. His first stay in CINVESTAV covered the period November 1962 to April 1965. As an assistant in the newly created Physics Department, (CINVESTAV) he taught courses on the mathematical formalism of quantum mechanics, working on the calculus of finite differences and pseudoHermitian operators. In 1964 he obtained his Ph.D. for a thesis on finite differences, under the direction of Dr. J. Plebanski.
Back in Warsaw (19651981), he works at the Institute of Theoretical Physics (ITF UW), continuing his interest in BCH formula. As a result of polemic discussions in the group of Professor Leopold Infeld, his interests shifted into the foundations of quantum mechanics. Between 1968 and 1976 published a sequence of works on the geometry of quantum theories. In 1973, he takes advantage of relative freedom of discussion in Poland, participating in the round table discussions of the weekly "Polityka"  against the plans to cut funds for basic sciences in order to strengthen the applied ones. His belief is that the science and technology form one organism, in which all organs are needed. If we cut the head off a cat, he will not grow a more splendid tail ("Polityka" 15.XII.1973, pag. 1).
From 19751980, due to his work on quantum geometry he is invited to Goteborg, Sweden (by N. Svartholm), King's College, London (F. Pirani), Imperial College (TW Kibble), Royal Inst of Technology, Stockholm ( B. Nagel), Hamburg (R. Haag), Marburg (G. Ludwig), Paris (M. Flato), Rockefeller University (M. Kac), Yeshiva University (D. Finkelstein), Genova, Italy (E. Beltrametti), Madrid, Univ Compultense (A. Galindo), Barcelona (P. Pascual), Geneva (C. Piron). Topics of discussion: What is necessary and what is superfluous in the formalism of Hilbert spaces in quantum mechanics. The control of quantum states and the "Doctor Faustus problem" of quantum systems. In 1976 and 1978 he attends the IAMC and Silarg conferences in Mexico.
In 1981 a basic change occurs in his curriculum. In November 1981, he comes with a short visit to CINVESTAV. However, in December 13, 1981, the martial law was declarated in Poland (to defend the tottering Communist regime against the Solidarity movement). News about repression against the disobedient intellectuals, convince him to accept the position in Mexico. In a gesture of friendship, colleagues in Warsaw assure him a latent position in ITF UW. From 1981 to 1986, he works in the Physics Department, CINVESTAV, on quantum evolution. He teaches quantum mechanics producing a hand written textbook, studies the deformed oscillators, collaborating with David Fernandez.
Between 1986 and 1987, he is back in ITF UW in Poland, occupying the position of Docent with teaching duties in mathematical physics and classical electrodynamics. He undertakes didactic experiments in order to make the material understandable.
In 1987, back in Mexico, in the Physics Department, CINVESTAV, he teaches courses in quantum mechanics, classical electrodynamics and mathematical methods of physics.
Because of the agreement between the Physics Department and the ITF UW Warsaw, he divideds his time between the CINVESTAV and ITF UW, working on quantum control. In 1989 he was nominated Professor of Physics at the University of Warsaw. In 1990, his simultaneous work comes to an end. After his sabbatical leave in Warsaw, Mielnik decides to stay permanently in Mexico.
Currently, he is Professor in Physics Department, CINVESTAV, a member of the Mexican Academy of Sciences, International Association of
Matematical Physics, National Research System III. He belongs to the Advisory Board of the Workshop on Geometry Methods in Physics, Bialowieza (ecological reserve)
Poland. His hobbies include history, sciencefiction, travel. Interested in ecology: instead of cutting jungles and developing the bureaucracy, he proposes to defend jungles and cut the bureaucracy.
