Ibragimov was born on January 18, 1939, in Urussu, in the Soviet Union (now in the Republic of Tatarstan in the Russian Federation).
He later dedicated the first volume of his selected works to Larisa Petrovna Barkhat, one of his schoolteachers in Urussu, and to the other teachers there.
[2] After Army service, he entered the Moscow Institute of Physics and Technology, but then transferred to Akademgorodok and then to Novosibirsk State University, from which he graduated in 1965.
His dissertation, Group properties of some differential equations, was supervised by Lev Ovsyannikov [ru; de].
[2] Yvonne Choquet-Bruhat recalls that he moved from Johannesburg because his wife and daughters found life there "excessively difficult" compared to the "smaller and more peaceful" town of Mmabatho and its University of Bophuthatswana, where she visited him.