His research spans several applications, from nuclear studies to astrophysics, and has contributed significantly to the field of sensitivity analysis.

[1] Ilya Meyerovich Sobol’ recognizes Aleksandr Khinchin, Viktor Vladimirovich Nemytskii, and A. Kolmogorov as his teachers.

In 1958, Sobol’ started to work on pseudo-random numbers, then to move on developing new approaches which were later called quasi-Monte Carlo methods (QMC).

The results were previously published in his well-known monograph "Multidimensional Quadrature Formulas and Haar Functions" [2] Sobol’ applied Monte Carlo methods in various scientific fields, including astrophysics.

He was actively working with a prominent physicist Rashid Sunyaev on Monte-Carlo calculations of X-ray source spectra which led to discovery of the Sunyaev-Zel'dovich effect, which is due to electrons associated with gas in galaxy clusters scattering the cosmic microwave background radiation.

[9][10] The key property of Sobol’ sequences is that they provide greatly accelerated convergence rate in Monte Carlo integration when compared with what can be obtained using pseudo-random numbers.

His achievements in astrophysics include application of Monte Carlo methods to the mathematical simulation of X-ray and gamma spectra of compact relativistic objects.