Minkowski had created the full-blown four-dimensional mathematical formalism of spacetime physics before the end of 1907 (which could have been highly improbable if Minkowski had not been developing his own ideas), both indicate that Minkowski might have arrived at the notion of spacetime independently of Poincare (who saw it as nothing more than a mathematical space) and at a deeper understanding of the basic ideas of special relativity (which Einstein merely postulated) independently of Einstein. So, had he lived longer, Minkowski might have employed successfully his program of regarding four-dimensional physics as spacetime geometry to gravitation as well. Moreover, Hilbert (Minkowski's closest colleague and friend) had derived the equations of general relativity simultaneously with Einstein.Apparently Max Born credited Minkowski with discovering special relativity independently of Einstein's work.
Minkowski's version was deeper because he had a fully 4-dimensional spacetime view with Maxwell's equations being covariant under the Lorentz group. Einstein's view was similar to Lorentz's.
It is strange to say that Poincare saw spacetime as nothing more than a mathematical space.
In order to understand better what Minkowski could have done, had he lived longer, it is important to take explicitly into account two indications of why he appears to have realized independently the equivalence of the times of inertial observers in relative motion (what Einstein postulated and which formed the basis of his special relativity) and that the Lorentz transformations can be regarded as rotations in a four-dimensional world (which was first published by Poincare but he did not see anything revolutionary in that observation since he believed that physical theories do not necessarily represent anything in the physical world since they are nothing more than convinient descriptions of physical phenomena).I understand concluding that Minkowski had a much deeper understanding of relativity than Einstein, and would have gone farther if he had lived. But what is this cheap shot at Poincare?
Poincare also wrote about his philosophy of science, and understood that we could have two mathematically equivalent theories for the same physical phenomenon. One theory might be more convenient than the other. He was completely correct about this.
Somehow Petrov (and others) want to turn this around to say Poincare was just a mathematician doing convenient mathematics, and not physics. They say this as if it were possible for Poincare to get all the mathematics of relativity right without understanding the physics. Weird. It is hard to see how anyone could misunderstand the math and philosophy of Poincare so badly.
Minkowski's first paper on relativity did cite Poincare's long famous 1905 paper. It appears to me that Minkowski was strongly influenced by Poincare, but I guess it is possible that Minkowski came to some of the ideas independently.