Schinzel was a professor at the Institute of Mathematics of the Polish Academy of Sciences (IM PAN). His principal interest was the theory of polynomials. His 1958 conjecture on the prime values of polynomials, known as Schinzel's hypothesis H, both extends the Bunyakovsky conjecture and broadly generalizes the twin prime conjecture. He also proved Schinzel's theorem on the existence of circles through any given number of integer points.