Hilbert did not give a rigorous explanation of what he considered finitistic and refer to as elementary. However, based on his work with Paul Bernays some experts such as William Tait have argued that the primitive recursive arithmetic can be considered an upper bound on what Hilbert considered finitistic mathematics.
In the years following Godel's theorems, as it became clear that there is no hope of proving consistency of mathematics, and with development of axiomatic set theories such as Zermelo?Fraenkel set theory and the lack of any evidence against its consistency, most mathematicians lost interest in the topic. Today most classical mathematicians are considered Platonist and readily use infinite mathematical objects and a set-theoretical universe.[citation needed]
