These discoveries, and some others that have not been mentioned, are important in understanding why many theories about the nature of mathematics have failed to pass the test of time. They always existed. The end result was already there. Platonism asserts that a mathematician is an empirical scientist who can only discover what is already there. He or she can't invent new mathematics.
Mathematical truth possesses absolute certainty.
Formalists assert that mathematics must be developed through axiomatic systems. Formalist and Platonists agree on the principles of mathematical proof, but Hilbert's followers don't recognize an external world of mathematics. Formalists argue that are no mathematical objects until we create them. Humans create the real number system by establishing axioms to describe it. All mathematics needs is inference rules to progress from one step to the next.