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.
The Formalists tried to prove that within the framework of established axioms, theorems, and definitions, a mathematical system is consistent. In the mid-twentieth century, formalism became the predominant philosophical attitude in math textbooks. Godel's Incompleteness Theorem contradicts the consistency philosophy of formalism. It has been pointed out that accepted results from theorems were used before axioms were created to establish the theorems. This school claims that mathematics is a vast tautology.