At each stage of in the advance of mathematical thought the outstanding characteristics are novelty and originality. That is why mathematics is such … - George Frederick James Temple

The history of mathematics throws little light on the psychology of mathematical invention.

There is the definition [of mathematics], boldly proposed by Pierce that 'Mathematics is the science which draws necessary conclusions', and more explicitly formulated by Russel that 'Pure Mathematics is the class of all propositions of the form "p implies q"... it was... the purpose of Russell's treatise to provide a complete, exact and convincing justification of this definition... instead, he and Whitehead collaborated to give a magisterial account of the Principia Mathematica.

The 'language theory' is inadequate as a description of the nature of mathematics.