Modern philosophy of mathematics is still in part shaped by debates starting well over a century ago, springing from the work of Frege and Russell, from Hilbert

Modern philosophy of mathematics is still in part shaped by debates starting well over a century ago, springing from the work of Frege and Russell, from Hilbert’s alternative response to the “crisis in foundations”, and from the impact of Gödel’s work on the logicist and Hibertian programmes. I wonder what the author thinks of Van Plato, The Great Formal Machinery Works and other works on the history of the foundational mathematics. One of the things that stands out in the book is that when notions of mathematical logic and foundations of arithmetic were being formulated by Frege and Grassman in the 19th century, neither the notation nor the concept of proof as a mechanical process existed and the process of creating theories about proof processes also involved laying down the concept of proof and creating tractable notations for it (Frege's original notation quickly becomes incomprehensible as expressions grow, for example). Principia Mathematica is notable for creating modern notation despite it's failure to be a complete foundation of mathematics.