> you can solve algebraic equations or calculus problems just by “pushing around the symbols”. But why can you do that? Where is the meaning, and how do the sym

> you can solve algebraic equations or calculus problems just by “pushing around the symbols”. But why can you do that? Where is the meaning, and how do the symbols capture the meaning? How does that work? The fact that symbols in general can somehow convey meaning is a deep philosophical mystery The correspondance between symbols and meaning can and has been studied rigorously — it’s a main theme of Gödel Escher Bach and I’d recommend reading it if you find these kind of questions fascinating, even though it doesn’t have much to say about notation. The basic idea is that mathematical notation is working as a formal system whose semantics correspond to those of arithmetic. By pushing around symbols you’re applying inference rules of the formal system that encode axioms of mathematics.