The revolution was clearly explained: it's the formalism viewpoint, most famously expounded by Hilbert, "mathematics is a game played with meaningless symbols f

The revolution was clearly explained: it's the formalism viewpoint, most famously expounded by Hilbert, "mathematics is a game played with meaningless symbols following rules on paper." What this means is that we can discuss mathematics discarding all personal biases and intuitions. We can give personal meaning to these meaningless symbols and abstract rules, but we don't need these biases when communicating to each other nor when we actually have to perform computations or deductions. The example given at the end is fractions, you can think of fractions in terms of pies and pizzas, but it's much more effective to ignore any of that when it comes to actually perform computations with that and simply focus on the "meaningless" symbols and manipulations that you do with them. It's a pity that you tl;dr'ed this.