Can Planck scale dynamics be fully understood with the mathematical tools we have at hand today?

Answer 1

Possibly so. Possibly no. I'd say the Heisenberg uncertainty principle comes foremost into play here. Maybe also Schrödinger's cat. Is it dead or still alive? That would make a significant difference, you know. These questions can't just be taken so lightly. And how could you even consider Y!A as a forum to resolve such complex issues as this? More to the point, even assuming Planck scale dynamics can be fully understood with the mathematical tools we have at hand today, where exactly does that get us? We still don't know what topping to put on our pizza this weekend. Or whether a third eye would make a good chick magnet. Or even whether that darn cat is still alive or dead.... 'tis an enduring mystery. And we wouldn't want to take all the mysterious challenge out of life, now would we?....Meow.

Answer 2

Probably not, or someone would have solved the problem by now. History supports this too. Newton needed to invent calculus. Later theories like electromagnetism and quantum mechanics had to develop new notations and theorems to make progress (Guass's law, differential forms, orthonormal sets, Hilbert space, Feynman diagrams). Sometimes notation can make all the difference in terms of making progress, so I'd call notation useful "tools".