It's an interesting perspective but I can't say I agree.
"I argue that there are many more cases where math is ineffective (non-compact) than when it is effective (compact). Math only has the illusion of being effective when we focus on the successful examples. But our successful examples perhaps only apply to a tiny portion of all the possible questions we could ask about the universe."
These are limitations of our models rather than of mathematics itself. The world is complex and necessitates complex mathematics but that doesn't mean math isn't the best approach or isn't the "mother tongue" of the physical world. Ultimately we can describe the entire physical universe with math.