First of all, math isn’t real any more than language isn’t real. It’s an entirely human construct, so it’s possible you cannot reach AGI using mathematical means, as math might not be able to fully express it. It’s similar to how language cannot fully describe what a color is, only vague approximations and measurements. If you wanted to create the color green, you cannot do it by describing various properties, you must create the actual green somehow.
As a somewhat colorblind person, I can tell you that the "actual green" is pretty much a lie :)
It's a deeply philosophical question what constitutes a subjective experience of "green" or whatever... but intelligence is a bit more tractable IHO.
I don't think it would be unfair to accept the brain state of green as an accurate representation of green for all intents and purposes.
Similar to how "computer code" and "video game world" are the same thing. Everything in the video game world is perfectly encoded in the programming. There is nothing transcendent happening, it's two different views of the same core object.
Fair enough. But then, AGI wouldn't really be based on math, but on physics. Why would an artificially-constructed physical system have (fundamentally) different capabilities than a natural one?