Biochemistry is broad and does really diverse things, and if your answer to "how does a mammalian brain allow it to reason through interactions with its physical environment" is "biochemistry", and that's also presumably the answer to "why is that pond scum green?" and "why are fingernails hard?", then it fails to be an explanation of any sort.
Similarly, if someone asks "why is your program dying on a division-by-zero error", it's not an explanation to say "well, that's just a matter of how the program executes when provided those particular inputs".
What _specifically_ about the biochemistry of our nervous systems allows us to solve problems, or communicate, as versus just metabolize sugar?
Consider that touch on the surface of my skin, which can be a few atoms of some object brushing a single cell -- that somehow "recuses up" the organic structure of my body (cell, tissue, organ, ...) both adapting it and coming to be "symbolically objectified" in my reasoning as "a scratch".
The relevant properties here are those that enable similar kinds of adaption (and physiological response) at all relevant scales from the cell to the organ to the whole-body.
I think cells-oragans-bodys are implementations of "scale-free adaption algorithms" (if you want to put it in those terms), which enable implementation of "higher-order intelligence algorithms".
If you want much much more than this, then even if I had the answer, it wouldnt be comment-sized, i'd be a textbook. But of course, no one has that textbook, or else we wouldnt be talking about this.
I think if you see cells as extremely self-reorganizing systems, and bodies as "recursive scale-free" compositions of "self-reorganizing adaptive systems", then you get somewhere towards the kinds of properties i'm talking about.
I think my ability to type because i can think, is a matter of that "organic recursion" from the sub-cellular to the whole-body.
We dont often describe reality with algorithms in the sciences, if reality admits a general algorithmic description, it is surely beyond any measurable level. So I dont think the answer to the problem of intelligence will require computer science till much later in the game; if it is even possible to actually artificially create it.
Whatever "algorithm" would comprehensively describe the relevant properties of cells, even if it could be written down, will never be implemented "from spec". One may as well provide the algorithm for "a neutron star" and expect playing around with sand will make one.