> Hint: if the first notation is so superior, why don't math papers use it.

Math papers usually use neither the first nor the second.

they use:

  (a + b)(c + d)

in the example you propose, and, reversing the operators so that the first style would have:

  (+ (* a b) (* b c))

and the second:

  (a * b) + (c * d)

math papers would usually have:

  ab + cd

So, I'm not sure "math papers do it differently" is the argument you want to use to advance your second syntax over the first.

Of course, since in lisp + and * are variadic rather than binary operators, they are a lot more like the pi and sigma operators applied to sets in mathematics than binary operators. Which are prefix, not infix. So, there's that.