The first one isn't really math-heavy, but it is symbol heavy (and there seem to have been some typos in the LaTeX or errors in generation, some subscripts are borked). The actual translation of the first image to Python-esque code is:

  def r(some_params):
    if predicate_11(some_params): return s(f1(some_params))
    else: return s(f2(some_params))
  def s(some_params):
    if predicate_21(some_params): return r(some_params)
    else: return t(f3(some_params))
  def t(some_params):
    if predicate_31(some_params): return f4(some_params)
    elseif predicate_23(some_params): return r(some_params)
    else: return t(f3(some_params))

I've replaced pi with `predicate` and xi with `some_params`.

The second one, structurally, can also be understood without knowing math but what's actually executed does require some familiarity with math. It's, like above, using a conditional expression described earlier and the lambda notation for defining anonymous functions (to be clear, he also uses it as an example of something that's not quite valid since the name `sqrt` will not be bound inside the lambda, but we can approximate it, invalid multi-line Python lambda incoming):

  sqrt = lambda a, x, epsilon: if abs(x*x - a) < epsilon: return x        # that is, we've found a close-enough approximation
                               else: return sqrt(a, (x+a/x)/2, epsilon)   # get a closer approximation to the square root

The previous line of code in that section (no lambda) is equivalent to a Python def:

  def sqrt(a,x,epsilon):
    if abs(x*x-a) < epsilon: return x
    else: return sqrt(a, (x+a/x)/2, epsilon)

(NB: All the extra `return`s have to be added because Python is not an expression-oriented language. The language McCarthy is describing is so each expression produces a new value without the need for explicit returns.)

Both of those are there to motivate the introduction of the label form at the bottom of that section.

Yes, you need to not run away as soon as a non-alphanumeric symbol is used. That's hardly even mathematical notation.