I don't know who the target audience was, but I found the lecture very confusing and the message really badly passed (he keeps talking what is already written in the slides, etc.). I had to play it at 1.6x the regular speed so I could move on with it.

Regarding the topic, I think there are multiple ways of expressing ideas, where math happens to be just one of them. For instance, for the Greatest Common Divisor example, you could just say that "if x equals y the cgd of x and y is x, else you need to keep subtracting the smallest number from the largest until both are equal".

You could use simple math, such as:

             / x if x=y
  gcd(x,y) = | gcd(x-y, y) if x > y
             \ gcd(x, y-x) if x < y

Or you could use code:

  def gcd(x,y):
      if x==y:
          return x
      elif x>y:
          return gcd(x-y, y)
      else:
          return gcd(x, y-x)

In essence, what I want to say is that his definition of beauty and power may not match mine, but I will not argue that math can be more succinct or allow for better abstractions in many cases.

In the end, I got the feeling that he is trying to "sell" us his TLA+ approach.