Can someone explain the "cognitive" logic of the math here? I find it impossible to concentrate or learn math without understanding the underlying meaning as much 'physically' as possible (I wonder if that's a problem or a virtue by the way). I had to prove that 1/P(A) + 1/(P(A') >= 4 given that 0<P(A)<1 The solution goes on to prove it by concluding that (2P(A)-1)^2 >= 0 which is true after transformations on the initial formula (P(A') = 1 - P(A) if you're unaware of it). Now, the thing is, how is that explained cognitively? What is the logical position of that last squaring there in the end? How does that "start" the logic of it (or ends it)? I mean, I see the math doing it, but not the cognitive logic behind it. If someone does not know of the solution, is there a cognitive meaning that would derive it early? Did someone just come up with the solution and did calculations to reach the initial to-be-proven formula? Does that mean it's just 'normal' to be 'unpredictable'?