Pull back a bit while watching this lecture.
Don’t think about the math itself. Observe the performance of the math, the presentation of the math, the steps of making a case for the math.
As the performance grows in sophistication (more examples, more tools, more context, more words) the understanding of the mathematical objects directly is offloaded to the understanding of the performance itself. Can you follow the performance on any level and any subset of the performance (any scene or photo or graft) without the full performance?
Unlikely. When we seek to explain a complex phenomena or pattern or set of objects (events, history, society, etc) our theories and explanations become at least as complex as the thing they explain.
So in the specific case of this lecture about the prime numbers… the explanations of the prime numbers becomes more complex than just looking at the prime numbers themselves.
that’s not a bad thing or an end of science/math thing. It is the only way it could work and is the direct result that there is a conservation of computation (aka conservation of information, energy, momentum) in reality. We compute, we do not create more computation, we just compute within the whole with the whole. (you can think more deeply about this by measuring how much energy the professors life has used, how much energy is computers use, the projector users, the audience uses… all to share in this understanding of “the primes”…. you will not have found more computational capability in the universe because of this lecture, somewhere there was computation lost by the gain of those in the room.)
Math is a computational performance within the wider space of everything. As soon as it “explains” something it opens up an equal amount of stuff it doesn’t explain.
more simply: the more you know the more you know you don’t know.