Because there is an infinite amount of numbers, there is also an infinite amount of prime numbers. These numbers space more and and more apart the larger the numbers get, but eventually, there will always be another number that doesn't hit anything to divide it by. It makes sense that the pattern of prime numbers continues into infinity, along with the numbers.
I'm not a mathematician. If he says so, then I'm inclined to agree with him. I find it easy to believe that there could be an infinite number of twin primes since there are an infinite amount of numbers. Although, I have to say either way I really don't care.
I agree that Zhang's surmise is correct and that there must be infinite pairs of prime numbers. My understanding of theoretical mathematics is not perfect but from the evidence and findings that I have reviewed it seems almost self-apparent to me that infinite pairs of prime numbers must exist within the field of mathematics.
Zhang's theory that there are an infinite number of twin prime numbers has not be proven. These are prime numbers in which is two or less away from each other. These become increasingly rare as numbers increase, as logic would dictate since there will be a greater chance it can be divisible.