Background: I am a complete layman in computer science.
I was reading about Busy Beaver numbers here, and I found the following passage:
Humanity may never know the value of BB(6) for certain, let alone that of BB(7) or any higher number in the sequence.
Indeed, already the top five and six-rule contenders elude us: we can’t explain how they ‘work’ in human terms. If creativity imbues their design, it’s not because humans put it there. One way to understand this is that even small Turing machines can encode profound mathematical problems. Take Goldbach’s conjecture, that every even number 4 or higher is a sum of two prime numbers: 10=7+3, 18=13+5. The conjecture has resisted proof since 1742. Yet we could design a Turing machine with, oh, let’s say 100 rules, that tests each even number to see whether it’s a sum of two primes, and halts when and if it finds a counterexample to the conjecture. Then knowing BB(100), we could in principle run this machine for BB(100) steps, decide whether it halts, and thereby resolve Goldbach’s conjecture.
Aaronson, Scott. "Who Can Name the Bigger Number?" Who Can Name the Bigger Number? N.p., n.d. Web. 25 Nov. 2016.
It seems to me like the author is suggesting that we can prove or disprove the Goldbach Conjecture, a statement about infinitely many numbers, in a finite number of calculations. Am I missing somehing?