You are missing the point. The logic goes as follows: Logically constructed unproven argument: Statement x is true for all numbers with y property Now how do

You are missing the point. The logic goes as follows: Logically constructed unproven argument: Statement x is true for all numbers with y property Now how do you go about proving or disproving the argument: One way is to provide a general proof that it is true for all numbers. A way to disprove it is to find a single number that doesn't work. This is basically why people have been running huge computations trying to find a number that disproves the Riemann hypothesis. What this article essentially says is that we can transform the hypothesis in such a way that the space within which we have to search for that magical number that disproves it has a certain property.