Will it halt?

This is perhaps the most important thing we should like to know about any process. OK I agree it doesn’t seem like an important thing to know. What’s the big deal? So lets just say, I have it with me: I have an algorithm to determine whether an algorithm will halt or not and it is always right. I call it $h(a,i)$. It takes any algorithm $a$ as it’s first input and an input string $i$, algorithm $a$ will work on, as its second input. It i.e. $h(a,i)$ returns “will halt” or “will not halt” as its output.

Imagine what I could do with this $h(a,i)$! I can prove the Goldbach’s conjecture and get the Field’s Medal with it. More importantly, I can prove everything and win all the field’s medals forever. ROFL!

OK here is how I will do it. But first, Goldbach’s conjecture:

Every even integer greater than 2 can be written as the sum of two primes.

Nobody has proved it as such. Distributed supercomputers have verified this to be true until $10^{18}$. But hey! I have $h(a,i)$! So I write a program $p(i)$ that loops over all possible even integers greater than $i$ and halts whenever it finds an even number that cannot be written as sum of two primes. Now the best part is I don’t even have to run $p$ till the end of time. All I have to do is run $h(p, 2)$. If it returns “will not halt”, then Goldbach’s conjecture is true or else it is false! What more evidence do we need than to know all even numbers greater than two can be written as sum of two primes? LOL!

Similarly, I could use $h(a,i)$ to prove everything and anything!