Of course I don't have a mathematical proof that P = NP cures cancer. Nor would an efficient algorithm for SAT immediately give a cancer cure. But it could work as follows:
- We need an appropriately shaped protein that would inhibit the cancer cells for a specific individual without harming the healthy cells. P = NP would help find these shapes perhaps just the DNA of the person and the type of cancer.
- At this point we don't understand the process that takes a ACGT protein sequence and describes that shape that it forms. But it must be a simple process because it happens quickly. So we can use P = NP to find a small circuit that describes this process.
- Use P = NP to find the protein sequence that the circuit from #2 will output the shape from #1.
Please note this is just a thought exercise since I strongly believe that P ≠ NP. I do not want to give false hope to those with friends and loved ones with the disease. If you want to cure cancer your first step should not be "Prove P = NP".