A) verifiable proof generation (a limited closed set of axioms and a minimal algorithm like Metamath's are enough to verify correct vs incorrect machine intuition, plus feeding back the rejection/acceptance to adjust the machine intuition)
B) optimizing an illposed problem (how do we define the inaccessible fitness function)
Yes the field of biology or medicine will advance faster, but only because the mathematics and physics will advance faster, any non-axiomatic or non-postulate ramifications actually depend on unknown variables like fitness functions etc. How do you model the environment? That model will necessarily be oversimplified. What makes us believe that a long tail of ever less frequent distinct failure modes (like cancers, cancer is not a single problem) can not be guessed. It would require oracles and crystal balls: if global warming brings malaria mosquito's up north, then "eliminating sickle cell anemia" can actually turn into a death sentence instead of a life-long disease, but perhaps malaria will not come to higher latitudes, it depends on the future!
I'm not making a maximalist argument; we might just be compatible here. But I'm not saying that life sciences will be accelerated solely because mathematics is advanced; I'm saying life sciences will be accelerated because the models make/accelerate discoveries in life sciences. The same mechanism that's enabling mathematics discoveries applies to other sciences, and while I get the sense that some people on this thread think of life science as bench science, an increasing amount of it is computational to begin with.
A) verifiable proof generation (a limited closed set of axioms and a minimal algorithm like Metamath's are enough to verify correct vs incorrect machine intuition, plus feeding back the rejection/acceptance to adjust the machine intuition)
B) optimizing an illposed problem (how do we define the inaccessible fitness function)
Yes the field of biology or medicine will advance faster, but only because the mathematics and physics will advance faster, any non-axiomatic or non-postulate ramifications actually depend on unknown variables like fitness functions etc. How do you model the environment? That model will necessarily be oversimplified. What makes us believe that a long tail of ever less frequent distinct failure modes (like cancers, cancer is not a single problem) can not be guessed. It would require oracles and crystal balls: if global warming brings malaria mosquito's up north, then "eliminating sickle cell anemia" can actually turn into a death sentence instead of a life-long disease, but perhaps malaria will not come to higher latitudes, it depends on the future!