I found this question on Quora.
I took “important” to mean “impactful”.
Here’s my answer:
The branch of science with the greatest impact on people historically is medicine. Its primary effect has been to prolong lives. Its secondary effect has been to allow people with prolonged life expectancy to affect other people and sciences. So it has a feedback loop which makes it very impactful.
The branch of science that will have the greatest impact on people in the future is artificial intelligence. Artificial intelligence has the potential to destroy humanity without even meaning to if it isn’t done just right. If done right, it will save humanity. Like medicine, it will have a feedback loop.