An example from Biology field I like is Dr. Stephen Quake, a physicist expecting a child, who was shockingly observing invasive Down syndrome tests done to his wife and an unborn baby. The general knowledge at the time was that the only deterministic test was amniocentesis, a painful procedure, which carries a risk of miscarriage. Biologists were exploring other options of blood testing, showing that there is baby’s blood contained in mother’s blood as well, therefore one could potentially get baby’s DNA there, searching for Down syndrome markers. However, they only got to the point of “it could be done but the error margin is too high”, without actually calculating this error. What happened is Dr. Quake reading existing research on the topic, writing down some equations and figuring out that if you run the test many times, the error is reduced significantly and result becomes practically deterministic. And he had statistical methods at disposal to prove his case. Based on his conclusions a device was designed and is now commonly used for screening of not just Down syndrome but many other things. What has happened is that by bringing “tools” from other fields into biology, a whole new world opened, which now makes it possible to do detailed DNA testing, new types of drugs, etc.