Radiology, Mathematics, Artificial Intelligence, And Human Understanding

Recently, mathematician Steven Strogatz wrote an excellent essay describing the upheaval within the world of mathematics caused by the latest advances in artificial intelligence. His article is well worth reading, but one passage in particular caught my eye. He quoted Curtis McMullen, a math professor at Harvard and a Fields Medalist: “Mathematics is not radiology. It is more like art or philosophy, and in fact, human understanding is what it is all about.”

Strogatz elaborated on this point, noting that in arenas like radiology we don’t understand exactly how AI arrives at a conclusion, but physicians will act on the results anyways: “If an AI model correctly predicts that you’re at heightened risk of developing breast cancer in the next five years, should you care that it can’t explain why, and neither can your radiologist? When lives are at stake, understanding becomes less urgent than just knowing the answer.”

As a radiologist, I’d like to respond to his question. Just for background, I have been a practicing radiologist for over 30 years. I also have an undergraduate degree in mathematics from MIT (but not a PhD). My father was a PhD mathematics professor for many years before he retired, and I have gotten to know many excellent radiologists and mathematicians over the years.

I completely recognize that for mathematicians, understanding how a result was derived or how a theorem was proved is of paramount importance. This is the heart of contemporary research mathematics.

However, radiologists also strongly desire fundamental understanding of disease processes in service of interpreting medical images. The best radiologists have a keen grasp of anatomy, physiology, and pathophysiology, and they utilize that knowledge every time they interpret a patient’s CT or MRI scan.