The first shows a man’s upper body studded with large melanomas. The second shows what happened when the man took a drug called vemurafenib. Vemurafenib belongs to a relatively new class of drugs, called targeted cancer therapy. Unlike earlier chemotherapy drugs, they attack specific molecules found only in cancer cells. In response to the vemurafenib, the tumors shrank in a matter of weeks, to the point that the man’s skin looked smooth and healthy.

The third picture is a case of déjà vu. After 16 weeks of treatment, the melanoma returned. “All the lesions reappeared — every single one,” said Dr. Vogelstein. “That struck me as nearly as amazing as the fact that they had disappeared.”

The man died several weeks later.

This short-lived reprieve is heartbreakingly common in targeted cancer therapies. To understand why — and how to get around it — Dr. Vogelstein has teamed up with mathematicians to create detailed models of cancer.

Their research demonstrates a little-appreciated but inescapable fact about cancer: It is an evolutionary disease. And their studies are provoking new thinking about ways to use drugs to kill cancerous cells. Some of their findings were published on Tuesday in a paper in the journal eLife.