Mathematician Granville Sewell uses a concept from mathematics by which a problem is proved to be unsolvable:

All one needs to do is realize that if a solution were found, we would have proved something obviously false, that a few (four, apparently) fundamental, unintelligent forces of physics alone could have rearranged the fundamental particles of physics into libraries full of science texts and encyclopedias, computers connected to monitors, keyboards, laser printers and the Internet, cars, trucks, airplanes, nuclear power plants and Apple iPhones.

Is this really a valid proof? It seems perfectly valid to me, as I cannot think of anything in all of science that can be stated with more confidence than that a few unintelligent forces of physics alone could not have rearranged the basic particles of physics into Apple iPhones. In the first half of my video “Why Evolution Is Different” I argue with a bit more scientific sophistication, and a bit more scientific detail, that problem #3 has no solution, but my arguments are still very simple. Unfortunately, most biologists don’t seem to be impressed by such simple proofs; they don’t believe it is possible to reject all solutions to a difficult problem without looking at the details of each. But mathematicians know that sometimes it is possible.

Granville Sewell, “Some Problems Can Be Proved Unsolvable” at Evolution News and Science Today

It’s been said that many biologists are poor mathematicians.

Here’s a vid where he makes the case: