I was listening to a podcast about the physicist Richard Feynman and I heard some professor utter this sentence. He meant the exact opposite, of course. What he wants us to understand is that Feynman’s contributions to physics were immense — that is to say, even if you tried, you couldn’t overestimate them. Garner’s Modern American Usage notes similar similar sentences from the Post, the Times, and the Globe. He compares it to the phrase “could care less”, which in informal usage is understood to mean the oppose of what the words seem to imply — that is, we use it to mean “couldn’t care less”. Garner rates “could care less” a 3, which means “Widespread but still considered incorrect”. He rates “impossible to underestimate” a 1 — that is, “Rejected”.
I have trouble with “impossible to underestimate” myself, so I have sympathy for the professor on the podcast. There’s some kind of double negative going on in the phrase that makes the logic hard to work out. If you just said, “Don’t underestimate Feynman’s contributions…” the usage would be correct, but “impossible to underestimate” just heads in the wrong direction.