At a family party some years ago, one of my uncles remarked on how little science really knows. For example, we still have no idea how gravity works - why things fall down.
"Actually, we do know how gravity works," I said. (My father, a Ph.D. physicist, was also present; but he wasn't even touching this one.)
"We do?" said my uncle.
"Yes," I said, "Gravity is the curvature of spacetime." At this point I had still swallowed Feynman's line about being able to explain physics to one's grandmother, so I continued: "You could say that the Earth goes around the Sun in a straight line. Imagine a graph that shows both space and time, so that a straight line shows steady movement and a curved line shows acceleration. Then curve the graph paper itself. When you try to draw a straight line on the curved paper, you'll get what looks like acceleration -"
"I never heard about anything like that," said my uncle.
When was the last time, in history, when it was possible for a single human to know the knowledge of the most advanced civilization? I've seen various estimates for this - usually in the form of polymaths nominated for the position of "last person to know everything". One plausible candidate is Leonardo da Vinci, who died in 1519 - shortly after the printing press began to become popular, and shortly before Copernicus inaugurated the scientific revolution.
In the ancestral environment it was possible to know everything, and nearly everyone did. In hunter-gatherer bands of less than 200 people, with no written literature, all background knowledge was universal knowledge. If one person, in a world containing 200 people total, discovered how gravity worked, you could certainly expect to hear about it.
In a world of 6 billion people, there is not one person alive who can say with certainty that science does not know a thing. There is too much science. Our current lifetimes are too short to learn more than a tiny fraction of it, and more is being produced all the time.
Even if last week's technical journal doesn't contain the answer to a mystery, that doesn't mean that no one knows it. Maybe someone out there is typing up the paper at this very moment. You can't generalize over all 6 billion people in the world because you haven't talked to all of them - which is a non-ancestral condition! For the vast majority of humanity's evolutionary history, it was possible to meet everyone in your little world. Now there's 6 billion people who might know the answer to any question you care to ask, and you can't ask all of them.
No one knows anymore what no one knows.
My uncle is not an isolated phenomenon. I've met people who think that science knows nothing about the brain, that thought is a complete mystery unto us. (My favorite was the fellow who confidently asserted that neuroscience had been unable to assign any function "to the cerebral cortex".) As Tom McCabe put it: "Anyone who claims that the brain is a total mystery should be slapped upside the head with the MIT Encyclopedia of the Cognitive Sciences. All one thousand ninety-six pages of it."
I haven't seen the movie What The Bleep Do We Know, but if the horror stories are true, it's one long celebration of imaginary ignorance. Particularly the "mysterious effect of conscious observation" in quantum physics, which was explained away as ordinary decoherence in the 1950s, but let's not get into that again.
Ignorance should not be celebrated in the first place; I've made this point before. It is a corruption of curiosity to prefer the question to its answer. Yet people seem to get a tremendous emotional kick out of not knowing something. Worse, they think that the mysteriousness of a mysterious phenomena indicates a special quality of the phenomenon itself, inferring that it is surely different-in-kind from phenomena labeled "understood". If we are ignorant about a phenomenon, that is a fact about our state of mind, not a fact about the phenomenon itself.
In the ancestral environment, there was a certain permanence to the division between ignorance and knowledge. If none of your fellow hunter-gatherers knew what made rain fall, it was likely that no one would ever find out in your grandchildren's lifetimes. Today, the absence of knowledge is a fragile and temporary condition, like the darkness in a closet whose door happens to be shut. A single thought can shatter the absence of thought. Every scientific discovery ever made, destroyed an ancient absence-of-knowledge dating back to the dawn of time. No one knows what 6 billion people don't know today, and still less does anyone know what 7 billion people will know tomorrow.
That's probably a misquote, it turns out. I can't find any source for it and Wikiquote agrees. The closest they could find was Ronald W. Clark claiming that Louis de Broglie claimed that Einstein believed "that all physical theories, their mathematical expressions apart, ought to lend themselves to so simple a description 'that even a child could understand them.'" (I'm interpreting this to mean that Clark attributed the outer quote to de Broglie, who attributed the inner quote to Einstein while giving his own explanation of the context.) Could be true, but our knowledge of it is a few degrees away from the primary source, so there's room for it to get corrupted or taken out of context along the way. And even if it is correctly attributed and interpreted, the "their mathematical expressions apart" bit redeems it somewhat (not completely). Though that does dilute the meaning of "understand[ing]" as used, or it identifies it with (as you've termed them) verbal understanding rather than technical understanding.
I'm going to tentatively reject the belief that the "...unless you can explain it to your grandmother"/"that even a child could understand them" quotes accurately describe Einstein's belief. He may have been a Traditional Rationalist, but he wasn't stupid, and I imagine he had a great deal of experience explaining things as well as he could but not having everyone (let alone children or stereotypical grandmothers) understand him.
(And I'm going to give myself a rationalist experience point for finding the original "grandmother" quote surprising enough that I thought to look it up.)
This was probably said by Feynman. I'm pretty sure because I have an auditory memory of him saying it in a video ... but I can't remember which one, and wonder if perhaps I read it after all in his Lectures.