— Albert Einstein German-born physicist and founder of the theory of relativity 1879 - 1955
variant: If you can't explain something to a six-year-old, you really don't understand it yourself.
variant: If you can't explain it simply, you don't understand it well enough.
Frequently attributed to Richard Feynman
Probably based on a similar quote about explaining physics to a "barmaid" by Ernest Rutherford
Page 418 of Einstein: His Life and Times (1972) by Ronald W. Clark says that Louis de Broglie did attribute a similar statement to Einstein:
: To de Broglie, Einstein revealed an instinctive reason for his inability to accept the purely statistical interpretation of wave mechanics. It was a reason which linked him with Rutherford, who used to state that "it should be possible to explain the laws of physics to a barmaid." Einstein, having a final discussion with de Broglie on the platform of the Gare du Nord in Paris, whence they had traveled from Brussels to attend the Fresnel centenary celebrations, said "that all physical theories, their mathematical expressions apart ought to lend themselves to so simple a description 'that even a child could understand them.' "
The de Broglie quote is from his 1962 book New Perspectives in Physics, p. 184 http://books.google.com/books?id=xY45AAAAMAAJ&q=%22mathematical+expression+apart%22#search_anchor.
Cf. this quote from David Hilbert's talk Mathematical Problems given in 1900 before the International Congress of Mathematicians:
: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street."
Cf. this quote from Kurt Vonnegut's novel Cat's Cradle: