Is there a word for a person who can understand difficult concepts or ideas quickly? [duplicate]
Solution 1:
Consider the noun use of the term natural
A person regarded as having an innate gift or talent for a particular task or activity: she was a natural for the sort of television work required of her [Oxford Dictionaries Online]
The term is applicable to almost any field that is difficult for the average person to master.
The adjectival form can be used in your second example.
Solution 2:
In everyday speech, we call such people "smart", "sharp", or "intelligent".
In a LiveJournal entry, by contrast, one might use:
perspicacious: having a ready insight into and understanding of things.
See also "astute".
Solution 3:
Adroit (from the freedictionary): quick or skillful or adept in action or thought; quick in thought or reaction; quick-witted.
Mrs. Whitman announced on Tuesday that she had hired Mr. McCarthy, one of the most adroit media consultants in the nation with an impressive track record that includes work on the 1985 re-election campaign of former Gov. Thomas H. Kean and the 1990 campaign of Gov. Pete Wilson of California.
But Mr. McCarthy is best remembered as the producer of the controversial Willie Horton ad, broadcast during the 1988 Presidential campaign between Vice President George Bush and Massachusetts Gov. Michael Dukakis. The ad attacked Mr. Dukakis as soft on crime and cited the case of Willie Horton, a black convicted murderer who escaped from a weekend furlough program in Massachusetts and attacked a white couple in Maryland. - NYT
Synonyms: adept, deft, nimble, masterful, proficient, artful, quick-witted, dexterous
Solution 4:
Not a single word, but quick study is the commonly used expression.
The Free Dictionary shows single word synonyms to be
sponge
assimulator
learner
scholar
And sponge means (from Memidex)
someone able to acquire new knowledge and skills rapidly and easily.
Sponge often used in the following way (as given in the example at Free Dictionary):
She soaks up foreign languages like a sponge.
but can just as readily be rephrased as
She is a sponge when it comes to learning foreign languages.