Rafiq Jan, in Qatar, asked about the meaning of the phrase "intellectually fertile."
Answer
To understand the meaning of a phrase, it's often helpful to look at the meanings of the individual words.
intellectually Intellectually is the adverb form of intellectual, which has the meaning “involving serious thought.”
fertile One of the meanings of fertile is “producing a large amount of something.”
Combining these two words
When these two words are combined, in the phrase intellectually fertile, they mean “producing a large amount of serious thought," or, put more naturally, "producing many serious ideas.”
Here is an example sentence with this phrase:
Sometimes the college dining hall can be a more intellectually fertile environment than the classroom.
In this sentence, the writer is saying that informal conversation in college dining halls can sometimes produce more serious ideas than class discussions.