Translation:It is important to have intellectual curiosity.
The first virtue is curiosity. A burning itch to know is higher than a solemn vow to pursue truth. To feel the burning itch of curiosity requires both that you be ignorant, and that you desire to relinquish your ignorance. If in your heart you believe you already know, or if in your heart you do not wish to know, then your questioning will be purposeless and your skills without direction. Curiosity seeks to annihilate itself; there is no curiosity that does not want an answer. The glory of glorious mystery is to be solved, after which it ceases to be mystery. Be wary of those who speak of being open-minded and modestly confess their ignorance. There is a time to confess your ignorance and a time to relinquish your ignorance.
But it just told me I was wrong when I typed out the same sentence. It said I had to say, "Es importante tener LA curiosidad intelectual."
Really? If you use "la", it would have said: "It is important to have THE intellectual curiosity". Maybe you should report the problem, so they can fix it.
why is there no "a", "para" or "de" before tener, like they go before many other verbs used in sentences that are infinitive?
This is because "to have intellectual curiosity" is the subject of the sentence. Many times in Spanish the subject comes after the first verb usually when that first verb is "es" and it is followed by something like facil or intereste.
Why? Your translation would be less common in English in my opinion, but more importantly, it is clear which word is the adjective and which is the noun in the sentence. A curious intellect would be un intelecto curioso, which is similar in meaning but different grammatically. There's no need to change it.