他终于领悟到数学的重要性。

Tā zhōngyú lǐngwù dào shùxué de zhòngyào xìng.

He finally understood the importance of mathematics.

她从那本书中领悟到人生的哲理。

Tā cóng nà běn shū zhōng lǐngwù dào rénshēng de zhélǐ.

She gleaned life's philosophy from that book.

在困境中，他终于领悟了友情的珍贵。

Zài kùnjìng zhōng, tā zhōngyú lǐngwù le yǒuqíng de zhēnguì.

In adversity, he finally realized the preciousness of friendship.