"search for wisdom" is correct and usable in written English.
You can use it in any context where you are talking about a person actively seeking out knowledge or understanding. For example, "The young man was determined to follow his own path and so embarked on a relentless search for wisdom."
The trouble is that philosophy is not that easy; the search for wisdom is actually quite hard.
Based on an old Chinese tale, it traces the Monkey King's search for wisdom and immortality with singing, acrobatics, martial arts and cartoon segments.
Her unprettiness is no longer a possible ally in her search for wisdom (prettiness is distracting) but something alarming to be suppressed.
In the East, he then believed, a man went to college not for vocational training but in disciplined search for wisdom and beauty, and nobody over the age of twelve believed that those words were for sissies.
Inevitably, its theme is that life goes on, and that every son is no less interesting than every father, that each generation's search for wisdom is different but no less important or dramatic than the previous generation's.
The British can help with this! Contrary to the idea that the gap year is a character-building opportunity, Americans need to grasp its fundamental point: the industrial-scale export of teenagers prior to college is not a search for wisdom or themselves, but for the elusive gap year anecdote.
Miller saw "Moneyball" as a search-for-wisdom story.
I've been actively searching for wisdom and fulfillment, both external and internal, for a few years now.
He originally started the practice to quiet his busy mind, according to his book What Really Matters: Searching for Wisdom in America.
He recently launched a new search engine for wisdom.
Today, he runs his Incubator/Investment vehicle Futurity Ventures, which recently launched a new search engine for wisdom.
