This is the 10039th most frequent Japanese word.
追い求め
"追い求め" means "to pursue" or "to seek earnestly."
The word '追い求める' here means 'to pursue' or 'to seek out,' specifically referring to striving for a desired goal or state—ideals in this case.
彼は長い間理想を追い求めてきました。
He has been pursuing ideals for a long time.
In this usage, '追い求める' pertains to striving towards achieving a tangible outcome—success.
成功を追い求める過程で、彼は多くの困難に直面しました。
In the process of pursuing success, he faced many difficulties.
Here, '追い求める' is employed to denote a determined effort to uncover or discover something—truth in this instance.