Ultimately, note that Bertrand Russell's essay is a criticism against the liberal arts education, particularly as it was practiced by the Victorians. In that context, education was largely focused upon the memorization of the Classics (i.e., Greek and Roman literature). For Russell, studying the Classics and the Arts wasn't itself the problem; rather, the problem lay in the single-minded zeal by which these subjects were celebrated as the quintessential high-water mark of human achievement.
Ultimately, for Russell, this kind of singular focus amounted to an intellectual dead end. This is because once one focuses one's attention so intently upon the past, one stops looking toward the future. In this essay, when Russell is discussing science, he isn't speaking so much about scientific knowledge, but, more deeply, he is discussing the mindset and perspectives which underlie the entire scientific process. Science is progressive. It is always looking toward the future, always looking to advance the boundaries of what is understood. Present practitioners are always building upon the achievements of their predecessors, just as future generations will build upon the achievements of the present one. To Russell, this mindset is itself of extraordinary value, as a cultivator of human achievement.