BOSTON — What is the mission of the Boston Symphony, the most generously endowed orchestra in America?

We are six seasons into Andris Nelsons’s tenure as music director of this storied ensemble, which appears at Carnegie Hall on Monday, but the answer to that question is still unclear.

When he arrived in September 2014, Mr. Nelsons, then just 35, was a young, safe, healthy pair of hands after the drama of James Levine, who had stepped down in 2011 after years of illness and cancellations.

Mr. Nelsons has led plenty of good performances — some very good — and has produced a number of fine recordings, including an ongoing Shostakovich survey that has rightly won him three Grammy Awards. Though his tenure has not been without controversy — including some frictions generated by an overhaul of the Tanglewood Festival Chorus and persistent issues surrounding the orchestra’s commitment to gender parity — two years ago I wrote that “there is probably no current music director in the country I would rather hear conduct on a weekly basis than Mr. Nelsons.”