LSO / Tilson Thomas, Barbican Hall, London

History has a habit of applying a little subtext of its own to composers' final utterances. Last works become last wills and testaments regardless of their circumstances. We all like to play the dangerous game of second-guessing creative genius in its final throes. In the introduction to his current series – Last Works – with the London Symphony Orchestra, Michael Tilson Thomas clearly doesn't try to do so but rather to show that the one thing all the works had in common was a search for resolution. The music should tell us to what extent they succeeded. And whether the business was unfinished when the candle finally went out.

Ruth Crawford Seeger was arguably the most radical – and unsung – American between Charles Ives and Elliott Carter. That's quite a space to fill. Her Andante for Strings (1938) – an arrangement of a String Quartet movement written some years earlier – was a telling way to start any of the concerts in this series. The effect of it is like a series of expressive but isolated notes striving to connect in some meaningful way – when all the time they are meaningful exactly the way they are.

Seeger had plainly heard the Berg Violin Concerto. The connections made in this piece are as logical and meaningful as any in 20th-century music, yet they still elude people, because you need to listen to hear. Here's a piece about the loss of innocence. Literally. Berg dedicated it "To the memory of an angel" – namely Manon, the 18-year-old daughter of Alma Mahler by her second marriage, to the architect Walter Gropius. But it's as much about Berg's search to find a balance between expression and the means to it. Tilson Thomas and his glamorous soloist, Anne-Sophie Mutter, made that easy to hear. Theirs was a forensic performance, its clarity and beauty more abstract than is sometimes the case. We heard everything. But what did we feel? It's one thing registering, for instance, that at the emotional height of the piece, Berg unites his soloist and first violins to intensify the sense of "communion", but I'm not sure I came away with a richer understanding of why.

Quite the reverse was true of Shostakovich's 15th, and final, Symphony. I sometimes feel that after a lifetime under state scrutiny, Shostakovich set out to confound his critics at the last. What an astonishingly wilful and profound piece this is – and what a cracking performance it received here. Tilson Thomas's natural affinity with Mahler paid off in spades; the pathos and bathos of the piece were rarely so dramatically counterpointed. From the trite but unsettling "nursery games" of the first movement – where the flippant transformation of one of Shostakovich's own themes into Rossini's William Tell has him cast as the lone ranger riding rampant through the playrooms of his past – to the lowering chorales and solo cello and trombone orations of the funereal second movement.

Did Shostakovich know that it was to be his last symphony? Surely yes. The final pages, in which the clockwork percussion motif from his Fourth Symphony – the one Stalin's regime made him withdraw from performance – tick away over a frozen A major chord in the strings, have to be his last laugh in perpetuity.