There’s something a bit ho-hum, mean and pinched about the reception of Sir Tom Stoppard’s new (and, he says, perhaps final play), Leopoldstadt. A minority has treated its opening this February in the 1899 Wyndham’s Theatre as a perfectly ordinary event, nothing special in the long history of the British theatre or, indeed, in the chronicles of theatre. This misses the significance, not of the matter of the play, but of the creation of the play itself. There was, after all, only one subject that remained for Stoppard to write about. He has in his dramas dealt with most of the perennial problems of philosophy, from the subjective versus mathematical conceptions of time and space, to language, logic and ontology, from ethics to politics, to our psychology and emotions from love to hate. He has posed problems, puzzles and their resolutions, teased us and played with us, his audience, almost always treating us as his moral and intellectual equals. He has never preached, or harangued us, or tried to teach us lessons, though there is much learning in his plays, and sometimes conclusions to be drawn.

Though, like the late Sir Jonathan Miller, and many others (including myself), Stoppard regards himself as Jew-ish, non-observant and unbelieving, it is obvious that this 82-year-old playwright had eventually to write about the Holocaust and, given his background and his gifts, that this play would be his masterpiece – and a major part of his legacy.

Why? Because the history of the Jews and what happened to them in the 20th century is also his story; he owns (at least a part of) it. Born Tomáš Straussler on 3 July 1937 in Zlín, Moravia, now part of the Czech Republic, Stoppard’s family left on 15 March 1939, the very day the Nazis invaded Czechoslovakia. Zlín was the company town of the huge Bata Shoe making firm; they had a factory in Singapore, and by all accounts tried to look after their Jewish employees. So his father, a Bata company doctor, was transferred there, before escaping to Australia, avoiding the Japanese invasion. In 1941, aged five, he was evacuated to Darjeeling with his brother, Petr. They were sent to Mount Hermon school, a Christian boarding school with an American-style curriculum. Following their father’s death, their mother married a British Army Major Kenneth Stoppard, and the boys took his surname. In 1946, the family arrived in England, and young Tom felt he had been given the (Cecil Rhodes attributed) winning ticket in the lottery of life.

This is the part of his own story that the playwright knew; the more interesting aspect is what he didn’t know, but discovered, and that allowed –compelled – him to write Leopoldstadt.

In 1996, following the death of his mother, Stoppard began to learn about his Czech family. All four grandparents were Jews, and died in camps such as Terezin and Auschwitz, as did three of his mother’s sisters. As long ago as 1998 he returned to Zlín, marking a milestone in his journey of appreciating his Jewishness. This gorgeous world première of Leopoldstadt, directed by Patrick Marber (a first-rate playwright in his own right), with stunning period sets and costumes by Richard Hudson and Brigitte Reifenstall, and cunning lighting by Neil Austin, opens with what appears to be an old family photograph. It is 1899, and the huge cast of upper bourgeois family and servants are led by Hermann Merz, a baptised Jewish businessman, and his Catholic wife, Gretl (excellent performances by a first complacent, then nervy Adrian Scarborough, and Faye Castelow, who is not so ditsy as she appears when attending her first family seder). There are several fine performances, including that of the playwright’s son, Ed Stoppard, as Merz’s Jewish brother-in-law, a mathematician obsessed with Riemann’s Conjecture; Sebastian Armesto, who plays Jacob in the 1924 segment of the play, and Nathan in 1955; and Luke Thallon, who excels both as Gretl’s lover, Fritz, in the 1900 portion, and Leo in 1955. In this last role, “Leo” seems to recapitulate the playwright’s own discovery of being Jewish and what that means.

The events depicted include a Christmas celebration where there’s a telling kerfuffle about whether to put a star of David at the top of the tree; a Passover seder; the painting of Gretl’s portrait by Klimt; and the Anschluss on 12 March 1938 – for Stoppard has set the play not in his native Czechoslovakia, but has moved it to Vienna.

This makes great dramatic – and historical – sense, as it makes more familiar to us the place and situation of the Jewish bourgeoisie as the new century unfolds. Indeed, the clue is in the name of the play. Before I saw the play or read the text, I was discussing it with a close friend, Dr Ernest Kafka, a Viennese-born, retired Freudian psychoanalyst. Until Anschluss he lived with his Jewish banker father and musician mother in a grand flat off the Ringstrasse. He queried the title of the play: Leopoldstadt, he explained, was where the less affluent, even working-class Jews lived, as many of them had come from the east, and were not always German-speakers. As Hermann puts it in the play, boasting of the family’s exodus from Leopoldstadt to the Ringstrasse, “My grandfather wore a caftan, my father went to the opera in a top hat, and I have the singers to dinner – actors, writers, musicians.”

The events of the play echo my friend Ernie’s childhood (as he has written about it in his soon-to-be published memoir). In particular, Hermann Merz’s misplaced earlier confidence in the shelter and beneficence of the Austro-Hungarian Empire, and his belief in assimilation as the solution to the Jewish predicament. For many years Ernie found fault with his own father for not moving the family from Austria before the Anschluss – until learning that his father, who owned one of the two Jewish banks authorised to do foreign exchange, had remained in Vienna (up to the point of being arrested by the Gestapo), in order to move to safety the assets of his Jewish clients.

So Stoppard has got the look, the tone (and thanks to Adam Cork, the sound) of the era exactly right. His invented stage family is almost too large to take in at a single viewing, and the play will reward repeated visits; but having read the near-novelistic script, I can appreciate retrospectively the nuances that the play makes visible. Grim though the end of the play has to be (if it is to respect history and truth, as well as evoke the only feelings it is possible to have), it is not without humour. Circumcision and its (to me, grisly) rites provide a good deal of comic business, amounting to farce when the young mother repeatedly changes her mind. There are some of Stoppard’s favourite mathematical conundrums, and a touch of philosophy, too, in the repeated motif of the cat’s cradle constructed by some of the terrific young actors – the kind of intellectually challenging fun Stoppard is so skilled in providing from Jumpers to Arcadia.

There’s a resonance in the ending of Leopoldstadt, to which not even all Jewish-descent families can lay claim, and for all its light-hearted moments, this drama is deadly serious. It is, after all, a chronicle of murder. Unlike many of Jewish descent, I have been spared: if members of my family were among the victims, I don’t know their identities. The litany of Stoppard’s lost relatives is a catalogue of grief, detailed with the grace and elegance we would expect from our greatest living playwright, in what, I am certain, will come to be seen as his finest play yet.