Dr Benjamin Binstock, who teaches art history at Cooper Union in New York, has kindly sent me a copy of his book, Vermeer’s Family Secrets: Genius, Discovery and the Unknown Apprentice. He was moved to write it partly by his indignation at the caricature of the Vermeer family that achieved blockbuster success as the novel and later the movie Girl With a Pearl Earring (2003). Binstock’s study of 37 surviving paintings shows that Vermeer’s principal models were his wife, 12 times, and his two daughters. His mother-in-law had sufficient faith in the 21-year-old’s talent, and his love for her daughter, to accept him as a member of her household, and to provide him with studio space and occasional funds. He had a single patron, Pieter van Ruijven, who paid him 100-200 guilders a year. After the artist’s death in 1675, his wife, who was left virtually penniless with 10 dependent children, had no choice but to pay the baker with paintings. Binstock sets out a convincing case that Catharina Vermeer served as her husband’s principal model until 1666, when, pregnant for the 11th time, she was relieved by her eldest daughter Maria, who was then 12. It is Maria who is the girl with a pearl earring. Less persuasive are Binstock’s detection of the hand of a single apprentice in eight paintings usually attributed to Vermeer, including the fabulous Girl With the Red Hat – and his identification of this apprentice as Maria Vermeer. As the model for this painting is the same person as in Earring, the inescapable conclusion is that Girl With the Red Hat is a self-portrait by Maria Vermeer. Binstock thinks Maria served as her father’s model until she was 16, when she was replaced by her younger sister. By then, her apprenticeship should have been well under way, if not complete, but Binstock thinks she did not even begin her training until 1671. He tries to make the case that artistic training of a daughter was so unusual as to be practically unheard of. He lists only Judith Leyster, Maria de Grebber, Maria van Pruijsen and Gesina ter Borch as Maria’s female contemporaries. De Grebber and Van Pruijsen are probably as insignificant as he assumes, but in this they are not representative of professional women painters in mid-17th-century Holland. Ter Borch trained not only his daughter Gesina but her sister Maria; the fact that Gesina’s only authenticated work is an album of lively sketches (now in the Rijksmuseum) is not evidence that she carried out no other work. Binstock makes the startling assertion that Judith Leyster (c1610–1660) “abandoned her vocation to take care of her family”. In 1633, Leyster was named as a member of the Haarlem painters’ guild, which signifies that she had completed an apprenticeship and was permitted to sign paintings as her own work. In 1636, she married the painter Jan Miense Molenaer and went to live in Amsterdam, where she bore three children. The inventory of Molenaer’s possessions at the time of his death in 1668 includes works by his wife. In 17th-century Holland, any woman who knew how to prepare canvases and grind and mix colours and glazes had the equivalent of a dowry. Anna Janssens was trained by her father, who also taught the man who became her husband, Jan Brueghel II. Sara Saftleven brought her training by her painter father to her marriage with the painter Jacob Adriansz Broers. A gifted woman painter could earn more than her painter husband. Willem van Aelst was by all accounts desperate to marry the flower-painter Maria van Oosterwijk, but she preferred to keep for herself the handsome fees she earned from Europe’s royal families. There would have been little point in Vermeer endowing a daughter with training if the matter was to be kept secret. Binstock thinks Maria’s paintings were passed off as by her father because, if his creditors had known they were not from his hand, they would not have accepted them in lieu of cash. But, unlike those of the 21st century, collectors in the 17th century didn’t buy paintings on the strength of a name. Maria Vermeer was married in 1674, a year before her father died, and not to a painter. The thought that a painting as innovative and bold as Girl With the Red Hat might be by a woman is exciting – but the corollary, that she did not think her art worth pursuing, is deeply depressing. Binstock thinks Maria’s in-laws forced her to give up – an even sadder conclusion. Vermeer probably did take on the occasional apprentice, and their hands probably can be seen in some of the less characteristic works, but it remains unlikely that Maria Vermeer was one of them.