She wasn't the father of the American detective novel, but her first novel, the Leavenworth Case (1878), was one of the first detective novels ever written*. One site describes the book's importance as follows:
That device has, of course, been used time and time again in mysteries, and for this and other reasons, it is sometimes tempting to fault The Leavenworth Case as a clichéd work…until one realizes that this is the book that established the situations and lines that would later become clichés (for instance, when asked whom he suspects of the murder, Gryce cryptically replies: “Every one and nobody”).
Arthur Conan Doyle and Wilkie Collins admired her work, and Agatha Christie specifically mentioned her as a role model.
I'm writing about her because I read quite a bit of her work over the weekend. Her style is Victorian florid, with upper class young women depicted as virginal frail flowers, wilting in the wind, petals dropping off if the woman forgets to wear a hat and so on. It may be that writing style which has kept Green in the shadows**. And the books I read have plenty of the kind of sexism and classism etc. which grates on the modern reader.
But Green was born in 1846, and for a woman to write in those days she had to write the way Green did, at least in the sense that the female characters had to comply with the then-common gender norms. A lot of fainting, a lot of trembling, and those would excuse her clever plot schemes. She can also create realistic characters when her pen describes older men or older women or charladies and others of lower class. Then she is both funny and perspicacious.
I wasn't familiar with Green's writings before. Perhaps you are, if you like detective novels. But it was pretty exciting to meet and spot the prototypes of Miss Marple, the basic plot of the Pale Horse and several other plot devices later writers have used. As that first quote pointed out, her work seems full of cliches until you realize that she created many of the ideas which now look old hat to us.
Why was I excited about all that? Because it's always nice to find how the magic trick was done, where, say, Agatha Christie and others got their basic ideas and how they built on those, and because it's nice to slot some of the missing puzzle pieces into the history of the detective novel. Anna Katherine Green certainly belongs there and is a major piece in the overall puzzle.
*She probably wasn't the very first woman to publish a detective novel in the US, so in that sense she wasn't the mother, either. Stepmother?
**On the other hand, the fainting and trembling women are not exactly uncommon in the books written by Victorian men and neither is the florid language.