This is a fascinating book. It is the story of a hyper-intellectual single mother raising a genius child, but I feel safe in saying that whatever narrative you have pre-conceived based on that description is wrong.
The mother, Sibylla, is a mess. She is in a constant battle against the world and its assorted hypocrisies, using logical argument as a bludgeon against any form of normalcy (she is given a brief biography nearly on to set up her personality). The story starts from her point of view and we have a certain sympathy. She has the same struggles all parents do, trying to provide the best for her son while his demands and neediness and out-right existence seem to conspire against her. She is relatively impoverished, wasting her intellect in drudgery to pay the bills all the while schooling her young genius, who has an incredible facility for languages among other prodigious skills. She sees a bit of potential relief when it comes time for the boy to finally go off to school -- imagine all she could accomplish with the five uninterrupted hours! But after a brief stint, it becomes clear that school will simply crush a beautiful outlier like her son, so she resorts to home schooling and trying not to go crazy.
As the boy ages our point of view changes. We start by getting regular and constant interruptions in the narrative as the boy, Ludo, pesters her questions. In time she suggests Ludo start a journal, from which we get occasional entries. From the journal we see she picks fights with strangers on the train who happen to passingly express more conventional views, or even just make small talk. More importantly, she is more brutally honest with the child than the child deserves (toying with him over the identity of his father), and she commits the grievous parental sin of making the child be the adult.
By midway through the book Ludo has reached his tween years and has taken over fully as narrator. He discovers who his father is -- a writer, held in artistic contempt by his mother -- and conspires to meet him. He turns out to be a very decent, rather normal man, but Ludo never reveals to him that he is his son. Either by his own mind or the influence of his mother or some combination thereof, Ludo feels he needs a father who does not feel the constraints of convention. So, influenced by his familiarity with the Kurosawa classic, The Seven Samurai (again, due to his mother's obsession), he hatches a plan to visit a series of outliers, both famous and infamous, and claim to be their child.
This sets up DeWitt to produce a wonderful series of character sketches. The potential "fathers" readily engage in biographic exposition for the precocious boy with the biting wit. This makes for some fun reading. When all's said and done though, the bigger-than-lifes either see through his ruse or are not worthy. But the point is made. Ludo is not going to be normal and no matter how much everyone thinks that he's being deprived of some vital experience for the lack of normalcy, he ends up with a vast amount of experience and ability that he would never have received had he been forced into a standard life-track. De-emphasized, but perhaps even more important is that he stumbles on a way to relieve his mother of the financial burden she struggles with.
DeWitt takes a lot of chances. She employs an unusual way of transcribing dialog, omitting quotes and simply prefacing standard text with "He saids" and "I said." It requires somewhat closer reading as she seems to have no strict method for when the "saids" appear, occasionally not even being in the same paragraph. It seems to work, at least for me, as it gave me a stronger sense of the dialog as emerging from memory, not intended as a transcription of real-time action. She also doesn't hesitate to spend some time indulging in descriptions of Ludo's lessons, which often take the form of extended lessons in the translation of ancient Greek or other languages, much only partially comprehensible to the average reader (such as me).
A clear theme to the book is the examination of the fate of those who are different, those who are dedicated to artistic or human endeavor that is beyond the paths most people take, and the reaction such people can expect from others. This is a treacherous trope -- the misunderstood genius -- but DeWitt brings to bear a great deal of sympathy to such people, and an appreciation of the courage it takes. A lesser talent would either turn the story into symbolic appeal for tolerance of the poor misunderstood geniuses, or a sentimental tale where normalcy is found to be not so bad after all. DeWitt sees the balance of the cost and rewards of such a life.
Should you read The Last Samurai? That's a tough one. I loved it. I found it beyond just affecting; it was truly stimulating, as you can tell from the length of this review. It is not, however, for the casual reader. Or at least the casual reader will not get out of it what a thoughtful, intellectually inquisitive reader would. But if you are one of the eternally shrinking pool of people who are dedicated to the written word, it's a gem at a minimum, perhaps one for the pantheon.