This novel, set in the time frame 1890s to 1920s interleaves several plots and styles, from boys' adventures to peacetime spies to gunslingers' revenges. The forces of progress stomp over all the little fellow, and the little fellow fights back. Scientific breakthroughs promise great gains for humanity and ever more terrible weaponry. Uncanny echoes of today's big issues, whether the Internet or the War on Terrorism, abound.

Mathematics is dense throughout the novel. The conflict between vectors and quaternions is practically a subplot of its own. Two major characters, Kit Traverse and Yashmeen Halfcourt, are mathematics students. Frequent allusions, and sometimes longer discussions, concern the Riemann zeta function. Most famous mathematicians of the nineteenth and early twentieth century are mentioned, and some, like Gibbs and Hilbert, even get a cameo. Two of the silly songs are about mathematics. ("Geniuses" is rhymed with "Frobeniuses").

All in all, Against the Day is a staggering achievement--Pynchon has basically out-Pynchoned himself.