[1] The book is about a young Sri Lankan mathematician who finds a short proof of Fermat's Last Theorem, while an alien invasion of Earth is in progress.

"[3] The San Francisco Chronicle, however, described the novel as a "fitting valedictory for Clarke, ... and a reminder of Pohl's great relevance to a genre he has championed for more than 70 years.

[6] But in 2006, at the age of 88, ill health brought on by complications from post-polio syndrome, and writer's block, impeded his progress, and he asked Pohl for help.

[8] Pohl, only two years younger than Clarke, had health problems of his own: he could no longer type and wrote the book out in longhand, leaving it up to his wife to translate his "indecipherable scribbles".

[13][14][15] The solar powered space yacht race was first featured in a short story of Clarke's, "The Wind from the Sun" (1964), and the concept of a "mysterious Elder Race" deciding our fate, in this case the Grand Galactics, has appeared in several of Clarke's previous novels, including Childhood's End (1953) and the Space Odyssey Series (1968–1997).

[23][24][17] In the novel's back-story, extraterrestrial sapients, the "Grand Galactics", are alarmed when they detect the photon shock waves from nuclear bomb detonations on Earth.

When these messages have no effect, the Grand Galactics order another race, the "One Point Fives", to launch an armada to Earth to exterminate the undesirable species.

To achieve this end, Pax per Fidem has developed "Silent Thunder", a non-lethal EMP nuclear superweapon that renders all electrical equipment in its path inoperable.

He does, however, accept a position on the advisory board of an international consortium building a space elevator in Sri Lanka, chosen because of its location on the equator.

[a] As the One Point Five fleet enters the Solar System, the Nine Limbeds orbit and observe Earth in cigar-shaped craft, sparking numerous UFO sightings.

But soon after the start of the race, Natasha's yacht malfunctions and she is abducted by the Nine Limbeds, who use a projection of her to interrogate prominent people on Earth, including Ranjit and Gamini, about Silent Thunder.

The One Point Fives land in the desolate Qattara Depression in the Libyan Desert, which they find quite habitable compared to their ruined homeworld.

The Americans send B-52 bombers to attack the One Point Fives' base, but the aliens electronically disable the aircraft, causing them to crash short of their target.

With the Grand Galactics absent, the aliens make decisions for themselves: the One Point Fives provide Earth with new forms of power and the Machine Stored reveal mind uploading technology.

"[2] The Washington Post said that "The Last Theorem reads like a dog-eared album of favorite themes from yesteryear", referring to Clarke and Pohl topics from the authors' earlier works.

It's a deeply disjointed one, a book that introduces a host of wonderful ideas and sympathetic, believable characters, only to decide it doesn't trust them to carry off the story in the end, ultimately falling back – disastrously – on dated and dubious formula.

"[17] Sheila Merritt at SciFi Dimensions said that while it should have been "a fine tribute and a fitting farewell to this master of science fiction", it turned out to be an "easy book to put down."

[8][16] Some critics also felt that the book ended "somewhat precipitously",[30] that after the aliens arrived, the crisis was resolved too quickly, giving the impression "that there was at least a good, long chapter missing.

He said that even though it is a collaboration, the book is still recognisably Clarke, "with the same humour, the same enthusiasm, the great flashes of inspiration, the big ideas and the same curious positivism that underlines most of Sir Arthur’s work.

"[10] Michael Berry at the San Francisco Chronicle said that the novel does a "stellar job of conveying some of the intellectual fun that can be had by manipulating math."