The Last Theorem is set in Sri Lanka in the early- to mid-21st century and follows the life of a mathematician, Ranjit Subramanian. While studying at Colombo University, he becomes obsessed with Fermat's Last Theorem and is determined to find a more elegant proof than the 100-page proof presented by Andrew Wiles in 1995. While still a freshman at University he befriends a student, Gamini Bandara, who later moves to London to study at the London School of Economics.

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. The Grand Galactics monitor and control the destinies of a number of high-performance sapient races and order one of these races, the Nine Limbeds, to send "cease and desist" messages to Earth. When these messages have no effect, they order the One Point Fives to launch an armada to Earth to exterminate the undesirable species.

Back on Earth, regional conflicts escalate and the United Nations struggles to contain them. In Sri Lanka, Ranjit unwittingly boards a cruise ship that is hijacked by pirates. When unknown security forces free the ship, Ranjit is arrested on suspicion of terrorism. For six months he is interrogated and tortured, but he cannot supply the information his captors want so he is locked up and "forgotten" for a further 18 months. During this period of incarceration, Ranjit dwells on Fermat's Last Theorem and, after several months, solves it with a three-page proof. Later Ranjit is rescued by his friend Gamini, who will not reveal who he is working for or where Ranjit was held captive.

Ranjit submits his proof for publication and achieves world-wide fame. He marries Myra de Soyza, an artificial intelligence specialist, and embarks on a speaking tour of the world. In the United States, he is briefly recruited by the CIA to work on cryptography. Gamini later reveals that he is working for Pax per Fidem (Peace through Transparency), an undercover United Nations organization established to bring about world peace. 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. Silent Thunder is deployed in North Korea and later in South America, and regional conflicts subside. Gamini invites Ranjit to join Pax per Fidem, but the authoritarian nature of Pax per Fidem and its "new world order" worry Ranjit and Myra, and Ranjit turns down the offer. 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 position on the equator.[nb 1]

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. A Grand Galactic member, who happens to be passing by, stops to observe the effects of Silent Thunder and returns to the Grand Galactic collective, who immediately suspend the One Point Fives's destruct orders pending further investigation.

The space elevator is completed and, for the first time, people and materials can be lifted into Earth orbit without the need of rockets. Natasha, Ranjit and Myra's daughter, competes in the first solar powered space yacht race from Earth- to Moon-orbit. 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. Satisfied that Earth has "reformed", Natasha is returned and the Nine Limbeds broadcast a message to Earth in which they announce that the Grand Galactics have decided not to sterilize Earth, and that the One Point Fives, with their Machine Stored navigators, cannot return home and will land and occupy unused areas of Earth.

The One Point Fives land in the desolate Qattara Depression in the Libyan Desert, which they find quite habitable compared to their ruined homeworld. With the Grand Galactics absent, the aliens start making decisions for themselves. The One Point Fives provide Earth with new forms of power and the Machine Stored reveal mind uploading technology. When Myra dies in a scuba diving accident, her mind is uploaded into cyberspace, with Ranjit joining her later.

After 13,000 years the Grand Galactics finally return to Earth and are astounded to see how fast the planet has developed. They had always interfered with the evolution of sentient species they had discovered, believing they could not be trusted to evolve on their own. Impressed with Earth's progress, the Grand Galactic relieve themselves of the burden of watching over intelligent life and hand the task over to Earth.

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