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BOOK REVIEW

A suspenseful tale of Descartes's secrets

Descartes’ Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe, By Amir D. Aczel, Broadway, 273 pp., illustrated, $24.95

Amir D. Aczel, a professor of mathematical sciences at Bentley College in Waltham, has made a name for himself unwrapping the mysteries of mathematics in ways that enlighten the uninitiated. Mathematics is intriguing, and its history is full of intrigue, the stuff of secrets, spies, and cloak-and-dagger films.

The titles of Aczel's previous nine nonfiction books attest to that -- the international bestseller ''Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem" (1996) and ''The Mystery of the Aleph: Mathematics, Kabbalah, and the Search for Infinity" (2000), among them.

His latest, ''Descartes' Secret Notebook," is a first-rate suspense story. It begins with an unsuspecting Aczel setting out to research the life and work of Renee Descartes when he finds the philosopher/mathematician kept a secret notebook. Aczel's project turned into a detective adventure, revealing occult science, a secret brotherhood, political and religious controversies, a locked box, romance, obsession, a jealousy that may have had fatal consequences, and Descartes's purloined skull.

Best known in nonmathematical circles for his mind-body philosophical statement ''I think, therefore I am," Descartes (1596-1650) was born in west-central France. His had a privileged upbringing, and the wealth he inherited afforded him the freedom to pursue his interests, including serving as a gentleman soldier, traveling, and, of course, studying and thinking deep thoughts.

The deepest of these thoughts Descartes recorded in a special notebook. ''He began to believe that mathematics held the secret to understanding the universe. . . . He worked out ancient Greek problems in geometry, but he soon concluded that the power of geometry transcended pure mathematics: geometry held the secret to all creation," writes Aczel.

Not only did he keep this journal hidden in a locked box, Descartes encrypted his entries, using symbols, number sequences, and obscure figures to ensure that the nature of his work would be disguised if his notebook was ever discovered.

A quarter of a century after Descartes died,Gottfried Wilhelm Leibniz, 30, whom history would recognize as one of the greatest mathematicians of all time, came to the end of his 3 1/2-year quest to find the hidden writings. The caretaker of Descartes's trove allowed Leibniz to copy only 1 1/2 pages of them, but Leibniz nevertheless was able to decipher the entire notebook. As promised, he remained silent about his findings.

Descartes's secret notebook disappeared about 20 years later. All that remains is Leibniz's copy, which bears an enigmatic notation that he made in the margin. Leibniz died in 1716, and it would be nearly 200 years before his transcription from Descartes's notebook was discovered. The transcription continued to perplex mathematicians until 1987, when French priest and mathematician Pierre Costabel broke the code.

From its dramatic first-person opening, ''Descartes' Secret Notebook" unfolds with the narrative structure of a film, employing back story and plot points that make its telling dynamic. Aczel's closing exposition on cosmology in the 21st century is necessarily a bit academic, but in this brief section he links modern scientists' efforts to discover the secrets of the universe to Descartes' work and gives readers a glimpse of the proposed new models of ''the geometry of the universe," which could suggest that Descartes was on the correct plane, so to speak, with his search for ''a divine truth about mathematics, nature, and the human condition."

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