Aczel, Amir D. Descartes’ Secret Notebook. New York: Broadway, 2005.
A famous mathematician with suspected ties to a secretive cabal of global reformers dies from possible poisoning at the hand of a doctor employed by a European power. A French official surveys his papers, including a coded notebook, and has them quietly sent to the safekeeping of a relative. Years later, another brilliant mathematician, suffering from attacks on his reputation, seeks out the notebook to uncover its secrets.
It sounds like the plot of a thriller. Amir Aczel uses it to frame his biography of philosopher and mathematician René Descartes.
Descartes’ greatest hit as a philosopher was, “Cogito, ergo sum” (I think, therefore I am). He was a leader in rationalism, a philosophy that emphasizes the discovery of truth by use of reason. His method focused on methodical doubt by which he aimed to find truth (to him, all knowledge was connected, not discreet, unrelated truths) by reasoning out those things that could not be doubted. Thusly he reasoned his existence because he couldn’t very well doubt it when he was sitting there thinking about it. His method set him against the prevailing philosophy of the day, scholasticism, which focused on learning from authoritative figures and sources, particularly Aristotle.
High school algebra students will immediately recognize Descartes’ contribution to math. From today’s perspective, it may be hard to understand why it was such a big deal in the 17th Century. Descartes created analytic geometry, which uses algebraic equations to describe and understand geometric shapes. Before this, geometry and algebra were distinct fields, not parts of a unified mathematics. As part of this, he gave us Cartesian coordinates, the familiar x,y graph that has makes so many high school kids cross-eyed. Despite complaints that they’ll never use it, behind the scenes Cartesian coordinates are ubiquitous.
Descartes was not part of a secret society. He was a devout Catholic and was careful not to publish anything that would put him in direct conflict with the church. Even so, the writings of the Rosicrucians, a group of philosophers who sought political and religious reform and the advancement of science, influenced him. He even knew one of the brotherhood, though he may have been unaware of it. Despite his efforts to distance himself from the Rosy Cross, his books used terms that made some believe he was a Rosicrucian and his notebook included alchemical symbols that the group used.
Gottfried Leibniz, co-creator of calculus, was under attack from proponents of Isaac Newton, who independently created calculus contemporaneously with Leibniz. Other accused Leibniz of deriving his work from Descartes, which is why he diligently tracked down the Frenchman’s papers.
What did Descartes’ secret notebook contain? Leibniz handily decoded it. Descartes discovered Euler’s theorem. For polyhedrons, the sum of the number of faces (F) and the number of vertices (V) minus the number of edges (E) is 2 (F + V – E = 2). Descartes kept his discovery secret because some may have construed it as supporting a theory of Johann Kepler that used regular polyhedrons to describe planetary orbits in a Copernican model of the solar system. This was contrary to the teaching of the church, which Descartes wanted to avoid because of his personal devotion and because conflict with the Inquisition could be a career-ending (and life-ending) move.
Amir D. Aczel also wrote Chance.
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