Classical mathematicians valued simplicity, settling such complex questions as the irrationality of √2 by elementary methods. Today, too, refractory problems in pure as well as applied mathematics are resoluble by simple, Classical methods. For instance, though the Goldbach, Twin-Prime and Cousin-Prime Conjectures have withstood proof for 2-3 centuries, they are here proven by a method two millennia old. Likewise, a simple method shows that most lives lost in the COVID-19 could have been saved by a staged treatment protocol combining vaccines with off-label medications each proven to reduce severe outcomes somewhat. Simple mathematics logically applied also defeat the principal arguments for mitigating global warming – the threat of dangerously rapid warming and the cost of inaction. After correction of a grave error of physics that arose in the 1980s, when feedback formulism borrowed from control theory was misunderstood, global warming will be small enough to be net-beneficial. It is proven by Classical simplicity that Western net-zero emissions would mitigate warming undetectably by 2050, at disproportionate cost. The rational economic choice is to do nothing.
Callimachus, the librarian of Alexandria in the early third century BCE (Fig. 1a), wrote 800 books. Few survive. They were probably short: he is known for his epigram μεγά βίβλιον μεγά κάκον – the bigger the book the badder. By contrast, the first of three volumes of the Sixth and latest Assessment Report of the Intergovernmental Panel on Climate Change (IPCC 2021) has almost 4000 pages.
William of Ockham, the 14th-century Cambridge philosopher (Fig. 1b), is celebrated for his simplicity principle: essentia non sunt multiplicanda praeter necessitatem. Where several explanations for a phenomenon compete, the least complicated is generally preferable. The art of Classical mathematics is not to find the most complex non-solution to a problem but to find the least complex solution. That straightforward principle may be usefully applied – but is not always currently applied – to apparently complex questions such as the COVID-19 pandemic and global warming.
Thales of Miletus (624-545 BCE: fig. 1c), the founder of the scientific method, is known for his theorem, an elegantly simple proof – here expressed in just two dozen words that will fit on a beermat (Fig. 2) – that the diameter of a circle subtends a right-angle to any point on the circumference.
Aristotle (384-322 BCE: Fig. 1d), the most influential of polymaths, studied biology, botany, chemistry, ethics, history, logic, metaphysics, rhetoric, psychology, philosophy of science, physics, poetics, political theory and zoology. At Plato’s Academy, Aristotle wrote the Topics, on how to construct one’s own argument, and the Refutations of the Sophists, on how to detect the dozen commonest logical fallacies in an interlocutor’s argument. From these fallacies, Aristotle derived formal logic, in which an argument comprises one or more declarative premises leading to a conclusion. If the premises properly entail the conclusion, the argument is valid; if they are all true, it is sound and its conclusion is true. Aristotle codified the art and science of logic in his Prior and Posterior Analytics.