The second part concerns England in the course and aftermath of the English revolution and focuses on debates between Thomas Hobbes and John Wallis. The first part is devoted to showing that the Jesuit brotherhood hindered the development of the precursor of the calculus and ultimately thwarted the development of mathematics in Italy until, I presume, the Risorgimento (Italy’s 19th century unification). This is an idiosyncratic book driven by its two-part thesis.

Infinitesimal: How a dangerous mathematical theory shaped the modern world, by UCLA professor Amir Alexander, is a history in two parts of certain mathematical ideas that emerged in 17th century Europe with a focus on Italy and England. If mathematics is not an unfolding of truths hidden in its logical structure, what propels it and can its progress be brought to a halt or accelerated? There can be no general answer to this question, but the study of particular developments in historical context can help us understand how and why certain ideas emerge at definite points in history at particular places.Įxamination of the historical record, and nuanced attempts to tease out the historical and social forces at play in the development of mathematics, are worthwhile. Thus all axiomatic systems are incomplete in the sense that the truth of all meaningful statements cannot be established. Gödel’s theorems proved that in any axiomatic system (sufficient for arithmetic), there are statements that can neither be proven nor disproven within that system. The project remained unfinished, not only due to the enormity of its own ambitions but irremediably with Kurt Gödel’s theorems from the 1930s showing the incompleteness of all logical systems. The view of mathematics as a closed axiomatic system was pursued to its utmost limits by Bertrand Russell and Alfred North Whitehead in the early part of the 20th century culminating in their Principia Mathematica, appearing in the 1910s.

The abilities of individual mathematicians play a role, but these abilities are fashioned and nurtured (or not) in definite historical and social circumstances as well as subcultures, households and families. It is not a closed logical system, and its history is like the history of any discipline - far from the sequential unraveling of truths immanent in its logical structure, it is a narrative of contingent goals and programs, varying material resources, demands of governments and society, the serendipitous coming together of communities of mathematicians, and the psychology and personal circumstances of individual mathematicians. Yet mathematics is decidedly not like that. The pace of this history would then be a function of the abilities of the actors engaged in carrying out these logical steps. MATHEMATICS CONCEIVED AS a closed logical system, based on a set of axioms, may suggest that its history would be an account of the inevitable logical development of these axioms. Scientific American/Farrar, Straus and Giroux, How a Dangerous Mathematical Theory Shaped the Modern World

Suggested Readings on/about Detroit's 1967 Rebellion.

Detroit's Rebellion & Rise of the Neoliberal State.

Dawn of 'Total War' and the Surveillance State.

Under Attack at San Francisco State University.

Infinity and infinitesimals book