533 citations
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12 papers · 1 filter
Exploring Felix Klein's contested modernism
Peter Heinig, Mikhail G. Katz, Karl Kuhlemann +2
An alleged opposition between David Hilbert and Felix Klein as modern vs countermodern has been pursued by marxist historian Herbert Mehrtens and others. Scholars such as Epple, Gr…
When does a hyperbola meet its asymptote? Bounded infinities, fictions, and contradictions in Leibniz
Mikhail G. Katz, David Sherry, Monica Ugaglia
In his 1676 text De Quadratura Arithmetica, Leibniz distinguished infinita terminata from infinita interminata. The text also deals with the notion, originating with Desargues, of…
Leibniz on bodies and infinities: rerum natura and mathematical fictions
Mikhail G. Katz, Karl Kuhlemann, David Sherry +1
The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpret…
Two-track depictions of Leibniz's fictions
Mikhail G. Katz, Karl Kuhlemann, David Sherry +2
Leibniz described imaginary roots, negatives, and infinitesimals as useful fictions. But did he view such 'impossible' numbers as mathematical entities? Alice and Bob take on the l…
Fermat's dilemma: Why did he keep mum on infinitesimals? and the European theological context
Jacques Bair, Mikhail G. Katz, David Sherry
The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparent…
Cauchy, infinitesimals and ghosts of departed quantifiers
Jacques Bair, Piotr Blaszczyk, Robert Ely +10
Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for t…