As a teenager, George Washington compiled two notebooks (179 pages) about the mathematics he studied: decimal arithmetic, geometry, logarithms and trigonometry, and surveying. We will examine an example of each of these, pointing out (when we can) where the explanations and problems came from, as well as a few errors in the manuscript.

These notebooks have had a hard life. For half of the nineteenth century they were on loan to biographers who treated them casually and dispersed some pages. We shall describe some of our success in locating these missing pages. Once they were sold to the government they were disbound and the pages reordered. This troublesome issue will also be described.

In 1960 the logician Abraham Robinson found a way to give a mathematically consistent theory of infinitesimals, thus justifying their use by Leibniz, Euler, and many others. We shall construct a model of the hyperreals that contains infinitesimals and infinite real numbers. Then we shall give definitions of the basic calculus notions, continuity, differentiability, and the integral. An abundance of easy examples and proofs will be provided to show that this approach is nicer than the standard epsilon-delta approach. This talk will be self contained and accessible to all.

 This is a presentation for students in a Foundations of Mathematics class, but everyone else is interested. We will present short biographies, descriptions of famous results, and ideas about further reading, devoting just six minutes to each of these individuals. We will paint the history of logic in the twentieth century in broad strokes.

Leśniewski (1886-1939) received his Ph.D. in Lwów under the direction of  Kazimierz Twardowski in 1912. After spending World War I in Russia, he was appointed, in 1919, professor of the philosophy of mathematics, at the newly reopened University of Warsaw. Starting in 1916 he began developing mereology, a theory of parts and wholes. This was followed by his ontology, a theory of names and it was underpinned by protothetic, a very general theory of deduction with quantifiers over all types of variables.

We shall not describe these theories in any detail, but will concentrate on discussing three of his important contributions: his analysis of Russell's antinomy, his views on definitions, and his precision in describing the rules of procedure for his logical systems.