We discussed "what is science" -- discussing issues like the "scientific method," the role of experiment, etc. We distinguished a hypothesis in mathematics which can be proven from a hypothesis in science which can only be shown to be false. (Falsifiability is an important feature of a scientific conjecture, and repeatability is an important aspect of a scientific observation/experiment.)

We started discussing Archimedes. We mentioned his work with simple machines (screws and levers), his achievement in math (some early results in integration, limits, etc.), and his work on buoyancy and the crown of gold story.