Analysis and synthesis are key experimental operations in modern science, most obviously in chemistry from the era of Lavoisier onward. But when and how did breaking bodies into their components and then resynthesizing them become a method of demonstrating truths about nature and a hallmark of rigorous science? As words and concepts, analysis and synthesis stretch back to Euclid, Plato, and Aristotle, and weave through proof, logic, and the practice of philosophy. This conference investigates the possible connections between mathematico-philosophical methodologies and the tradition of material decomposition and resynthesis, as in post-Lavoisian chemistry. More broadly, it explores the concatenation of disciplines, both scientific and artisanal, that may have contributed to the experimental development of analysis and synthesis as complementary tools par excellence for understanding material and conceptual matters.