Logical positivism, also known as logical empiricism, is a philosophical movement that developed in the early 20th century, primarily in the context of the Vienna Circle and the work of philosophers such as Moritz Schlick, Rudolf Carnap, and A.J. Ayer. It sought to synthesize elements of empiricism and formal logic, emphasizing the importance of scientific knowledge and the use of logical analysis in philosophical inquiry.

Unsolved problems in mathematics refer to questions or conjectures that have not yet been proven or disproven despite significant effort from mathematicians. These problems span various fields of mathematics, including number theory, algebra, geometry, and analysis. Some of these problems have been known for many years, while others are more recent.

Japanese mathematics refers to both historical and contemporary mathematical practices and developments in Japan. The term can encompass a variety of topics, including traditional Japanese mathematics (often called "wasan"), modern mathematical education, and contemporary research and contributions to global mathematics. ### Historical Context: Wasan 1. **Wasan (和算)**: This term specifically refers to traditional Japanese mathematics that developed from the 17th century until the 19th century.

Alan C. Gilmore may refer to a specific individual or a name associated with various contexts, but there is limited publicly available information on a notable figure by that name. Without additional context, it is difficult to provide a precise answer.

"North American physicists" broadly refers to physicists who are based in or are citizens of countries in North America, primarily the United States, Canada, and Mexico. These scientists engage in research and education in various fields of physics, including but not limited to, condensed matter physics, particle physics, astrophysics, and applied physics. North American physicists often work in academic institutions, research laboratories, and industry, contributing to advancements in scientific knowledge, technology, and education.

Physics departments in Canada can be found at various universities across the country, each offering a range of undergraduate and graduate programs in physics. These departments are involved in teaching, research, and contributions to various fields of physics, including theoretical and experimental physics, astrophysics, condensed matter physics, and more.