Magnetic monopoles are hypothetical particles that are theorized to be isolated magnetic charges, similar to how electric charges exist as positive or negative entities. In classical electromagnetism, magnetic fields are produced by electric charges, and magnetic poles always occur in pairs—every magnet has a north and a south pole. The idea of magnetic monopoles was first introduced by physicist Paul Dirac in 1931.

Physics beyond the Standard Model refers to theoretical and experimental research that seeks to address limitations and unanswered questions associated with the Standard Model of particle physics. The Standard Model successfully describes the fundamental particles and their interactions through the electromagnetic, weak, and strong forces, but it has several significant shortcomings: 1. **Gravity**: The Standard Model does not incorporate gravity, which is described by General Relativity. A complete theory of quantum gravity remains elusive.

The 19th century was a significant period for physics in Austria, with notable contributions from several prominent physicists. Here are a few key figures: 1. **Ernst Mach (1838-1916)**: Mach was an influential physicist and philosopher known for his work in mechanics, particularly in relation to the concept of shock waves and supersonic speeds. He is also known for the Mach principle and contributions to the philosophy of science, questioning the foundations and interpretations of physical theories.

Guo Shoujing (1231–1316) was a prominent Chinese astronomer, engineer, and hydrologist during the Yuan Dynasty. He is best known for his work in advancing astronomical observation and developing more accurate calendars. Guo played a crucial role in the construction of large astronomical instruments, including the armillary sphere, and improved the accuracy of measurements for time and celestial events.

Heinz Rutishauser refers to a notable Swiss mathematician known for his contributions to mathematical logic and computational theory, particularly in the areas of recursive functions and general recursive mathematics. He is best recognized for his work on algorithms and computability during the mid-20th century.

Tom Lehrer is an American singer-songwriter, pianist, and mathematical scientist, known for his satirical and humorous songs. He gained popularity in the 1950s and 1960s for his witty lyrics, which often addressed social and political issues, presenting them in a comedic light.

Zhang Heng (78–139 AD) was a prominent Chinese polymath during the Eastern Han Dynasty, known for his contributions to the fields of astronomy, mathematics, engineering, and literature. He is particularly famous for several achievements: 1. **Seismology**: Zhang Heng invented the first known seismoscope, called the "Houfeng Didong Yi," around 132 AD. This device could detect the direction of an earthquake and was significant in the study of seismic activity.

Zu Chongzhi was a Chinese mathematician and astronomer who lived during the Northern and Southern dynasties period (circa 429–500 AD). He is best known for his work in mathematics, particularly for his calculation of the value of π (pi). Zu Chongzhi calculated π to be approximately 3.1415926, which was remarkably accurate for his time and remained the most precise approximation for over a thousand years.

The Fellows of the Association for Women in Mathematics (AWM) is an honorary designation that recognizes women who have made significant contributions to the field of mathematics. This initiative is aimed at highlighting the achievements of women mathematicians, promoting their work, and encouraging the inclusion of women in mathematics. The fellowship honors those who have demonstrated excellence in research, teaching, or service to the community, and recipients are typically nominated by their peers.