The concept of an "exceptional set" is generally used in various fields of mathematics, often in set theory, topology, and functional analysis. Exceptional sets can refer to specific sets of points that possess unique properties or which deviate from typical behavior in some way. Below are some common types of exceptional sets across different areas of mathematics: 1. **Lebesgue Null Sets**: These are sets of Lebesgue measure zero in \( \mathbb{R}^n \).

Amateur mathematicians are individuals who engage in mathematical activities, research, or problem-solving out of personal interest and passion rather than as a professional mathematician. They may not have formal training or qualifications in mathematics, but they often pursue mathematical ideas, concepts, and problems independently or within informal communities. Amateur mathematicians have historically contributed to various areas of mathematics, sometimes making significant discoveries or advancements.

The Josiah Willard Gibbs Lectureship is an esteemed honor awarded by the American Chemical Society (ACS) in recognition of outstanding contributions in the field of chemical thermodynamics or statistical mechanics. Named after the prominent American scientist Josiah Willard Gibbs, who made significant advancements in these areas, the lectureship is typically awarded to chemists who have demonstrated exceptional research and scholarly activities. The recipient is invited to give a lecture at an ACS national meeting, showcasing their research and contributions to the field.

Math rock is a subgenre of rock music that emerged in the late 1980s and gained prominence in the 1990s. It is characterized by its complex time signatures, intricate guitar work, and experimental structures. Musicians in this genre often employ unconventional rhythms and polyrhythms, as well as dissonant chords and unusual scales.

The Fellows of the American Mathematical Society (AMS) is an honorary program that recognizes members of the American Mathematical Society who have made notable contributions to the advancement of mathematics. Established in 2012, the program honors individuals for their exceptional achievements in research, education, and service to the mathematical community. Selection as a Fellow of the AMS is based on nominations and includes criteria such as outstanding contributions to the mathematical sciences and a sustained record of research and scholarship that has significant impact.

Fictional mathematicians are characters in literature, film, television, and other forms of storytelling who are depicted as mathematicians, mathematicians' assistants, or individuals deeply involved in mathematical concepts. These characters may be central to the plot or serve as supporting roles, and their mathematical pursuits can range from abstract theory to practical problem-solving.

LGBT mathematicians refer to individuals within the field of mathematics who identify as part of the LGBTQ+ community—encompassing lesbian, gay, bisexual, transgender, queer, and other sexual and gender minorities. Like in other fields, LGBT mathematicians have made significant contributions to mathematics, research, and education, although their experiences may have been shaped by the challenges and discrimination often faced by marginalized groups.

Mark Reed is a notable physicist recognized for his contributions to the field of applied physics, particularly in nanotechnology and quantum mechanics. He is known for his work on nanoelectronic devices and quantum systems, which play a crucial role in the development of advanced materials and technologies. Reed has conducted research on various topics, including quantum-dot systems, single-electron transistors, and topological insulators.

Lists of mathematicians typically refer to compilations or directories that catalog mathematicians, often organized by various criteria such as their fields of study, significant contributions, historical periods, or nationalities. These lists may include biographical information, notable works, and theorems or discoveries made by each mathematician.

There are many concepts, theorems, structures, and other mathematical entities that are named after mathematicians, often to honor their contributions to the field. Here are some examples spanning various areas of mathematics: ### Theorems and Results 1. **Pythagorean Theorem** (Pythagoras) - Relates the sides of a right triangle.

"Mathematician stubs" typically refers to short articles or entries on mathematicians, often found on platforms like Wikipedia, that provide minimal information about a specific mathematician. These stubs may include only basic details such as the mathematician's name, birth and death dates, and a few key contributions or works.

"Mathematicians by award" typically refers to notable mathematicians recognized for their contributions to the field through various prestigious awards and honors. Here are some of the most renowned awards in mathematics and a few prominent mathematicians associated with those awards: 1. **Fields Medal**: Often referred to as the "Nobel Prize of Mathematics," it is awarded every four years to mathematicians under 40 years of age for outstanding achievements. - Notable recipients: André Weil, John G.

"Mathematicians by city" typically refers to discussions or listings of notable mathematicians who were born in, lived in, or significantly worked in specific cities. This concept could cover a range of topics, including: 1. **Famous mathematicians from specific cities**: For example, you might find lists of mathematicians from Paris, Berlin, Cambridge, or New York.

Mathematicians can be categorized by their areas of specialization, reflecting the diverse fields within mathematics. Here are some key fields and notable mathematicians associated with them: 1. **Pure Mathematics**: - **Algebra**: Focuses on structures such as groups, rings, and fields. Notable mathematicians include Évariste Galois and Emmy Noether. - **Geometry**: The study of shapes, sizes, and properties of space.

The Presidents of the European Mathematical Society (EMS) are the elected leaders who guide the organization, which aims to promote and support mathematics in Europe. The EMS organizes conferences, supports research and education in mathematics, and fosters collaboration among mathematicians across European countries. The presidency is typically held for a term of several years, during which the president oversees the activities of the society, represents it in international mathematical organizations, and works to enhance the visibility and development of mathematics in Europe.

The Presidents of the International Mathematical Union (IMU) are the leaders of the organization, which is a worldwide body dedicated to promoting international cooperation in mathematics. The IMU was established in 1952 and is responsible for organizing international mathematical congresses, supporting mathematical research, and fostering connections among mathematicians globally. The IMU's presidency typically serves a term of four years, during which the president represents the Union at international mathematical events, oversees its activities, and contributes to the development of mathematics worldwide.

Pseudonymous mathematicians are individuals in the field of mathematics who publish their work under a pseudonym, rather than their real name. This practice has historical roots and has been used for various reasons, including: 1. **Privacy**: Some mathematicians may prefer to keep their identity private for personal or professional reasons. 2. **Political or Social Context**: In certain countries and historical contexts, publishing under a pseudonym can provide some protection against political persecution or societal backlash.

"Second Wranglers" might refer to different contexts depending on the field of interest, but it is not a widely recognized term as of my last knowledge update in October 2023. However, if you're referring to a term related to the entertainment industry, work teams, or perhaps a specific organization or a project, additional context would be necessary to provide a precise response.

"Senior Wranglers" typically refers to a specific group of individuals, often associated with the University of Cambridge, who hold a prestigious academic title. At Cambridge, "Wrangler" is a term used for students who excel in mathematics, particularly those who achieve high scores in their final examinations for the Mathematics Tripos. The term "Senior Wrangler" designates the top-ranking student in this examination. The title is historically significant and is regarded as a mark of distinction within the university's mathematics community.