The primary goal of mathematical societies is to promote the advancement of mathematics by providing a forum for mathematicians to share their research, educating the public about mathematics, and supporting the professional development of mathematicians.

Mathematical societies have a variety of specific objectives, including organizing conferences and workshops, publishing journals and books, awarding prizes and grants, and advocating for the interests of mathematicians.

The London Mathematical Society is the oldest mathematical society in the world, founded in 1865.

The American Mathematical Society has over 30,000 members, making it one of the largest mathematical societies in the world.

The Steele Prize is the most prestigious award given by the American Mathematical Society, awarded annually to mathematicians for outstanding research.

The International Mathematical Union is an international organization that promotes international cooperation in mathematics, organizes the International Congress of Mathematicians, and awards the Fields Medal.

The International Congress of Mathematicians is held every four years.

The Fields Medal is awarded to mathematicians under the age of 40 who have made outstanding contributions to mathematics, including those who have won the Abel Prize.

Two Fields Medals are awarded each year.

The Mathematical Association of America is a professional organization that promotes the understanding and appreciation of mathematics, improves the teaching of mathematics, and supports research in mathematics.

The Mathematical Association of America has over 30,000 members, making it one of the largest mathematical societies in the world.

The Chauvenet Prize is the most prestigious award given by the Mathematical Association of America, awarded annually to authors of outstanding expository articles on mathematics.

The Society for Industrial and Applied Mathematics is a professional organization that promotes the development of applied mathematics, provides a forum for mathematicians and engineers to share their research, and supports the professional development of applied mathematicians.

The Society for Industrial and Applied Mathematics has over 15,000 members, making it one of the largest mathematical societies in the world.

The John von Neumann Prize is the most prestigious award given by the Society for Industrial and Applied Mathematics, awarded annually to individuals who have made outstanding contributions to the theory, analysis, or practice of scientific computing.