The Mathematics that Counts - Professor Robin Wilson

TL;DR

Combinatorics is a branch of mathematics concerned with selecting, arranging, counting, and listing collections of objects. It has both historical and modern significance.

Transcript

well good evening and thank you very much for coming and particularly welcome to those of you who are here for the first time and also welcome to the launch of common Toric's ancient and modern a recent book on the history of common Toric's and we believe actually the first full-length book on the subject so the purpose of the day is to tell you wh... Read More

Key Insights

• 👂 Combinatorics is the branch of mathematics concerned with selecting, arranging, counting, and listing collections of objects.
• 🌍 The history of combinatorics includes contributions from ancient China, India, the Islamic world, and Renaissance Europe.
• 🎨 Modern combinatorics encompasses topics such as graph theory, block designs, and Latin squares.
• 👾 Combinatorial problems are found in various fields, including mathematics, computer science, and even games and puzzles.

Questions & Answers

Q: What is combinatorics?

Combinatorics is the branch of mathematics that deals with selecting, arranging, counting, and listing collections of objects, particularly finite collections.

Q: What are some examples of combinatorial problems?

Combinatorial problems include permutations and combinations of objects in a set, recreational problems from graph theory, magic squares, Latin squares, and Sudoku puzzles.

Q: How did combinatorics develop throughout history?

Combinatorics has a multicultural origin, with contributions from ancient China, India, the Islamic world, and Jewish scholars. It later developed in Renaissance Europe and continued to evolve with modern topics such as graph theory and block designs.

Q: Who are some notable mathematicians in the field of combinatorics?

Donald Knuth, Peter Cameron, Leonard Euler, Arthur Cayley, Benjamin Franklin, and Andreas Evars are some notable mathematicians who have made significant contributions to combinatorics.

Summary & Key Takeaways

• Combinatorics is the branch of mathematics concerned with selecting, arranging, and counting collections of objects, such as permutations and combinations.

• The book "Combinatorics: Ancient and Modern" explores the history of combinatorics, including its multicultural origins and its development in Renaissance Europe.

• The book also covers modern topics in combinatorics, such as graph theory, block designs, and Latin squares.