Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline. This second edition covers theorems proved in 2001-2025.

The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given.

Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own.

Bogdan Grechuk fell in love with mathematics as a child, taking part in various mathematics competitions, including the International Mathematical Olympiad where he won a gold medal in 1997. He has been at the University of Leicester (UK) since 2011, where he is currently an associate professor.