Books:
* A Course of Pure Mathematics (1908): This classic textbook introduced rigorous methods and abstract concepts to a wider audience, becoming a standard for mathematics education.
* Orders of Infinity (1910): A foundational work on the theory of transfinite numbers and the concept of infinity.
* The Theory of Numbers (1912): A comprehensive treatment of number theory, covering topics like Diophantine equations, quadratic residues, and analytic number theory.
* Some Famous Problems of the Theory of Numbers (1920): A collection of essays on unsolved problems in number theory, inspiring future generations of mathematicians.
* Inequalities (1934): A collaborative work with J. E. Littlewood, offering a systematic exploration of inequalities and their applications.
* A Mathematician's Apology (1940): A personal and philosophical reflection on the nature of mathematics, its beauty, and its relevance to life.
Important Papers:
* Contributions to the theory of Riemann's zeta function: Hardy made significant contributions to the study of the zeta function, including proving the infinitude of prime numbers and establishing the distribution of prime numbers.
* Hardy-Littlewood Circle Method: A powerful technique for analyzing problems in number theory, developed in collaboration with John Littlewood.
* Papers on Diophantine Approximation: Hardy's work in this area contributed significantly to understanding the approximation of real numbers by rational numbers.
Other Contributions:
* Hardy was a strong advocate for pure mathematics and its importance in the scientific world.
* He was known for his collaborations with other mathematicians, notably John Littlewood and Srinivasa Ramanujan.
* Hardy's writings are characterized by their clarity, elegance, and insight, making them both accessible and inspiring to mathematicians and non-mathematicians alike.
His work continues to influence mathematicians today, solidifying his position as one of the most important mathematicians of the 20th century.