Mathematics Mathematics is the body of knowledge centered on concepts such as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions". Other practitioners of mathematics maintain that mathematics is the science of pattern, that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.
Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Knowledge and use of basic mathematics have always been an inherent and integral part of individual and group life. Refinements of the basic ideas are visible in mathematical texts originating in ancient Egypt, Mesopotamia, ancient India, ancient China, and ancient Greece. Rigorous arguments first appear in Euclid's Elements. The development continued in fitful bursts until the Renaissance period of the 16th century, when mathematical innovations interacted with new scientific discoveries, leading to an acceleration in research that continues to the present day.
Today, mathematics is used throughout the world in many fields, including natural science, engineering, medicine, and the social sciences such as economics. Applied mathematics, the application of mathematics to such fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although applications for what began as pure mathematics are often discovered later.
Simon Singh's site on the search for a solution to the great mathematical problem
Fermat’s Last Theorem is the most notorious problem in the history of mathematics and surrounding it is one of the greatest stories imaginable. This section explains what the theorem is, who invented it and who eventually proved it. When finished, it will also tell the fascinating stories of the some of the other mathematicians whose lives were tormented by this beautiful and intriguing problem.
Fermat’s Last Theorem dominated my own life for four years, because I made a TV documentary, wrote a book and then lectured on the subject. Getting involved in Fermat’s mischievous conundrum set me on the path towards being an author and ignited an interest in mathematics that has continued ever since. As a physicist, I was always interested in mathematics as a tool for studying the universe, but learning about Fermat’s Last Theorem taught me to love mathematics for its own sake. There is a Mathematics Corner currently being developed for this site. Sign up to my newsletter to find out when it is launched.
This section also has some pages on the some of wackier aspects of the Last Theorem; a romantic story, a few poems and limericks, and an off-Broadway musical! And once you’ve explored this site then you can visit some of the other Fermat websites. Or try out the Fermat quiz, which is not as hard as proving the Last Theorem and somewhat more trivial.
Over the next few months, more material will be added to the Fermat corner. There will be a special section that contains material for teachers and a collection of articles that I have written about Fermat’s Last Theorem.
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