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A Mathematician's Apology
''A Mathematician's Apology'' is a 1940 essay by British mathematician G. H. Hardy, which offers a defence of the pursuit of mathematics. Central to Hardy's " apology" — in the sense of a formal justification or defence (as in Plato's '' Apology of Socrates'') — is an argument that mathematics has value independent of possible applications. Hardy located this value in the beauty of mathematics, and gave some examples of and criteria for mathematical beauty. The book also includes a brief autobiography, and gives the layman an insight into the mind of a working mathematician. Background Hardy felt the need to justify his life's work in mathematics at this time mainly for two reasons. Firstly, at age 62, Hardy felt the approach of old age (he had survived a heart attack in 1939) and the decline of his mathematical creativity and skills. By devoting time to writing the Apology, Hardy was admitting that his own time as a creative mathematician was finished. In his foreword ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mathematics
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. History The origin of mathematics is subject to arguments and disagreements. Whether the birth of mathematics was a random happening or induced by necessity during the development of other subjects, like physics, is still a matter of prolific debates. Many thinkers have contributed their ideas concerning the nature of mathematics. Today, some philosophers of mathematics aim to give accounts of this form of inquiry and its products as they stand, while others emphasize a role for themselves that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academia
An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary education, secondary or tertiary education, tertiary higher education, higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and Skills, skill, north of Ancient Athens, Athens, Greece. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, ''Akademos''. Outside the city walls of Athens, the Gymnasium (ancient Greece), gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive Grove (nature), grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions into a method of teaching philosophy and in 3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aesthetics Books
Aesthetics, or esthetics, is a branch of philosophy that deals with the nature of beauty and taste, as well as the philosophy of art (its own area of philosophy that comes out of aesthetics). It examines aesthetic values, often expressed through judgments of taste. Aesthetics covers both natural and artificial sources of experiences and how we form a judgment about those sources. It considers what happens in our minds when we engage with objects or environments such as viewing visual art, listening to music, reading poetry, experiencing a play, watching a fashion show, movie, sports or even exploring various aspects of nature. The philosophy of art specifically studies how artists imagine, create, and perform works of art, as well as how people use, enjoy, and criticize art. Aesthetics considers why people like some works of art and not others, as well as how art can affect moods or even our beliefs. Both aesthetics and the philosophy of art try to find answers for what exact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biographies And Autobiographies Of Mathematicians
A biography, or simply bio, is a detailed description of a person's life. It involves more than just the basic facts like education, work, relationships, and death; it portrays a person's experience of these life events. Unlike a profile or curriculum vitae ( résumé), a biography presents a subject's life story, highlighting various aspects of their life, including intimate details of experience, and may include an analysis of the subject's personality. Biographical works are usually non-fiction, but fiction can also be used to portray a person's life. One in-depth form of biographical coverage is called legacy writing. Works in diverse media, from literature to film, form the genre known as biography. An authorized biography is written with the permission, cooperation, and at times, participation of a subject or a subject's heirs. An autobiography is written by the person themselves, sometimes with the assistance of a collaborator or ghostwriter. History At first, bio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1940 Non-fiction Books
Year 194 ( CXCIV) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Septimius and Septimius (or, less frequently, year 947 ''Ab urbe condita''). The denomination 194 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Emperor Septimius Severus and Decimus Clodius Septimius Albinus Caesar become Roman Consuls. * Battle of Issus: Septimius Severus marches with his army (12 legions) to Cilicia, and defeats Pescennius Niger, Roman governor of Syria. Pescennius retreats to Antioch, and is executed by Severus' troops. * Septimius Severus besieges Byzantium (194–196); the city walls suffer extensive damage. Asia * Battle of Yan Province: Warlords Cao Cao and Lü Bu fight for control over Yan Province; the battle lasts for over 100 days ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy (journal)
''Philosophy'' is the scholarly journal of the Royal Institute of Philosophy. It is designed to be intelligible to the non-specialist reader and has been in continuous publication since 1926. It is published by Cambridge University Press and is currently edited by Maria Alvarez and Bill Brewer Bill Brewer is a British philosopher and Susan Stebbing Professor of Philosophy at King's College London. He was previously the Head of the Department of Philosophy. He was a scholar at Oriel College, Oxford, reading Maths and Philosophy an .... The journal was established in 1926 "to build bridges between specialist philosophers and a wider educated public." Each issue contains a "New Books" section and an editorial on a topic of philosophical or public interest. References External links * Royal Institute of Philosophy Philosophy journals Cambridge University Press academic journals English-language journals Publications established in 1926 Quarterly journals 1926 establ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including (ε, δ)-definition of limit, codify ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Évariste Galois
Évariste Galois (; ; 25 October 1811 – 31 May 1832) was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem that had been open for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra. He was a staunch republican and was heavily involved in the political turmoil that surrounded the French Revolution of 1830. As a result of his political activism, he was arrested repeatedly, serving one jail sentence of several months. For reasons that remain obscure, shortly after his release from prison he fought in a duel and died of the wounds he suffered. Life Early life Galois was born on 25 October 1811 to Nicolas-Gabriel Galois and Adélaïde-Marie (née Demante). His father was a Republican and was head of Bourg-la-Reine's liberal party. His father became may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rolle's Theorem
In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one stationary point somewhere between them—that is, a point where the first derivative (the slope of the tangent line to the graph of the function) is zero. The theorem is named after Michel Rolle. Standard version of the theorem If a real-valued function is continuous on a proper closed interval , differentiable on the open interval , and , then there exists at least one in the open interval such that f'(c) = 0. This version of Rolle's theorem is used to prove the mean value theorem, of which Rolle's theorem is indeed a special case. It is also the basis for the proof of Taylor's theorem. History Although the theorem is named after Michel Rolle, Rolle's 1691 proof covered only the case of polynomial functions. His proof did not use the methods of differential calculus, which at that point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public-key Cryptography
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. In a public-key encryption system, anyone with a public key can encrypt a message, yielding a ciphertext, but only those who know the corresponding private key can decrypt the ciphertext to obtain the original message. For example, a journalist can publish the public key of an encryption key pair on a web site so that sources can send secret messages to the news organization in ciphertext. Only the journalist who knows the corresponding private key can decrypt the ciphertexts to obtain the sources' messages—an eavesdropp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
