Musings of the Masters: An Anthology of Mathematical Reflections (Spectrum)

The anthology is a collection of articles contiguous to the humanities written by renowned mathematicians of the twentieth century. The articles cover a variety of topics that, for want of a better name, shall be referred to as humanistic. An important criterion, thereby limiting the choice, is that the articles should be accessible to the literate reader who may or may not have technical knowledge of mathematics. The articles span roughly a century in time and a wide range in subject. They are by mathematicians acknowledged by their peers as outstanding creators whose work has added richly to the discipline. Each article is preceded by a brief biographical sketch of the author and a brief indication of the content. The material is accessible to a wide audience, lay as well as academic. This Anthology Is A Collection Of Articles Written By Renowned Mathematicians Of The 20th Century. The Articles Are On A Variety Of Topics That We Refer To, For Want Of A Better Name, As Humanistic. An Important Criterion, Thereby Limiting The Choice, Is That The Articles Should Be Accessible To The Literate Reader Who May Or May Not Have A Technical Knowledge Of Mathematics. The Articles Span Roughly A Century In Time And Touch On A Wide Range Of Subjects. They Are By Mathematicians Acknowledged By Their Peers As Outstanding Creators Whose Work Had Added Richly To The Discipline. Each Article Is Preceded By A Brief Biographical Sketch Of The Author And Some Indication Of The Content. In Many Articles There Is A Common Theme - The Attempt To Define The Role Of Intuition In Mathematical Activities - Intuition As Contrasted With Pure Formalism, A Contrast That Can Be Briefly, If Too Simply, Described By Asking Whether Mathematics Is Invented Or Discovered.--jacket. Pt. 1. Mathematics And The Intellect. Mathematics And Thinking Mathematically / Mary Cartwright -- Mathematical Invention / Henri Poincaré -- Thoughts On The Heuristic Method / Jacques Hadamard -- Mathematical Proof / G.h. Hardy -- The Unity Of Knowledge / Hermann Weyl -- Pt. 2. Mathematics And Human Understanding. Mathematics And The Arts / Marston Morse -- Intuition, Reason And Faith In Science / George David Birkhoff -- Logic And The Understanding Of Nature / David Hilbert -- The Cultural Basis Of Mathematics / Raymond Wilder -- Pt. 3. Mathematics And Society. Presidential Address To The British Association / J.j. Sylvester -- The Mathematician / John Von Neumann -- The Community Of Scholars / André Lichnerowicz -- History Of Mathematics: Why And How / André Weil -- Pt. 4. Miscellaneous. Does God Exist? / Paul Lévy -- Goethe And Mathematics / Wilhelm Maak -- Leonardo And Mathematics / Francesco Severi -- The Highest Good / Norbert Wiener. Edited By Raymond G. Ayoub. Includes Bibliographical References (p. 271-272) And Index. Cover......Page __sk_0000.djvu Copyright......Page __sk_0002.djvu Contents......Page __sk_0015.djvu Introduction......Page __sk_0007.djvu Mathematics and Thinking Mathematically — Mary Cartwright......Page __sk_0019.djvu Mathematical Invention — Henri Poincaré......Page __sk_0033.djvu Thoughts on the Heuristic Method — Jacques Hadamard......Page __sk_0047.djvu Mathematical Proof — G. H. Hardy......Page __sk_0061.djvu The Unity of Knowledge — Hermann Weyl......Page __sk_0081.djvu Mathematics and the Arts — Marston Morse......Page __sk_0097.djvu Intuition, Reason, and Faith in Science — George David Birkhoff......Page __sk_0111.djvu Logic and the Understanding of Nature — David Hilbert......Page __sk_0131.djvu The Cultural Basis of Mathematics — Raymond Wilder......Page __sk_0145.djvu Presidential Address to the British Association — J.J. Sylvester......Page __sk_0167.djvu The Mathematician — John von Neumann......Page __sk_0185.djvu The Community of Scholars — André Lichnerowicz......Page __sk_0201.djvu History of Mathematics: Why and How — André Weil......Page __sk_0215.djvu Does God Exist? — Paul Lévy......Page __sk_0233.djvu Goethe and Mathematics — Wilhelm Maak......Page __sk_0247.djvu Leonardo and Mathematics — Francesco Severi......Page __sk_0263.djvu The Highest Good — Norbert Wiener......Page __sk_0273.djvu Sources of the Articles......Page __sk_0287.djvu Index......Page __sk_0289.djvu Dame Mary Lucy Cartwright (1900-1998), D.B.E., F.R.S., to give her full name and honors, was born in Northamptonshire, the daughter of a rector.