This is a volume of essays and reviews that delightfully explore mathematics in all its moods โ from the light and the witty, and humorous to serious, rational, and cerebral. Topics include: logic, combinatorics, statistics, economics, artificial intelligence, computer science, and applications of mathematics broadly. You will also find history and philosophy covered, including discussion of the work of Ulam, Kant, Heidegger among others. "...these papers reflect on mathematics and its influence on human society. They can help the specialist to notice what is going on around him, and they may lead educated people from other domains to a better understanding of mathematics. Many of these papers can advise educators how to form a modern mathematics education, which develops approved ideas and institutions...I admire the stimulating perspectives of the authors."---American Mathematical Society "'Mathematicians, like Proust and everyone else, are at their best when writing about their first love' โฆ They are among the very best we have; and their best is very good indeed. โฆ One approaches this book with high hopes. Happily, one is not disappointed."--- From The Mathematical Intelligencer "Mathematics is shaped by the consistent concerns and styles of powerful minds โthree of which are represented here. Kac's work is marked by deep commitment and breadth of inquiry. Rota is the easiest of these authors to readโฆa delight: witty and urbane, with a clear and interesting agenda and an astonishing intellectual range. To read him is to be a part of a pleasant and rewarding conversation.โMathematics Magazine
CONTENT
Discrete Thoughts -- Discrete Thoughts -- I -- Mathematics: Tensions -- The Pernicious Influence of Mathematics on Science -- Statistics -- Statistics and Its History -- Combinatorics -- Computer Science -- Mathematics: Trends -- The Future of Computer Science -- Economics, Mathematical and Empirical -- II -- Complicating Mathematics -- Mathematics and Its History -- Academic Responsibility -- Husserl and the Reform of Logic -- Husserl -- Artificial Intelligence -- Computing and Its History -- Will Computers Replace Humans? -- Computer-Aided Instruction -- Misreading the History of Mathematics -- The Wonderful World of Uncle Stan -- Ulam -- Kant -- Heidegger -- Doing Away with Science -- More Discrete Thoughts
