Mathematics Without Borders (translated by Lehto and Wang Shanping, Shanghai Education Publishing House) is a book about the development history of the international mathematical union, which reminds us of Hilbert's famous saying: "For mathematics, the whole civilized world is a country". Why is the International Congress of Mathematicians the biggest event in the scientific community? This is because mathematics is more holistic and universal than other disciplines, and it is also the result of the unremitting efforts of the International Mathematical Union. The latter is most detailed in Mathematics Without Borders. The development of mathematics in the 20th century was not smooth, and the sudden change of political situation spread to the field of mathematics. It can be seen from the book that the attitude of French mathematicians towards defeated German mathematicians after World War I is different from that of the International Mathematical Union towards the Soviet Union during the Cold War. After the reform and opening up, China has also become a member of the International Mathematical Union. Today, the International Mathematical Union can really be called "International".
Mathematics culture course
Mathematics is a science, but it is also a culture. Just as Chen Shengshen, a master of mathematics, advocated "creating mathematical culture in the new century", in recent years, the publishing industry has shown great sensitivity and enthusiasm for this proposition, and has published a number of excellent books one after another. The Translation Series of Popular Mathematics Masterpieces by Shanghai Education Publishing House is the most striking book of this kind, and it has been published in 18 varieties. Most of his selected works are excellent works widely circulated abroad and praised by the public. They include different kinds in content, and some introduce the great achievements and applications of contemporary mathematics in simple words; Some follow the lead to inspire mathematical thinking and discovery skills; Some explain the relationship between mathematics and nature or other sciences from a philosophical point of view, providing people with a new perspective, so as to spy on the development of modern mathematics and appreciate the richness of mathematical culture.
The recent new varieties of the Translation Series of Popular Mathematical Masterpieces are: The Trail of Ants (USA) edited by David Gale and translated by Zhu Huilin; Topology experiment (USA) by Stephen Barr, translated by Xu Ming; Geometric Properties of Conic Curves Written by A. Cockshort and F. B. Walters (UK), translated by Jiang Sheng.
In Topology Experiment, a vivid and classic book in its field, an interesting topology master invites readers to boldly enter the fascinating topological kingdom of continuity and connectivity through Klein bottle and Mobius belt. The Geometric Properties of Conic Curves is an old book published more than a century ago, but it can give people a refreshing feeling, just like watching a costume TV series. For a long time, the cognitive demand for the elementary geometric properties of conic curves has reached a kind of * * * knowledge, so it adopts a comprehensive method to deal with conic curves, focusing on plane geometry knowledge, from graphics to graphics, straightforward. In the appendix, a summary article about butterfly theorem and an article introducing the historical data of conic curve contain precious information that is difficult to see elsewhere. Such alternative books provide a different landscape for popular mathematics reading materials.
The Selected Works of World Popular Science published by Hunan Education Publishing House also contains several wonderful math books, some of which are new.
Panorama of mathematics, reprint of the curiosity of topology, and newly launched mathematical tour.
(Author Givas Peterson). These books are all written by Mr Qiu Guangming, an old translator.
History of mathematics
American mathematician Klein's ancient and modern mathematical thoughts
(Shanghai Science and Technology Publishing House) is a masterpiece in the history of mathematics, with four volumes in Chinese translation, *** 1500 pages and nearly1200,000 words, which has been translated by many academicians and professors of Peking University Department of Mathematics 10 for many years. Starting from ancient Egypt and Babylon, this book describes the development of mathematics in a comprehensive, in-depth and detailed way until AD 1930. The mathematics in the book is expressed in the form of academic discussion and debate among mathematicians, and great attention is paid to placing mathematics in the cultural background. It is also interspersed with the short life of a great mathematician from time to time, so it is very interesting.
Mathematics after 1930 is not mentioned in ancient and modern mathematical thoughts. Considering the complexity and profundity of mathematics in the 20th century, it is almost impossible to write a decent history of mathematics in the 20th century. At this time,
Mathematical latitude and longitude in the 20 th century
(Zhang Dianzhou, East China Normal University Press) is out. Professor Zhang has interviewed many times and is very thoughtful. Moreover, he loved literature since he was a child and his writing style was quite good. In the 70 chapters of the book * * *, more than 100 masters have been biographed, often with only a few strokes, and the images and achievements of the masters are vividly on the paper, which makes readers admire them. Jingwei means that 70 sections are independent and not written in historical order, but you can still clearly see the central idea of the book, which is to tell you what is good and representative mathematics. Masters like Poincare and Atia focus on grasping mathematics as a whole, promoting the development of mathematical theory, promoting the connection between mathematics and related disciplines, or studying important issues such as three-body and Fermat's Last Theorem. This is good mathematics, which requires deep intuition and insight; The simple pursuit of technical difficulty (a large number of problems in elementary number theory are most suitable for this appetite) can only be regarded as "not bad" mathematics at most; As for some artificially defined concepts and axioms, they are very isolated and have no direct relationship with mainstream mathematics. They can't help solve practical problems, or they are doing "bad" mathematics. All extreme and artificial practices are not long-lasting. Everything belongs to nature and to the middle way. This is the truth. Liaoning Education Publishing House has been making great efforts in publishing books on the history of mathematics. Their latest contributions are Collation and Interpretation of Zu Chongzhi's Scientific Works (by Yan Dunjie) and General History of the History of Mathematics in the World (by Liang Zongju, Volume I and II). Liang Zongju is a professional researcher in the history of mathematics. He used to be vice chairman of chinese society of history of science and technology and vice chairman of the National Society of Mathematical History. The book General History, with a total of 1.3 million words, describes in detail the history of the emergence and development of mathematics in various civilizations in the world, including some original opinions of several authors, such as the classification of notation at home and abroad, Taylor's measurement of pyramids, and new understanding of Fermat's last theorem. The second volume of this book was written by Mr. Liang Zongju's students on the basis of his manuscript after his death, which was very impressive.
Recently, there is a book "The Story of Mathematics" (Hainan Publishing House), which was recommended by two experts, Wang Yuan and Hu Zuoxuan. It tells the story of past lives in mathematics from a cultural point of view. The illustrations are particularly beautiful and suitable for people who don't know much about mathematics. History of Mathematics (written by Scott, translated by Hou Derun of Guangxi Normal University Press) is also a well-known book, which reflects the earlier history of mathematics and is quite innovative in content.
Biography of mathematicians
My brain is open (by Schechter, translated by Wang Yuan, etc. , Shanghai Translation Publishing House) is the biography of the famous mathematician Ai Duoshi, and Ai Duoshi is the biography of Erdos in Digital Love, but the translation name is different. The content of the two books is not much different, and the translation style is similar. Wang Yuan is a famous mathematician in China, so there is no problem in mathematics, unlike some popular mathematics books, which are full of mistakes. Anecdotes about Ai Duoshi are not mentioned here. It is worth mentioning that after reading these two books, we should realize that Ai Duoshi is not a real eccentric, but a Platonist. He thinks that mathematics is a lofty knowledge entity independent of human beings, and our task is to find her. This is what his famous saying "the best proof is written in the book of God" expresses. Barrow's Pi in the Sky and Penrose's The Emperor's New Brain both quoted this sentence. We don't have to imitate Ai Duoshi, but we should learn from his super-utilitarian spirit.
The "Sorcerer's Stone Series" published by Shanghai Science and Technology Education Press will soon publish the biographies of Smale, Godel and Lamanukin, all of which are translated versions. All three of them are legends. Among them, Ramanujin's book is Kanigher's masterpiece The Knower Without Limits. The other two books were also highly praised. "A Beautiful Mind-Biography of Nash" has been introduced a lot, so I won't leave much ink here.
In addition, Shanghai Science and Technology Publishing House published Hilbert-Alexander in the Mathematical World two years ago, which is also a concern of friends who love mathematics.
Puzzle (or "game") mathematics
The most representative in this respect is Gardner's Interesting Mathematics Series published by Shanghai Science and Technology Education Press.
Martin gardner is a world-famous writer of mathematics popularization. He presided over the "Game Mathematics" column of Scientific American magazine for a long time. His works are characterized by "packaging" serious and cold mathematics with colorful social life, and integrating mathematics into games, entertainment, culture and even art, which makes people interested in reading.
From 65438 to 0999, Shanghai Science and Technology Education Press began to publish "Gardner's Interesting Mathematics Series". So far, eight kinds have been published, namely: fascinating and interesting mathematical problems, Sam Lloyd's interesting mathematical problems, the continuation of Sam Lloyd's interesting mathematical problems, Dr. Matrix's magic number, testing your logical reasoning ability and new interesting logical reasoning problems.
"If three cats catch three mice in three minutes, how many cats will catch 100 mice in 100 minutes?" Such interesting math problems will make you experience the fun of intellectual gymnastics and enrich your spare time.
After the publication of this series, it won the first prize of the second national mathematics education book award and the second prize of the ninth Shanghai excellent extracurricular reading materials for primary and secondary schools. The circulation is also rising, and now the largest variety has reached more than 60,000 copies. At the most, 10 copies were printed.
A story about a branch or theme of mathematics.
Masterpieces are not a flash in the pan, a bit like old wine, and every serious reader will definitely have a lesson. Symmetry (Will, translated by Feng Chengtian, etc. ), natural encounter-the origin of chaos and stability (Diacu, Wesley Wang) and how to solve problems-the new face of mathematics teaching method (Paulia, translated by Tu Hong), etc. ) In Shanghai Science and Technology Education Press, Princeton Library is undoubtedly a world-famous masterpiece.
It has long been observed that symmetry is an important order in the objective world, which is related to mathematics, material, culture, life and other disciplines. Only recently 100 years has it become an important way for scientists to look at the world. Among them, Will is indispensable. He creatively applied the symmetry theory in mathematics-group theory to quantum mechanics and gauge field theory.
As one of the greatest mathematicians in the 20th century, Weil is probably the most qualified person to talk about symmetry in mathematical science. In order to greatly expand the symmetrical readers, Weil also collected a large number of exquisite art and biological pictures, and vividly and rigorously described various concepts such as bilateral symmetry, translational symmetry and rotational symmetry through these examples. From the perspective of symmetry, the book almost gives a comprehensive mathematical explanation of the inorganic and biological world and even human culture.
Group theory is an important foundation of modern science, which has very practical and endless significance, but the current teaching is poor because it is divorced from reality. Symmetry, on the other hand, can effectively guide people into the world of groups and fully enjoy the beauty of science. For example, after introducing the crystal structure, Weil finally pointed out that "whenever people deal with an entity given a structure, they try to determine its automorphism group ... by using this method, you can expect to understand the structure of S". This kind of words that can make people feel enlightened and so powerful are everywhere, which makes people feel that they are grasped at will rather than carefully arranged. This is precisely because Wyle's understanding has reached the level of transparency. This booklet reflects the characteristics of master science popularization in a simple way.
Destiny is an equally wonderful work with an intriguing history. 10 years ago, Gleike's Chaos: Creating a New Science swept the world. Gerecke is a journalist, emphasizing the portrayal of his contemporaries; The famous popular science writer Stewart's "Does God Roll Dice" gives an artistic description of some theories and history. The book God is really wonderful, but the author of Meet in Heaven is not satisfied. They want to reflect the origin of the chaos in1970s from a higher level.
The originator of chaos can be said to be Poincare's study of three bodies. This masterpiece was completed around 1900. Because axiomatic and structured mathematics was advocated at that time, even Poincare, as the last person who crossed several disciplines, did not get the due evaluation. By the early 1960s, mathematicians, physicists and astronomers were even accused of "going their separate ways". But with the development of computer technology, physicists put forward "chaos", and mathematicians are more and more interested in nonlinear problems. People finally realized that the work of Poincare and his successors was the mainstream of mathematics in the 20th century.
Meet in Heaven is closely related to the century-old history of celestial mechanics and dynamic system. At first, Poincare was the main theme, followed by several major themes, including the famous Cam theory, which shone with the wisdom of top masters such as Colmo Grove and Arnold. In particular, Xia Zhihong, a young mathematician in China, solved the Painleve conjecture that lasted for a hundred years. Painleve speculates that there is the possibility of non-collision singularity in the initial condition of a given star under the action of universal gravitation. In other words, there is no collision between stars, and some stars have gone to infinity. It seems impossible, but Xia Zhihong constructed five examples of celestial bodies more than 10 years ago, when he was less than 30 years old, and his paper was recognized after many twists and turns. The description of this in the book is very detailed and touching.
To understand chaos, it is best to read the above three books.
After God, Stuart's other masterpiece is The Second Mystery (translated by Zhou Zhongliang, Shanghai Science and Technology Publishing House). Stuart has a great advantage. His popular science is "keeping pace with the times". With the determination of the fund group sequence of human beings and various creatures, it seems that it is time to do something in mathematics and analyze the countless information contained in it. This is not a simple statistical problem. Natural science has positivism spirit. It first obtains phenomena and data through experiments, and then systematizes them with mathematics. This is obviously the worst in biology. However, because economics cannot simply conduct empirical research on society, mathematics has penetrated a lot. For example, game theory and stochastic differential equations, all of which are profound and have won the Nobel Prize in Economics. Recently, the mathematical tool "density functional theory" even won the chemistry prize.