Here are 100 books that Euclid's Elements fans have personally recommended if you like
Euclid's Elements.
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As a professor, I see students fascinated by science, but petrified to take a science class. This is in part because we have dehumanized science, removed the story, edited out the human, deleted the parts that allow people to connect with it. Science does not get delivered by gods, but is created by people: smart, quirky, sometimes immoral people. As a writer, my hope is to be able to reinsert life into readers’ understanding of our greatest advances. As a reader myself, I am deeply appreciative when other authors do it too.
David Hilbert was the most important mathematician at the dawn of the 20th century. In 1900, he gave the mathematical community its homework for the next 100 years setting out the list of open problems that had to be solved by 2000. While to the rest of the mathematicians, he may have appeared as their professor, he was also the class clown. As colorful and funny as he was brilliant, you cannot but come away loving this great mathematical genius.
"It presents a sensitive portrait of a great human being. It describes accurately and intelligibly on a nontechnical level the world of mathematical ideas in which Hilbert created his masterpieces. And it illuminates the background of German social history against which the drama of Hilberts life was played. Beyond this, it is a poem in praise of mathematics." -SCIENCE
I love mathematics and truly believe that “Functions Describe the World.” I'm deeply satisfied that I've spent my professional life discovering new mathematics and explaining known mathematics to others. I was an undergraduate at the University of Texas, Austin, got my PhD from Brown University, then spent three years as a G.C. Evans Instructor at Rice University, before moving to Williams, where I've been ever since. Besides writing All the Math You Missed (But Need to Know for Graduate School), I've also written Algebraic Geometry: A Problem Solving Approach (with a number of co-authors) and Electricity and Magnetism for Mathematicians: A Guided Path from Maxwell’s Equations to Yang-Mills, and a number of research articles.
Ulam was a Polish mathematical prodigy, publishing significant mathematics by the time he was 20. He was part of the rich Polish math community centered around Stefan Banach. Unlike most, he was heading to the United States in 1939 (with his younger brother) when Germany invaded Poland. All the rest of his family were murdered by the Nazis. He on the other hand ended up in Los Alamos, providing critical help on the Manhattan Project. Later in life, he wrote this book, his autobiography. Based on his history, one could well think that it would be a book full of tragic grief. Instead, it is a pean to the joys of doing mathematics and of living a life full of mathematics, without downplaying the horrors of the mid-twentieth century.
This autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his…
I love mathematics and truly believe that “Functions Describe the World.” I'm deeply satisfied that I've spent my professional life discovering new mathematics and explaining known mathematics to others. I was an undergraduate at the University of Texas, Austin, got my PhD from Brown University, then spent three years as a G.C. Evans Instructor at Rice University, before moving to Williams, where I've been ever since. Besides writing All the Math You Missed (But Need to Know for Graduate School), I've also written Algebraic Geometry: A Problem Solving Approach (with a number of co-authors) and Electricity and Magnetism for Mathematicians: A Guided Path from Maxwell’s Equations to Yang-Mills, and a number of research articles.
Most mathematicians believe that the Riemann Hypothesis is the most important open question in mathematics, including me. But it is almost impossible to explain why this is such a central concern. This book is one of the attempts to explain to the non-mathematician why the Riemann Hypothesis is so important. As a partial spoiler alert, it has to do with the nature of prime numbers, which in part explains the title. It is not a book to read in one sitting, but it with a little work is great for seeing, at least in part, the big picture.
The definitive story of the Riemann Hypothesis, a fascinating and epic mathematical mystery that continues to challege the world.
In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled “On the Number of Prime Numbers Less Than a Given Quantity.” Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it.
Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and…
I love mathematics and truly believe that “Functions Describe the World.” I'm deeply satisfied that I've spent my professional life discovering new mathematics and explaining known mathematics to others. I was an undergraduate at the University of Texas, Austin, got my PhD from Brown University, then spent three years as a G.C. Evans Instructor at Rice University, before moving to Williams, where I've been ever since. Besides writing All the Math You Missed (But Need to Know for Graduate School), I've also written Algebraic Geometry: A Problem Solving Approach (with a number of co-authors) and Electricity and Magnetism for Mathematicians: A Guided Path from Maxwell’s Equations to Yang-Mills, and a number of research articles.
Gamma is a number, though little understood. Even its most basic properties are still unknown. We don’t even know if it is a rational number (a ratio of integers). This wonderful book explains why anyone would care. While it does require some mathematical background, anyone who has had calculus and is willing to read the book with a notepad and pen next to them in order to check and explore the formulas on their own will come away with a true appreciation of gamma and its impact.
Among the many constants that appear in mathematics, ?, e, and i are the most familiar. Following closely behind is ?,, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1…
In my writing about science, I am always keen to include the artistic and literary dimension that links the science to the broader culture. In Huygens, a product of the Dutch Golden Age, I found a biographical subject for whom it would have been quite impossible not to embrace these riches. This context – including painting, music, poetry, mechanics, architecture, gardens, fashion and leisure – is crucial to understanding the life that Huygens led and the breakthroughs he was able to make.
Baruch Spinoza was the philosophical flower of the Dutch Golden Age. Bertrand Russell called him the "noblest and most lovable of the great philosophers", and I am certainly not going to disagree. Like many of the innovators of the Golden Age, his ideas still seem fresh. Expelled from his Jewish community in Amsterdam for his ‘heresies’, we now find his conception of God as nature highly congenial. We probably share his dislike of ritual and perhaps aspire to his renunciation of materialism. His advice neither to fear nor to hope when it concerns things we can do nothing about is as good now as it was when it appeared in his most famous work, Ethics, in 1677.
Spinoza’s philosophy is hard to approach in the original – his arguments are rigorously constructed in the style of ancient Greek mathematics proofs. But Steven Nadler, as well as producing a towering biography…
From Pulitzer Prize-finalist Steven Nadler, an engaging guide to what Spinoza can teach us about life's big questions
In 1656, after being excommunicated from Amsterdam's Portuguese-Jewish community for "abominable heresies" and "monstrous deeds," the young Baruch Spinoza abandoned his family's import business to dedicate his life to philosophy. He quickly became notorious across Europe for his views on God, the Bible, and miracles, as well as for his uncompromising defense of free thought. Yet the radicalism of Spinoza's views has long obscured that his primary reason for turning to philosophy was to answer one of humanity's most urgent questions: How…
I have always been passionate about knowledge and learning and started my higher education by studying and teaching in the sciences. But I soon fell in love with the humanities, an ocean that brought me a new way of looking at the world and reinforced my intuition that the sciences and humanities are not ‘two cultures’ as sometimes portrayed but complementary endeavors as clear by historical studies themselves. My latest training in the history of science and the multi-cultural aspects of early science, in particular, has added a new passion, one for human understanding, tapping into our common heritage, as highlighted in my list, for serving an increasingly divided world.
I find this book fascinating and pioneering in more than one way. Not only does it uncover the historical development of the important science of optics in terms of theories of vision, the predominant form of the subject in premodern times.
But the book also covers key concepts and models in visual theory starting from ancient and medieval periods, including the extramission models of ancient Greek mathematicians and physicians, the intromission models of medieval Islamic and European natural philosophers, and the critical combination of those models and disciplines in generating dependent breakthroughs.
This is among a few monographs devoted to the subject that successfully draw on our common heritage in documenting and explaining the course of the field’s transmission and transformation.
Kepler's successful solution to the problem of vision early in the 17th century was a theoretical triumph as significant as many of the more celebrated developments of the scientific revolution. Yet the full import of Kepler's arguments can be grasped only when they are viewed against the background of ancient, medieval, and Renaissance visual theory. David C. Lindberg provides this background, and in doing so he fills the gap in historical scholarship and constructs a model for tracing the development of scientific ideas.
I have taught undergraduate and PhD students physics and biophysics for 36 years, and I never get tired of it. I always look for hot new topics and everyday things that we all see but rarely notice as interesting. I also look for “how could anything like that possibly happen at all?”-type questions and the eureka moment when some idea from physics or math pries off the lid, making a seemingly insoluble problem easy. Finally, I look for the skills and frameworks that will open the most doors to students in their future work.
A readable, yet profound tour of what math is really all about.
This book will help you have your own ideas because it opens your eyes to mathematical themes that go to the heart of things you care about yet may never have thought of as mathematical. For me, the analysis of gerrymandering was a sobering prime example.
“Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times
From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything.
How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning…
If I was asked to describe the central theme of my life's work in a phrase, it would be 'geometry in the arts'. I'm an architect originally, now a professor in London, and have always loved drawing and the art of perspective. In the 1990s I became fascinated with the idea that Johannes Vermeer used the camera obscura, an obsession that led to my book Vermeer's Camera. I'm now working on Canaletto's Camera. And I have ideas for yet another book, on perspective, to be called Points of View. I've chosen five books on these topics that I've found most thought-provoking and inspiring.
Robin Evans was a versatile architectural historian and theorist who died too young. This highly original and unusual book, published after his death, is about the relationship of geometry to architecture, and how methods of drawing, including perspective and orthographic projection, can influence what is conceived and built. I admire the way in which Evans, unlike many architectural historians, is able to combine deep scholarship with a working practical understanding of how buildings are made, and how they are used in practice. There has been no other recent writer on architecture with so subtle a mind.
Robin Evans recasts the idea of the relationship between geometry and architecture, drawing on mathematics, engineering, art history, and aesthetics to uncover processes in the imagining and realizing of architectural form.
Anyone reviewing the history of architectural theory, Robin Evans observes, would have to conclude that architects do not produce geometry, but rather consume it. In this long-awaited book, completed shortly before its author's death, Evans recasts the idea of the relationship between geometry and architecture, drawing on mathematics, engineering, art history, and aesthetics to uncover processes in the imagining and realizing of architectural form. He shows that geometry does…
I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.
This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.
Continuum has repackaged some of its key academic backlist titles to make them available at a more affordable price. These reissues will have new ISBNs, distinctive jackets and strong branding. They cover a range of subject areas that have a continuing student sale and make great supplementary reading more accessible. A comprehensive, authoritative and constructive guide to teaching algebra.
Explaining math demands great visuals. I should know: I explain math for a living, and I cannot draw. Like, at all. The LA Times art director once compared my cartoons to the work of children and institutionalized patients. (He printed them anyway.) In the nerdier corners of the internet, I’m known as the “Math with Bad Drawings” guy, and as a purveyor of artless art, I’ve developed an eye for the good stuff: striking visuals that bring mathematical concepts to life. Here are five books that blow my stick figures out of the water. (But please buy my book anyway, if for no deeper reason than pity.)
I stumbled on this in a used bookstore. What a find! The old-school, kid-friendly illustrations lead swiftly from simple beginnings (“What happens when you stretch a painting?”) to the depths of undergraduate topology. I haven’t used this in the classroom yet, but honestly, I could imagine busting it out with anyone from first-graders to first-year PhD candidates.
