Read e-book online A history in sum : 150 years of mathematics at Harvard PDF

By Steve Nadis

ISBN-10: 067472500X

ISBN-13: 9780674725003

ISBN-10: 0674726553

ISBN-13: 9780674726550

In the 20 th century, American mathematicians started to make serious advances in a box formerly ruled through Europeans. Harvard's arithmetic division was once on the heart of those advancements. A historical past in Sum is an inviting account of the pioneers who trailblazed a exceptionally American culture of mathematics--in algebraic geometry and topology, advanced research, quantity concept, and a number of esoteric subdisciplines that experience infrequently been written approximately open air of magazine articles or complicated textbooks. The heady mathematical recommendations that emerged, and the boys and girls who formed them, are defined right here in energetic, available prose.

The tale starts in 1825, while a precocious sixteen-year-old freshman, Benjamin Peirce, arrived on the collage. He may develop into the 1st American to supply unique mathematics--an ambition frowned upon in an period whilst professors principally constrained themselves to educating. Peirce's successors--William Fogg Osgood and Maxime Bôcher--undertook the duty of remodeling the mathematics division right into a world-class learn heart, attracting to the school such luminaries as George David Birkhoff. Birkhoff produced a blinding physique of labor, whereas education a iteration of innovators--students like Marston Morse and Hassler Whitney, who solid novel pathways in topology and different components. Influential figures from all over the world quickly flocked to Harvard, a few overcoming nice demanding situations to pursue their elected calling.

A background in Sum elucidates the contributions of those remarkable minds and makes transparent why the heritage of the Harvard arithmetic division is a vital a part of the historical past of arithmetic in the United States and beyond.

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Coast Survey. S. ”56 Before discussing Hamilton’s work on quaternions and the effect it had on Peirce, it is worth saying a few words about algebra in general and how it began to change, and open up, in the early nineteenth century. That is when British mathematicians began transforming mathematics from the “science of quantity” to a much more liberalized and abstract system of thought. 57 Hamilton carried this a step further by introducing complex numbers into his algebra. Complex numbers assume the form of a + bi, where a and b are real numbers and i, the square root of −1, is an imaginary number.

18 Peirce’s 1855 treatment of analytical mechanics, for example, did attract some favorable notice. Soon after its publication, an American student in Germany asked an eminent German professor what book he should read on that subject. 21 Peirce’s lectures were a mixed bag as well. The average person found them almost impossible to follow—some saying that the speed of Peirce’s mental processes made it difficult for him to put things in a way 13 14 A H I S T O RY I N S U M that others could comprehend.

D. degrees. D. under Peirce’s tutelage. The graduate program that existed at the time was not geared to turning out students ready for original research, 33 34 A H I S T O RY I N S U M despite Eliot’s goal of transforming Harvard into a modern university. Although Eliot made progress in many Harvard departments, change was slow to come in the mathematics department. An important milestone occurred in 1876, the nation’s hundredth anniversary, with the founding of Johns Hopkins University—the nation’s first research-oriented university.

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A history in sum : 150 years of mathematics at Harvard (1825-1975) by Steve Nadis

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