Download e-book for iPad: A history in sum : 150 years of mathematics at Harvard by Steve Nadis

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 severe advances in a box formerly ruled via Europeans. Harvard's arithmetic division used to be on the heart of those advancements. A background in Sum is an inviting account of the pioneers who trailblazed a extraordinarily American culture of mathematics--in algebraic geometry and topology, complicated research, quantity concept, and a number of esoteric subdisciplines that experience not often been written approximately open air of magazine articles or complex textbooks. The heady mathematical thoughts that emerged, and the lads and girls who formed them, are defined right here in energetic, available prose.

The tale starts in 1825, whilst a precocious sixteen-year-old freshman, Benjamin Peirce, arrived on the collage. He may turn into the 1st American to supply unique mathematics--an ambition frowned upon in an period whilst professors mostly restricted 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 examine middle, 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 parts. Influential figures from world wide quickly flocked to Harvard, a few overcoming nice demanding situations to pursue their elected calling.

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

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Although Johns Hopkins was the first university of its kind in the United States, Peirce and his Lazzaroni friends had dreamed of creating just such an institution around 1850 or so. In their fantasies, however, the new university was to reside in Albany, New York, rather than in Baltimore, Maryland, but those plans never materialized. The establishment of Johns Hopkins, a quarter of a century later, was widely seen as an important step in the advancement of American mathematics, though it produced a temporary setback for Harvard’s fledgling graduate program as the new university started attracting many of the best graduate students.

Simply put, the texts were too demanding for all but the most exceptional students. ”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.

Campbell showed that the inner portion of the rings orbits more rapidly than the outer portion. Even though Peirce’s idea did not prevail in the end, his analyses helped advance science by spurring Maxwell. In an 1857 letter to the physicist William Thomson (better known as Lord Kelvin), Maxwell wrote: “As for the rigid ring I ought to first speak of Prof. Peirce. ”47 At this stage in his career, Peirce was already shifting his attention to geodesy—the branch of science concerned with measuring, monitoring, and representing Earth’s shape and size, while also determining the precise location of points on the surface.

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

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