By Steve Nadis
In the 20 th century, American mathematicians started to make severe advances in a box formerly ruled by way of 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 notably American culture of mathematics--in algebraic geometry and topology, advanced research, quantity concept, and a bunch of esoteric subdisciplines that experience hardly been written approximately outdoor of magazine articles or complex textbooks. The heady mathematical innovations that emerged, and the lads and ladies who formed them, are defined the following in vigorous, available prose.
The tale starts off in 1825, while a precocious sixteen-year-old freshman, Benjamin Peirce, arrived on the collage. He could turn into the 1st American to supply unique mathematics--an ambition frowned upon in an period whilst professors mostly restricted themselves to instructing. Peirce's successors--William Fogg Osgood and Maxime Bôcher--undertook the duty of remodeling the mathematics division right into a world-class study heart, attracting to the college such luminaries as George David Birkhoff. Birkhoff produced a stunning physique of labor, whereas education a new release of innovators--students like Marston Morse and Hassler Whitney, who solid novel pathways in topology and different components. Influential figures from around the globe 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 heritage of the Harvard arithmetic division is a vital a part of the historical past of arithmetic in the US and beyond.
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Extra info for A History in Sum: 150 Years of Mathematics at Harvard (1825–1975)
52 Although Peirce devoted countless hours to this cause, he did not neglect his personal interests altogether. Of those, he considered pure mathematics his first love, even though he was not able to spend as much time on it as he might have liked. Indeed, only a small fraction of his published papers were in that area, with the bulk lying in more applied realms. That, however, may merely reflect the practical demands placed on his career, rather than his true intellectual leanings. It is often said that a mathematician makes his or her most significant contribution early in life—typically by the age of thirty or so.
The sphere of mathematics is here extended, in accordance with the derivation of its name, to all demonstrative research, so as to include all knowledge strictly capable of dogmatic teaching . . Mathematics, under this definition, belongs to every enquiry, moral as well as physical. 71 Peirce thus rejected the notion that mathematics is merely the science of quantity in favor of the much broader notion of mathematics being a science based on inference and deduction. ”72 Benjamin Peirce and the Science of “Necessary Conclusions” Peirce’s views about mathematics were deeply colored by his fervent religious convictions.
13 His 1832 paper on perfect numbers concerned a topic that had attracted attention since antiquity. , that if 2n − 1 is a prime number, then 2n−1(2n − 1) 11 12 A H I S T O RY I N S U M is a perfect number. Roughly 2,000 years later, Leonhard Euler proved that every even perfect number must be of this form. 14 He was alluding to the question of whether odd perfect numbers might exist. This was among the oldest open problems in mathematics, and it remains unsolved to this day. But Peirce gave a partial answer to that question, proving that an odd perfect number—if there is one—must have at least four distinct prime factors.