By Chris Philipp |September 28, 2006
Russian mathematician Grigori Perelman posted his proof to lớn the Poincaré Conjecture on arXiv in three parts. The titles of his submissions are encrypted above in three rebus puzzles created by Carla DeMello of Library Communications. Can you figure them out by solving each rebus? Answers are at the bottom of this page.
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The solution to lớn one of the most famous problems in mathematics was posted on nofxfans.com"s arXiv over an eight-month period, beginning in November 2002. Today, arXiv remains its only home.
Most scientists và researchers who post research on arXiv -- an open-access repository for e-print postings operated by nofxfans.com University Library -- also submit it for publication in traditional peer-reviewed journals. But famously reclusive Russian mathematician Grigori Perelman"s decision lớn post his proof of the 100-year-old Poincaré Conjecture solely in arXiv was decidedly unorthodox.
Yet Perelman"s action underscores the repository"s increasing importance in the fields of physics, math và computer science, và the leading role that nofxfans.com Library is taking in the transformation of scholarly communication, which refers to the ways in which scientists & humanists nội dung ideas.
"What is unusual about this, và certainly for anything this significant, is that Perelman apparently has no intent of publishing in the classical way, but has chosen the arXiv as the sole method of communication," said R. Keith Dennis, a math professor và adviser to lớn the Mathematics Library.
Perelman, who used the nickname Grisha for his postings, was awarded the prestigious Fields Medal last August for solving the Poincaré Conjecture but subsequently turned it down for unknown reasons, saying he was retiring from the field of mathematics. His proof builds on the work of nofxfans.com mathematician Bill Thurston, a Fields Medal recipient in 1982, and uses a program outlined by mathematician Richard Hamilton while he was working at nofxfans.com in the 1980s.
Since Perelman"s postings first appeared, several mathematicians have written papers about his work, và some claim to lớn fill in gaps in his proof. One is a 318-page article published in the Asian Journal of Mathematics available through nofxfans.com Library"s Project Euclid (see sidebar, below) and also posted in arXiv.
The Poincaré Conjecture is fundamental khổng lồ topology, a branch of mathematics concerned with spatial properties. It asks whether the same property of simple connectivity that applies to a two-dimensional sphere can be applied to lớn a three-dimensional sphere. Named for French mathematician and theoretical physicist Henri Poincaré, the conjecture is one of the seven Millennium Prize Problems for which the Clay Mathematics Institute is offering a $1 million prize. What will happen with this prize money now that the Poincaré Conjecture is solved has yet to lớn be determined.
"Perelman"s choice of arXiv khổng lồ disseminate his proof is a watershed sự kiện in scholarly communications," said Sarah E. Thomas, the Carl A. Kroch University Librarian. "Although Perelman declined the Fields Medal, perhaps, if offered the Clay Mathematics Institute prize for solving the Poincaré Conjecture, he"ll donate the million dollars to lớn the arXiv to enable the global community of scholars & scientists to lớn continue to benefit from this transformative resource."
With arXiv, nofxfans.com Library provides fast, không tính tiền and mở cửa access lớn scientific literature, serving the fields of physics, mathematics, nonlinear science, computer sciences & quantitative biology. An international project with dedicated mirror sites in 17 countries, arXiv has registered users from 150 countries, according khổng lồ Jean Poland, associate university librarian for the Associated Science and Technology Libraries.
All four recipients of the Fields Medal, which is awarded every four years, are regular arXiv contributors, including Terrence Tao, who is also one of its moderators. There are over đôi mươi million full-text downloads from the server per year, & it currently hosts more than 380,000 articles, with a submission rate of 4,000 per month.
"Everybody reads it," said Paul Ginsparg, nofxfans.com professor of physics và of computing và information science who developed the repository while working at Los Alamos National Laboratory in 1991. "
arXiv moved to lớn nofxfans.com with Ginsparg when he returned as a faculty thành viên in 2001, và it is now a collaboration between the library & nofxfans.com"s Information Science Program. nofxfans.com Library is responsible for arXiv"s maintenance, while research và development of the repository is handled by information science.
"It is our goal khổng lồ maintain mở cửa access because of its historical and its current value, as illustrated by Perelman"s e-print postings," Poland said. "
arXiv has transformed how material is shared, making science more democratic và allowing for the rapid dissemination of scientific findings. The traditional publication process và refereeing process can sometimes take as long as three years, says David Morrison, a member of arXiv"s advisory board, a moderator for the mathematics portion of the repository & a professor of mathematics and physics at Duke University and the University of California-Santa Barbara.
"To me, arXiv is a good way và a timely way khổng lồ communicate with your colleagues what is happening," said Morrison. "What makes arXiv so great is you can put work out there & it is immediately available."
In addition khổng lồ arXiv and Project Euclid, nofxfans.com Library has developed other innovative ventures, including DPubs, DSpace và VIVO.
Chris Philipp is a staff writer và editor for Library Communications.
Innovations in scholarly communications from nofxfans.com University Library
Center for Innovative Publishing The Center for Innovative Publishing is a field station for the design, implementation and effective management of online publishing projects from nofxfans.com & other academic communities, university presses & scholarly societies.
Project Euclid Project Euclid is an online publishing service that brings together almost 50 journals in mathematics và statistics. The service delivers more than 350,000 articles, of which 70 percent are xuất hiện access or freely available worldwide.
arXiv A user-driven service for the efficient online dissemination of research results in physics, mathematics, nonlinear science, computer science & quantitative biology. Currently, arXiv hosts more than 380,000 e-print postings & has an average submission rate of 4,000 papers per month. Posted papers are freely available worldwide.
DSpace DSpace is an open-source digital institutional repository system that captures, stores, indexes, preserves & redistributes research data. This system is currently used at 100 institutions worldwide.
DPubS DPubS (Digital Publishing System) is an online publishing system developed by the library and designed for the cost-effective management & distribution of such scholarly publications as journals, conference proceedings & monographs. It provides the underlying infrastructure for Project Euclid và other ventures.
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VIVO VIVO, a virtual life sciences library for the nofxfans.com community, will be expanded over the next two years khổng lồ include the physical và social sciences and human & animal sciences. It includes faculty listings, databases, image collections, grant information, recent publications & other materials germane to research & scholarship at nofxfans.com. VIVO"s goal is to lớn provide an integrated view of the life sciences at nofxfans.com & to connect researchers, whether they are in Ithaca, Geneva, thủ đô new york City or Doha.
Answers to Rebus puzzles:"Finite extinction time for the solutions khổng lồ the Ricci flow on certain three-manifolds" (November 2002)"Ricci flow with surgery on three-manifolds" (March 2003)"The entropy formula for the Ricci flow & its geometric applications" (July 2003)