{"@context": "http://iiif.io/api/presentation/2/context.json", "attribution": "Art Collection", "sequences": [{"canvases": [{"description": "", "height": 4961, "width": 4106, "@type": "sc:Canvas", "images": [{"on": "https://images.is.ed.ac.uk/luna/servlet/iiif/m/UoEart~1~1~75443~198424/canvas/c1", "motivation": "sc:painting", "resource": {"service": {"profile": "http://iiif.io/api/image/2/level2.json", "@context": "http://iiif.io/api/image/2/context.json", "@id": "https://images.is.ed.ac.uk/luna/servlet/iiif/UoEart~1~1~75443~198424"}, "format": "image/jpeg", "height": 4961, "width": 4106, "@id": "https://images.is.ed.ac.uk/luna/servlet/iiif/UoEart~1~1~75443~198424/full/!1024,1024/0/default.jpg", "@type": "dctypes:Image"}, "@type": "oa:Annotation"}], "label": "P Versus NP", "@id": "https://images.is.ed.ac.uk/luna/servlet/iiif/m/UoEart~1~1~75443~198424/canvas/c1", "thumbnail": {"@id": "https://images.is.ed.ac.uk/MediaManager/srvr?mediafile=/Size0/UoEart~1~1/437/0152469c.jpg"}, "metadata": [{"value": "0152469", "label": "Work Record ID"}, {"value": "EU5469", "label": "ID Number"}, {"value": "01 Sep 2017", "label": "ID Date"}, {"value": "P Versus NP", "label": "Title"}, {"value": "Karp, Richard M (b.1935)", "label": "Creator"}, {"value": "Artist", "label": "Creator Role"}, {"value": "Concinnitas is a portfolio of 10 aquatints with accompanying statements, one each by the following participants: Michael Atiyah, Enrico Bombieri, Simon K. Donaldson, Freeman Dyson, Murray Gell-Mann, Richard Karp, Peter Lax, David Mumford, Stephen Smale and Steven Weinberg. It has been curated and includes and introduction by Daniel Rockmore. The portfolio has been printed in an edition of 100 copies, numbered 1-100, with 15 additional copies lettered AP 1-15. Each of the 10 aquatints has been prepared and printed on Rives BFK White 300g paper using Gamblin Portland Black ink and editioned at Harlan & Weaver, New York City, New York, under the supervisiion of Felix Harlan, Carol Weaver and Derick Wycherly. The artist statements and signature cards have been printed on Crane's Lettra paper by Jenn Lawrence at Letterpress PDX in Portland, Oregon. Published in 2014 by Parasol Press, Ltd., Portland, Oregon, Yale University Art Gallery, New Haven, Connecticut and in association with Bernard Jacobson Gallery, London, England.", "label": "Production Notes"}, {"value": "Harlan & Weaver, Inc. (estab. 1984)", "label": "Creator"}, {"value": "Printer", "label": "Creator Role"}, {"value": "Parasol Press Ltd.", "label": "Creator"}, {"value": "Publisher", "label": "Creator Role"}, {"value": "Rockmore, Daniel", "label": "Creator"}, {"value": "Collaborator", "label": "Creator Role"}, {"value": "2014", "label": "Date"}, {"value": "The portfolio Concinnitas is the result of a collaboration between Dan Rockmore (Professor of Mathematics, Dartmouth College); ten renowned mathematicians and physicists; the publisher Robert Feldman (who earlier produced seminal Conceptual art print portfolios); and the New York printing house Harlan & Weaver. It takes its title from a term used by the Renaissance artist and architect Leon Battista Alberti (1404\u20131472) to indicate the proportions of beauty. Each print represents a participant\u2019s answer to Rockmore\u2019s prompt to represent the \"most beautiful mathematical expression\" they had encountered in their work or study. Rendered so as to mimic the aesthetics of a handwritten equation, such as those immortalized in photographs of Albert Einstein\u2019s blackboard, Concinnitas also echoes Conceptual artists\u2019 engagement with language and systems. While to the layperson the mathematical content may remain enigmatic or require further research, the prints persist on their own as powerful visual signs communicating the gesture and intentions of their creators. Artist's statement: Computational complexity theory is the branch of theoretical computer science concerned with the fundamental limits on the efficiency of automatic computation. It focuses on problems that appear to require a very large number of computation steps for their solution. The inputs and outputs to a problem are sequences of symbols drawn from a finite alphabet; there is no limit on the length of the input, and the fundamental question about a problem is the rate of growth of the number of required computation steps as a function of the length of the input. Some problems seem to require a very rapidly growing number of steps. One such problem is the independent set problem: given a graph, consisting of points called vertices and lines called edges connecting pairs of vertices, a set of vertices is called independent if no two vertices in the set are connected by a line. Given a graph and a positive integer n, the problem is to decide whether the graph contains an independent set of size n. Every known algorithm to solve the independent set problem encounters a combinatorial explosion, in which the number of required computation steps grows exponentially as a function of the size of the graph. On the other hand, the problem of deciding whether a given set of vertices is an independent set in a given graph is solvable by inspection. There are many such dichotomies, in which it is hard to decide whether a given type of structure exists within an input object (the existence problem), but it is easy to decide whether a given structure is of the required type (the verification problem). It is generally believed that existence problems are much harder to solve than the corresponding verification problems. For example, it seems hard to decide whether a jigsaw puzzle is solvable, but easy to verify that a given arrangement of the puzzle pieces is a solution. Similarly, it seems hard to solve Sudoku puzzles but easy to verify given solutions. Complexity theory provides precise definitions of \u201cP\u201d, the class of all existence problems that are easy to solve, and \u201cNP\u201d, the class of existence problems whose solutions are easy to verify. The general belief that verifying is easier than solving strongly suggests that the class NP properly includes the class P, but this claim has never been proven. The question of whether P = NP is the most central open question in theoretical computer science, and one of the most notorious open questions in all of mathematics. In a 1972 paper entitled \"Reducibility Among Combinatorial Problems\" I demonstrated a technique that has made it possible to prove that thousands of problems, arising in mathematics, the sciences, engineering, commerce and everyday life, are equivalent, in the sense that an efficient algorithm for any one of them would yield", "label": "Description"}, {"value": "aquatint/Etching", "label": "Material"}, {"value": "Art Collection", "label": "Repository"}, {"value": "AP12", "label": "Source"}, {"value": "Modern and Contemporary Art Collection", "label": "Repository"}, {"value": "AP12", "label": "Source"}, {"value": "Mathematics", "label": "Subject Category"}, {"value": "\u00a9 the artist", "label": "Rights Statement"}, {"value": "P Versus NP", "label": "Repro Title"}, {"value": "0152469c.tif", "label": "Repro ID Number"}, {"value": "P Versus NP", "label": "Repro Description"}, {"value": "\u00a9 University of Edinburgh Art Collection", "label": "Repro Rights Statement"}, {"value": "Full public access", "label": "Repro Publication Status"}]}], "viewingHint": "individuals", "@type": "sc:Sequence"}], "logo": "https://images.is.ed.ac.uk/luna/images/LUNAIIIF80.png", "@id": "http://collections.ed.ac.uk/manifests/EU5469.json", "@type": "sc:Manifest", "related": "https://images.is.ed.ac.uk/luna/servlet/iiif/m/UoEart~1~1~75443~198424/manifest", "label": "P Versus NP"}