Experimental mathematics, computers and the a priori.
In recent decades, experimental mathematics has emerged as a new branch of mathematics. This new branch is defined less by its subject matter, and more by its use of computer assisted reasoning. Experimental mathematics uses a variety of computer assisted approaches to verify or prove mathematical h...
| Publicado en: | Synthese Vol. 190; no. 3; pp. 397 - 413 |
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| Formato: | Artículo |
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Springer Nature
Feb2013
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=84765288&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 84765288 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Feb2013 vid: 190 iid: 3 pid: 237 pub: Springer Nature artinfo: ui: 84765288 10.1007/s11229-011-0035-1 ppf: 397 ppct: 16 formats: fmt: @attributes: type: P size: 197KB tig: atl: Experimental mathematics, computers and the a priori. aug: au: McEvoy, Mark affil: Department of Philosophy, Hofstra University, Hempstead 11549 USA su: Experimental mathematics Hypothesis Mathematicians Empirical research Inductive teaching sug: subj: Experimental mathematics Hypothesis Mathematicians Empirical research Inductive teaching keyword: Computer assisted proofs Mathematical apriorism Non-deductive methodology ab: In recent decades, experimental mathematics has emerged as a new branch of mathematics. This new branch is defined less by its subject matter, and more by its use of computer assisted reasoning. Experimental mathematics uses a variety of computer assisted approaches to verify or prove mathematical hypotheses. For example, there is 'number crunching' such as searching for very large Mersenne primes, and showing that the Goldbach conjecture holds for all even numbers less than 2 × 1018. There are 'verifications' of hypotheses which, while not definitive proofs, provide strong support for those hypotheses, and there are proofs involving an enormous amount of computer hours, which cannot be surveyed by any one mathematician in a lifetime. There have been several attempts to argue that one or another aspect of experimental mathematics shows that mathematics now accepts empirical or inductive methods, and hence shows mathematical apriorism to be false. Assessing this argument is complicated by the fact that there is no agreed definition of what precisely experimental mathematics is. However, I argue that on any plausible account of 'experiment' these arguments do not succeed. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2013. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2013 holdings: @attributes: islocal: N |
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