The Goldbach Conjecture: Why Is It Difficult?

Autor/in	Turner, Paul
Titel	The Goldbach Conjecture: Why Is It Difficult?
Quelle	In: Australian Senior Mathematics Journal, 30 (2016) 2, S.48-56 (9 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0819-4564
Schlagwörter	Mathematics; Professional Personnel; Validity; Mathematical Logic; Mathematical Concepts; Mathematics Instruction; Secondary School Mathematics; Mathematics Curriculum; Foreign Countries; Australia + Suchen Sie Ihr Suchwort? Mathematik; Personalbestand; Gültigkeit; Mathematical logics; Mathematische Logik; Mathematics lessons; Mathematikunterricht; Ausland; Australien
Abstract	The opinion of the mathematician Christian Goldbach, stated in correspondence with Euler in 1742, that every even number greater than 2 can be expressed as the sum of two primes, seems to be true in the sense that no one has ever found a counterexample. Yet, it has resisted all attempts to establish it as a theorem. The discussion in this article is intended to explain, partially and from a naïve point of view, why the search for a proof has been difficult. This is not to say a student, captivated by the prospect of an open question, should not make the attempt. The value in considering arguments that do not lead to a proof may lie in the potential for hinting at hidden depths to be explored and new approaches to be looked for. If further justification were needed for including such a discussion in a journal mainly read by senior secondary mathematics teachers, one could point to the stated aims of the Specialist Mathematics course in the Australian Curriculum. While number theory as a topic is not included in the Australian Curriculum, the aim to develop students' "reasoning in mathematical and statistical contexts " and "ability to construct proofs" is clearly stated. (ERIC).
Anmerkungen	Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2021/2/06