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ERIC Number: EJ1121409
Record Type: Journal
Publication Date: 2016
Pages: 9
Abstractor: ERIC
ISSN: ISSN-0819-4564
The Goldbach Conjecture: Why Is It Difficult?
Turner, Paul
Australian Senior Mathematics Journal, v30 n2 p48-56 2016
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.
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:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Australia
Grant or Contract Numbers: N/A