Formal outline for research paper

In January 2003, Hales announced the start of a collaborative project to produce a complete formal proof of the Kepler conjecture. The aim was to remove any remaining uncertainty about the validity of the proof by creating a formal proof that can be verified by automated proof checking software such as HOL Light and Isabelle . This project is called Flyspeck – the F, P and K standing for Formal Proof of Kepler . Hales estimated that producing a complete formal proof would take around 20 years of work. The project was announced completed on August 10, 2014. [4] In January 2015 Hales and 21 collaborators submitted a paper titled "A formal proof of the Kepler conjecture" to arXiv , claiming to have proved the conjecture. [5] In 2017, the formal proof was accepted into the Forum of Mathematics journal. [1]

The notion of non-formal education has been a significant feature of policy debates around education in southern countries for three decades. It has drawn attention to the importance and potential of education, learning and training that takes place outside recognized educational institutions. There are questions about usefulness of the notion when looking at the process of education. It has also gone in and out of fashion. Fordham (1993) comments that if we try to correlate the flourishing of non-formal education and political change then the 1970s can certainly be described as the decade of non-formal education (Rubenson 1982). Similarly the 1980s saw the neglect of non-formal education and Fordham suggests that this was in tune with the politics of the decade, accompanied by greater inequalities both within and between countries. Given the extent to which notions of lifelong learning and associated ideas have gained ground in recent years it will be interesting to see how the language of policy debates will change over the next few years.

Formal outline for research paper

formal outline for research paper


formal outline for research paperformal outline for research paperformal outline for research paperformal outline for research paper