Norris, R.R.NorrisBasu, K.K.BasuBrown, M.M.BrownCARRETTI, ETTOREETTORECARRETTIKapinska, A. D.A. D.KapinskaPRANDONI, ISABELLAISABELLAPRANDONIRudnick, L.L.RudnickSeymour, N.N.Seymour2020-03-252020-03-25201597819092047061824-8039http://hdl.handle.net/20.500.12386/23562We show that, in addition to specific science goals, there is a strong case for conducting an all-sky (i.e. the visible 3-pi steradians) SKA continuum survey which does not fit neatly into conventional science cases. History shows that the greatest scientific impact of most major telescopes (e.g., HST, VLA) lies beyond the original goals used to justify the telescope. The design of the telescope therefore needs to maximise the ultimate scientific productivity, in addition to achieving the specific science goals. In this chapter, we show that an all-sky continuum survey is likely to achieve transformational science in two specific respects: (1) Discovering the unexpected (2) Transforming radio-astronomy from niche to mainstreamELETTRONICOenConference paper10.22323/1.215.0086https://pos.sissa.it/215/086/2015aska.confE..86NFIS/05 - ASTRONOMIA E ASTROFISICAScienze Fisiche Settori ERC (ERC) di riferimento::PE9 Universe sciences: astro-physics/chemistry/biology; solar systems; stellar, galactic and extragalactic astronomy, planetary systems, cosmology, space science, instrumentation