The story of continuous casting is remarkable because it exemplifies how a single technology can propel and sustain an industry through an unparalleled period of change; a period marked by an oil crisis,several major recessions,growing environmental pressures and an enduring threat of substitution.The frontiers of continuous casting have been advanced by ingenuity,innovation,intellectual power,and risk-taking,qualities that also describe the very unique individual,Julian Szekely,whose life and career we honor in this symposium.But there is another connection between Julian Szekely and continuous casting,and it is mathematical modelling,a field that Julian Szekely has undoubtedly earned the distinction of pioneering.Mathematical models have advanced the frontiers of continuous casting since its inception.In this paper major achievements in the field,that are rooted in the application of mathematical models,will be explored.They range from improved understanding of the process.to advances in design and operation for the reduction of defects,new thin slab processes and the application of artificial intelligence for on-line detection of defects.If the past is an indicator of the future,then it is clear that continuous casting will continue to be driven by ingenuity and risk-taking,and mathematical models will undoubtedly play a key role in its evolution.
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