| The Ansatz Ansatz The HOLONOMIC ANSATZ I. FOUNDATIONS and Applications to Lattice Path Counting (2008) | |||||||||||||
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| be thus dubbed the Paradigm Paradigm. Doron Zeilberger, not-yet so famously, believes that Mathematics, in the future, will be ansatz-based, so my approach to mathematical research could be called the Ansatz Ansatz. What is an Ansatz? According to Eric Weisstein’s mathworld.com wonderful website, in an entry contributed by Mark D. Carrara[CaW], “An ansatz is an assumed form for a mathematical statement that is not based on any underlying theory or principle.” In other words, you make a wild guess that the desired solution has a certain form, featuring some undetermined coefficients, “plug ” that form into the conditions of the problems, and try to solve for the coefficients. If in luck, you find a solution, and then, since the proof of the pudding is in the eating, you have an a posteriori justification for choosing that ansatz, and more importantly for your short-term goals, you have solved the problem! In addition, your present success will give you more confidence that this ansatz might possibly work for similar problems in the future. A More Relaxed Definition of Ansatz | |||||||||||||
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