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Hilbert’s twentyfourth problem
 American Mathematical Monthly
, 2001
"... 1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Cong ..."
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1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Congress of Mathematicians (ICM) in Paris has tremendous importance for all mathematicians. Moreover, a substantial part of
CARATHÉODORY’S ROYAL ROAD OF THE CALCULUS OF VARIATIONS: MISSED EXITS TO THE MAXIMUM PRINCIPLE OF OPTIMAL CONTROL THEORY
"... (Communicated by the associate editor name) Abstract. The purpose of the present paper is to show that the most prominent results in optimal control theory, the distinction between state and control variables, the maximum principle, and the principle of optimality, resp. Bellman’s equation are imm ..."
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(Communicated by the associate editor name) Abstract. The purpose of the present paper is to show that the most prominent results in optimal control theory, the distinction between state and control variables, the maximum principle, and the principle of optimality, resp. Bellman’s equation are immediate consequences of Carathéodory’s achievements published about two decades before optimal control theory saw the light of day. 1. Introduction. The Theory of Optimal Control