The ideas presented in these papers are a cornerstone of the modern theory and practice of systems and control. Not only have they led to eminently useful developments, such as the Kalman-Bucy filter, but they have contributed to the rapid progress of systems theory, which today draws upon mathematics ranging from differential equations to algebraic geometry.
Rudolf Kalman was not present at the 93rd American Mathematical Society Annual meeting in San Antonio, Texas, to receive the Prize but his response, attempting to explain the significance of the papers cited for the award, was read at the meeting: |

I have been aware from the outset (end of January 1959, the birthdate of the second paper in the citation) that the deep analysis of something which is now called Kalman filtering were of major importance. But even with this immodesty I did not quite anticipate all the reactions to this work. Up to now there have been some 1000 related publications, at least two Citation Classics, etc. There is something to be explained.

To look for an explanation, let me suggest a historical analogy, at the risk of further immodesty. I am thinking of Newton, and specifically his most spectacular achievement, the law of Gravitation. Newton received very ample "recognition" (as it is called today) for this work. it astounded - really floored - all his contemporaries. But I am quite sure, having studied the matter and having added something to it, that nobody then (1700) really understood what Newton's contribution was. Indeed, it seemed an absolute miracle to his contemporaries that someone, an Englishman, actually a human being, in some magic and un-understandable way, could harness mathematics, an impractical and eteral something, and so use mathematics as to discover with it something fundamental about the universe. ... Newton showed that

mathematics + reality >> zero-sum game.

This is symbiosis between mathematics and physical reality. After Newton mathematics advanced quickly but the symbiosis has gradually vanished. Physics cannot be done today without electronics but mathematics hardly matters. (This is, of course, a purely personal observation.)

Yet there is a new symbiosis between mathematics and reality. We have a new game and it is a nonzero sum. Miraculous, if you like. The new magic is that mathematics helps to conceive machines, systems, before they are actually built. Unlike at the time of Newton, there are many today who understand this process. Perhaps this is why my papers that you have so kindly cited turned to be so influential.

There has been much noise lately about the "relevance" of mathematics. I do not share this worry and I try to explain why not. Newton turned out to be a difficult role model to follow. But then, through the advancement of technology - which is neither mathematics nor physics, something quite different though not unrelated - a substitute has appeared. Its name is system theory. With system theory there is a new and harmonious relationship of mathematics to reality. Without having to veil any of her unbelievable but delicate beauty, mathematics has become the much-loved partner of a new kind of relevance.

JOC/EFR February 2010

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