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‘Problem-solving’? Or problem solving?

Published online by Cambridge University Press:  01 August 2016

A. Gardiner
A. Gardiner*
Affiliation:
School of Mathematics, University of Birmingham B15 2TT
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Extract

David Hilbert (1862–1943) was one of the most outstanding mathematicians of the modern era. At the International Congress of Mathematicians in Paris in 1900 he presented twenty-three major research problems which he felt would be important for the development of mathematics in the twentieth century. These problems all seemed very hard, but in bringing them to the attention of other mathematicians Hilbert felt the need to stress that this should not be used as an excuse to put off trying to solve them.

‘ However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes. This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason. In Mathematics there is no ignorabimus.’ [1]

Type
Mathematics Teaching - Past and Future
Information
The Mathematical Gazette , Volume 80 , Issue 487 , March 1996 , pp. 143 - 148
Copyright
Copyright © The Mathematical Association 1996

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References

1. Hilbert, D., Mathematical problems, Bulletin of the American Mathematical Society 8 (1902) pp. 437–479 (the German original appeared in the Göttinger Nachrichten (1900) pp. 253–297).CrossRefGoogle Scholar
2. Gardiner, A., Mathematical challenge, Cambridge (1996).Google Scholar
3. Gardiner, A., More challenging mathematics, Cambridge (1996).Google Scholar