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TOP TEN REASONS FOR DUMPING THE RIEMANN INTEGRAL #7

#7. "The old man who refuses to travel in a train."

I should like to add a few words, in thanking Mr. Carey Francis for his paper. I hope the members of the Association realise that in order to be a serious mathematician it is necessary to have some knowledge of modern theories of integration. To be a serious pure mathematician and not to use the Lebesgue integral is to adopt the attitude of the old man in a country village who refuses to travel in a train.

It is necessary to learn these things and to get rid of the sort of terror which they appear to engender. It is true that the Lebesgue integral is very much easier than the Riemann, though naturally the beginnings of it are bound to be a little more difficult. And it is true, in a sense, that the Riemann integral is riddled with awkwardness and exceptions, but when one gets beyond the root of the subject, then the integral of Lebesgue is not really that of generalisation, but of simplification.

[These remarks were made by the President of the society after the presentation of the paperMODERN THEORIES OF INTEGRATION. by E. C. FRANCIS, M.A., Fellow and Lecturer of Peterhouse, Cambridge in 1926. The paper itself along with these remarks can be found in the Mathematical Gazette, Vol. 13, No. 181 (Mar., 1926), pp. 72-77.]

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