Re: [HM] formal author of the mathematical induction method
David Fowler (david.fowler@warwick.ac.uk)
Sat, 6 Mar 1999 11:02:27 -0700
>Alexander Zenkin wrote:
>> 1) George Polya { "Mathematical Discovery", John Willey & Sons, Inc.,
>> N.Y.-London, Vol.I (1962), Chapter 3.7, Mathematical Induction} writes:
>> "...his (B.Pascal's, the XVII Century) proof is the first application of
>> a new fundamental method of reasoning, which, usually, is called by the
>> mathematical induction"
>> 2) On the other hand, N.Bourbaki {Russian Translation: The Set
>> Theory. - Moscow: "MIR", 1965, editor V.A.Uspensky, p. 325, the historic
>> essay} writes:
>> "... using only the operation x --> x+1 and the induction principle.
>> The last principle was first explicitly stated and used in the XVI
>> Century by Italian Maurolico F."
There is an exchange of articles in the Italian journal Physis between
Sabetai Unguru and me on the possibility of (unformalised) induction
arguments in Greek mathematics:
SU, Greek mathematics and Greek induction, Physis 28 (1991) 273 - 289.
DHF, Could the Greeks have used mathematical induction? Did they use it?,
Physis 31 (1994) 253 - 265.
SU, Fowling after induction, Physis 31 (1994) 267 - 272.
and there are some unpublished notes by me on these papers.
If you send me an address, I may be able to send photocopies of the bundle.
David Fowler