From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: Who/What deserves the credit? (Was: Re: Could have Archimedes invented Calculus?)
Date: 30 Sep 92 14:20:58 GMT
Organization: Univ. of South Florida, Math Department

In article <1992Sep27.084240.6804@Csli.Stanford.EDU> hiraga@Csli.Stanford.EDU (Yuzuru Hiraga) writes:
>In article <19qhk2INN6dp@hilbert.math.ksu.edu> bennett@math.ksu.edu (Andy Bennett) writes:
>>hiraga@Csli.Stanford.EDU (Yuzuru Hiraga) writes:
>>:* The crux of calculus, and the reason Newton and Leibniz are credited
>>:  for its invention, is in the discovery of the fundamental theory [theorem!
>>:  yikes!] of calculus ...
>>
>>This is false, though I imagine you can find plenty of calculus texts 
>>which make this claim. The fundamental theorem of calculus first appears
>>in Barrow's Geometrical Lectures, not in the work of Newton and Leibniz.
>
>Thanks to you, as well as Paul R. Chernoff, Dave Joyce, and other people
>who responded -- I stand corrected.
>Having that settled, then, one would be tempted to ask:
>was my comment on the "credit" so outright false?
>No, I'm not trying to defend myself, just wondering.
>
>Some questions coming to mind --
>If "plenty of texts make the claim", wouldn't it be the de facto credit?
>If the results were obtained independently, would the one who comes
>after qualify for no credit at all?
>What if the result went unnoticed, leaving no trace of influence to
>later work?
>Seen from the other side, what if the "rediscovery" is backed by a far
>greater generality, provides greater perspective, or inspires substantial
>work to follow?
>What if the claimed results were true, but the proof was faulty?
>And so on.
>
>* What about the Japanese mathematician Takakazu Seki (early 17C), 
>  whose works marked some peaks of analysis, while being totally
>  obscure from the Western Tradition?
>* Changing the field, what about the long debated, Theory of Evolution?
>  Should Darwin yield more to Wallace?
>* And Quantum mechanics -- can Schroedinger and Heisenberg said to have
>  discovered the same thing?
>* For that matter, Church, Turing, Post, Goedel... on computability?
>
>...
>Comments and related issues welcome!
>
>-Yuzuru Hiraga


Most of these major developments took many years and 
many people to get them developed.  Its rather like 
saying that a certain player in a basketball team 
won the game because he/she scored the last point.
(Sometimes its not the last point----its the most 
widely celebrated point.)  For a story on this theme, 
see PROOF AND REFUTATION by Lakatos.

Another example:  evolution.  Both ancient India and 
ancient Greece had evolutionists of sorts.  Evolution 
became popular in the 18th century with the notion 
of "progress".  Much of evolutionary theory appeared 
in the late 18th century with the theory of the evolution 
of language (and some, like Lord Monboddo, tried to 
carry the principles over to biology).  The Uniformitarian 
principle (in geology) was most clearly stated by Burton, 
and supported by Darwin's mentor, Lyall [sic?].  Lamarck
developed a theory of evolution that didn't fly very 
well, but was obviously influenced by contemporary theories 
of the evolution of language.

We do know that Darwin was influenced by Malthus's theory 
of human populations---we do not know to what extent 
he was influenced by a micro-theory of natural selection 
on conifers by someone whose name escapes me.  Darwin 
kept quiet about the Theory of Natural Selection 
(telling only a few friends about it) and several years 
later, Wallace came up with a similar theory, and wrote 
Darwin about it.  They presented a joint paper to the 
Royal Society, and later Darwin wrote his book.  For 
a good account, see Eiseley's Darwin's Century.

-----Greg McColm

PS:  Church, Turing, Goedel, etc, discovered different 
pieces of the same field.  Heisenberg's algebraic 
construction was somewhat different from Schrodinger's 
DE construction.  And I thought that T. Seki was obscure 
because so little was known about him.