From: hiraga@Csli.Stanford.EDU (Yuzuru Hiraga)
Subject: Who/What deserves the credit? (Was: Re: Could have Archimedes invented Calculus?)
Organization: Stanford University CSLI
Date: Sun, 27 Sep 1992 08:42:40 GMT

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.

Some example along the line --
* If Newton "cheated" on Barrow, he is obviously in a bad position to claim
  any credit.  But what about Leibniz?  Hadn't he worked out independent
  from Newton, or Barrow, for that matter?  [Yes, I know about the
  controversy between Newton and Leibniz.]
* Hasn't Leibniz shed new light on the theorem?  Especially when regarding
  the influence brought by himself as well as his followers -- Bernoullies,
  Euler, etc.?
* Should Gauss receive credit for the "Gaussian" plane for representing
  complex numbers?  Or is this name already obsolete, in place of
  "Arg??? [gosh! forgot the name!] Plane"?
* On the other hand, can Gauss count as (among) the discoverers
  of Non-Euclidean geometry?
* Can Galois be credited for the unsolvability of quintuple equations,
  or does all reward go to Abel?
* What about the Japanese mathematician Takakazu Seki (early 17C), 
  whose works marked some peaks of analysis, while being totally
  obscure from the Western Tradition?
* Isn't "Pell" in the "Pell Equations" a misnomer?  Shouldn't we change
  the name?
* Does Cauchy qualify for the discovery of "Cauchy's Theorem" in complex
  analysis, if his proof (at least the initial one) is quite flawed
  seen from modern standards?
* Who discovered "Green's Theorem" anyway?
* 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
Newsgroups: sci.math