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I am very much interested in listening to the history behind the exact sequence. We know that the exact sequence is sequence of objects with morphisms such that image of one morphism equals to the kernel of the next one.

But how did the whole idea start ? .

What is the motivation behind considering the image and kernel equality and linking groups ? .

How did the exact sequences come into play ?.

I want to hear some on some of the above things.

Thank you.

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This is not an answer. But here is a link you might find useful: Check out the pdf file. – Rankeya May 11 '12 at 9:47
While the concept of an exact sequence is purely algebraic, I dare guess that the origin is from topology/analysis/differential equations. At least yours truly first encountered the word "exact" during an elementary course on differential equations. See this. I'm no historian, so my impression may be false, and only reflects the order in which I was exposed to various parts of math. – Jyrki Lahtonen May 11 '12 at 9:53
Weibel has some remarks about the history of exact sequences in Chapter 1 of An introduction to homological algebra. – Zhen Lin May 11 '12 at 10:00
Sir, Can you tell any motivation behind the kernel image equality ?. Why one needs to consider that ? @ZhenLin – Iyengar May 11 '12 at 10:18
IMHO the first time a keen student encounters the kernel image equality is with theorems like (in $\mathbf{R}^3$) The curl of a vector field vanishes, iff the vector field is the gradient of a function and the divergence of a vector field vanishes, iff the vector field is the curl of another. Of course, these are just reinterpretations of the vanishing of certain de Rham cohomology groups, but they do show up many times, when learning vector analysis. See Poincaré Lemma (in the link of my previous comment). – Jyrki Lahtonen May 11 '12 at 19:36

In A History of Algebraic and Differential Topology, Chapter 5, §5, Dieudonné says that Hurewicz introduced exact sequences in 1941.

On the other hand, Weibel in his History of Homological Algebra [1] says that Kelley and Pitcher coined the term “exact sequence” in 1947 [2].

[1] History of Homological Algebra, in History of topology (edited by I. M. James), 1999.

[2] Exact homomorphism sequences in homology theory, Annals of Math. 48 (1947), 682–709.

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+1: But this answer is not complete one. I asked the motivation too ( regarding the kernel image equality , and why one needs to consider that ? ) . But any way thank you. – Iyengar May 11 '12 at 13:15
@Iyengar, I don't know about motivation but Dieudonné says that equality was "Hurewicz's essential remark". Read that section in Amazon or Google Books. – lhf May 11 '12 at 14:05
I found the reference to Weibel's survey in…. – lhf Jun 4 '12 at 22:01
There is an anecdote about the origin of "exact sequence" at this MO question:… – Raeder Jun 4 '12 at 22:25
@lhf : Thank you sir. – Iyengar Jun 5 '12 at 5:23

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