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This question is inspired in part by this answer of Bill Dubuque, in which he remarks that the fairly common belief that Kummer was motivated by FLT to develop his theory of cyclotomic number fields is essentially unfounded, and that Kummer was instead movitated by the desire to formulate and prove general higher reciprocity laws.

My own (not particular well-informed) undestanding is that the problem of higher reciprocity laws was indeed one of Kummer's substantial motivations; after all, this problem is a direct outgrowth of the work of Gauss, Eisenstein, and Jacobi (and others?) in number theory. However, Kummer did also work on FLT, so he must have regarded it to be of some importance (i.e. important enough to work on).

Is there a consensus view on the role of FLT as motivating factor in Kummer's work? Was his work on it an afterthought, something that he saw was possible using all the machinery he had developed to study higher reciprocity laws? Or did he place more importance on it than that? (Am I right in also thinking that there were prizes attached to its solution which could also have played a role in directing his attention to it? If so, did they actually play any such role?)

This question is inspired in part by this answer of Bill Dubuque, in which he remarks that the fairly common belief that Kummer was motivated by FLT to develop his theory of cyclotomic number fields is essentially unfounded, and that Kummer was instead movitated by the desire to formulate and prove general higher reciprocity laws.

My own (not particular well-informed) undestanding is that the problem of higher reciprocity laws was indeed one of Kummer's substantial motivations; after all, this problem is a direct outgrowth of the work of Gauss, Eisenstein, and Jacobi (and others?) in number theory. However, Kummer did also work on FLT, so he must have regarded it to be of some importance (i.e. important enough to work on).

Is there a consensus view on the role of FLT as motivating factor in Kummer's work? Was his work on it an afterthought, something that he saw was possible using all the machinery he had developed to study higher reciprocity laws? Or did he place more importance on it than that? (Am I right in also thinking that there were prizes attached to its solution which could also have played a role in directing his attention to it? If so, did they actually play any such role?)

This question is inspired in part by this answer of Bill Dubuque's, in which he remarks that the fairly common belief that Kummer was motivated by FLT to develop his theory of cyclotomic number fields is essentially unfounded, and that Kummer was instead movitated by the desire to formulate and prove general higher reciprocity laws.

My own (not particular well-informed) undestanding is that the problem of higher reciprocity laws was indeed one of Kummer's substantial motivations; after all, this problem is a direct outgrowth of the work of Gauss, Eisenstein, and Jacobi (and others?) in number theory. However, Kummer did also work on FLT, so he must have regarded it to be of some importance (i.e. important enough to work on).

Is there a consensus view on the role of FLT as motivating factor in Kummer's work? Was his work on it an afterthought, something that he saw was possible using all the machinery he had developed to study higher reciprocity laws? Or did he place more importance on it than that. (Am I right in also thinking that there were prizes attached to its solution which could also have played a role in directing his attention to it? If so, did they actually play any such role?)

This question is inspired in part by this answer of Bill Dubuque, in which he remarks that the fairly common belief that Kummer was motivated by FLT to develop his theory of cyclotomic number fields is essentially unfounded, and that Kummer was instead movitated by the desire to formulate and prove general higher reciprocity laws.

My own (not particular well-informed) undestanding is that the problem of higher reciprocity laws was indeed one of Kummer's substantial motivations; after all, this problem is a direct outgrowth of the work of Gauss, Eisenstein, and Jacobi (and others?) in number theory. However, Kummer did also work on FLT, so he must have regarded it to be of some importance (i.e. important enough to work on).

Is there a consensus view on the role of FLT as motivating factor in Kummer's work? Was his work on it an afterthought, something that he saw was possible using all the machinery he had developed to study higher reciprocity laws? Or did he place more importance on it than that? (Am I right in also thinking that there were prizes attached to its solution which could also have played a role in directing his attention to it? If so, did they actually play any such role?)