Who: Lucjan Emil Boettcher (1872-1937), working in the theory of iteration, dynamics of rational maps and functional equations.

Criticism/rejection: Boettcher studied mathematics in Warsaw and engineering in Lvov, and completed a doctorate in mathematics in Leipzig with Sophus Lie. Afterwards he became a lecturer ("docent") at Lvov Polytechnics, teaching also some courses at Lvov University. In the years 1901-1919 he made four attempts at getting habilitation at the University (a process similar to tenure review). All were unsuccessful. Here are samples of the evaluations:

...the results of Dr. B\"ottcher seem to be too formalistic developments, and therefore can be only one-sided contributions to the theory of solutions of functional equations." (1911)

....The method used by the Candidate in his works cannot be considered scientific. The author works with undefined, or ill-defined, notions (e.g., the notion of an iteration with an arbitrary exponent), and the majority of the results he achieves are transformations of one problem into another, no less difficult. In the proofs there are moreover illegitimate conclusions, or even fundamental mistakes." (1918)

...Dr. B\"ottcher's works do not yield any positive scientific results. There are many formal manipulations and computations in them; essential difficulties are usually dismissed with a few words without deeper treatment. The content and character diverges significantly from modern research." (1918)

What he is nowadays famous for: Boettcher theorem, Boettcher equation and Boettcher coordinate. All these related notions describe behavior of an analytic function $f(z)=a_pz^p+..., \ p \geq 2$ in a neighborhood of the fixed point $z=0$. They are important in holomorphic dynamics.

Who first recognized his work: Joseph Fels Ritt, in his paper On the iteration of rational functions. Trans. Amer. Math. Soc. 21 (1920), no. 3, 348-356. Ritt seems to have given the first complete proof of Boettcher's theorem.

What else should he be famous for: Boettcher gets credit for constructing the first Lattes-type example of an everywhere chaotic map (see this MO question: http://mathoverflow.net/questions/66075/the-half-life-of-a-theorem-or-arnolds-principle-at-work/112444#112444). But he also should be recognized for pioneering the Fatou-Julia theory (20 years before Julia and Fatou, and without the advantage given by the notion of normal families) in his study of regions of convergence of iterates of rational maps and their boundaries. E.g. he described the Julia set for a monomial and for a Chebyshev polynomial of an arbitrary degree no less than two. More importantly, he also first stated an upper bound for the number of non-repelling cycles of a rational function in terms of the number of its critical points (in 1920s conjectured again by Fatou and proved to be sharp in 1980s by Shishikura).

An interesting twist: In principle, the committee members were right! At best, Boettcher only sketched his ideas. At worst, he really worked with ill-defined objects (he did study iterates with arbitrary exponents...) or made mistakes (e.g., in describing properties of boundary curves" of regions of convergence, better known as Julia sets). He also published some of his results multiple times and often devoted many pages to detailed analysis of other mathematicians' work (Koenigs, Leau etc.), so his articles could come across as derivative.

More to read, for those interested: Lucjan Emil B\"ottcher and his mathematical legacy, by Stanis\law Domoradzki and Ma\lgorzata Stawiska, http://arxiv.org/pdf/1207.2747.pdf