A profile of N. H. Abel

Abel made contributions to many different areas of mathematics and summarising these is the idea behind this article. The areas include ‘the theory of equations’, ‘elliptic integrals and elliptic functions’ and ‘infinite series’. A general description is given of his work on the theory of equations. The extensive proof of his main contribution to the theory is not given and can be found in other authors' work. For the topic of ‘elliptic integrals’, however, so as not to overwhelm the reader the mathematics presented is background material that is not directly attributable to Abel. (For more detailed information, such as ‘why ellipses are not elliptic curves’ the reader can consult other literature.) As regards ‘infinite series’, reference is made to Abel's comments on Cauchy's sum theorem; more detailed information on understanding these, i.e. exceptions and counterexamples, can be found in other literature.