Memorandum by Henry John Stephen Smith, on a paper 'On Fermat’s theorem of the polygonal numbers, with supplement' by Jonathan Frederick Pollock Not recommended for publication in the 'Philosophical Transactions of the Royal Society'. Provides a rigorous proof to the demonstrations in the paper. Admits he may have misunderstood the argument of the author, in which case the referee suggests some rearrangement of the paper and proof to aid clarity and prevent similar misunderstandings in future. Subject: Mathematics [Published in the Proceedings of the Royal Society of London, 1864] 12 November 1863