Arabic numerals
The first mentions of the numerals in the West are found in the "Codex Vigilanus" of 976.
Number theory
Other than a treatise on squares in arithmetic progression by Fibonacci (ca. 1175–1200)—who lived and studied in north Africa and Constantinople—no number theory to speak of was done in western Europe during the Middle Ages. Matters started to change in Europe in the late Renaissance, thanks to a renewed study of the works of Greek antiquity. A catalyst was the textual emendation and translation into Latin of Diophantus's "Arithmetica" (Bachet, 1621, following a first attempt by Xylander, 1575).
Pierre de Fermat (1601–1665) never published his writings; in particular, his work on number theory is contained almost entirely in letters to mathematicians and in private marginal notes. He wrote down nearly no proofs in number theory; he had no models in the area. He did make repeated use of mathematical induction, introducing the method of infinite descent.