A mathematics journal is a scientific journal which publishes exclusively (or almost exclusively) mathematics papers. A practical definition of the current state of mathematics, as a research field, is that it consists of theorems with proofs published in a reputable mathematics journal, and which usually have passed through the process of peer review. In some exceptional cases, the statement of a conjecture, or the introduction of some new method or definition might assume relevance. A relatively small proportion of mathematics papers concerned with pure mathematics are published through more general, science-based learned journals. Applied mathematics may be published in publications more oriented towards engineering, but sometimes also biology and other sciences.
Hundreds of such journals exist. Some of the most prestigious journals in pure mathematics are Annals of Mathematics, Publications Mathématiques de l'IHÉS, Acta Mathematica, and Inventiones Mathematicae.