There are many ways you can browse the mathematics section of the arXiv. You can refine by date and focus only on new articles or those submitted on a specific day, month, or year. You can filter even more using the arXiv's 36 mathematics subject categories, such as Functional Analysis, Combinatorics, and Metric Geometry. Within the categories you can again use dates to refine your results.
Note: The information on the arXiv has been submitted the article authors, while some may have been refereed there is no peer review required for articles in the arXiv.
When searching the arXiv for mathematics it is keep in mind that you are searching hundreds of thousand highly technical research papers. This makes it very important to think deeply and try to make your searches as specific as possible. In general, unless you know an article's title or arXiv-id stick to the advanced search instead of using the search box on the front page.
With arXiv's advanced search you can search for an article by its title, abstract, arXiv subject category, DOI, and Mathematical Subject Classification or for an author by their name, ORCID ID, and arXiv id, as well as filter by subject and date. For more general searches choose All Fields from the drop down and if you are searching for an author by name use the last name, first name format.
The arXiv has two services which will allow you to automatically receive all of the new articles from subject areas of interest.