The arXiv is the number one pre-print article database for mathematics, computer science, and physics. While it was original developed for physics, mathematics now represents around a quarter of all submissions
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. Instructions follow.
Send an email to email@example.com with the subject line set to subscribe *Your Name* and add *Name of Category* as the email's message.
For example to all the newly submitted Number Theory articles you would write add Number Theory in the email.
To then stop receiving email alerts about Number Theory articles you would send a second email with del Number Theory
The arXiv provides an RSS feed for all new mathematics articles, as well as mathematics specific feeds.
You can find the RSS for all mathematics articles at https://arxiv.org/rss/math
For a specific category just add .XY to the end of the URL, where XY is the category code.
For example the Group Theory RSS URL would be https://arxiv.org/rss/math.GR. You can find the category codes on the front page of the mathematics arXiv.