In most US patent descriptions, I see serial numbers like [0001], [0002] etc.
Are they there for readability or are they a requirement?
I'm working on provisional patent application. Does a provisional patent application contain those serial numbers in the description?
These are paragraph numbers. They are considered good practice to include since they aid referencing portions of the description, but are not mandatory.
They are described in a extremely detailed manner by 37 CFR § 1.52(b)(6), which provides:
Other than in a reissue application or reexamination or supplemental examination proceeding, the paragraphs of the specification, other than in the claims or abstract, may be numbered at the time the application is filed, and should be individually and consecutively numbered using Arabic numerals, so as to unambiguously identify each paragraph. The number should consist of at least four numerals enclosed in square brackets, including leading zeros (e.g., [0001]). The numbers and enclosing brackets should appear to the right of the left margin as the first item in each paragraph, before the first word of the paragraph, and should be highlighted in bold. A gap, equivalent to approximately four spaces, should follow the number. Nontext elements (e.g., tables, mathematical or chemical formulae, chemical structures, and sequence data) are considered part of the numbered paragraph around or above the elements, and should not be independently numbered. If a nontext element extends to the left margin, it should not be numbered as a separate and independent paragraph. A list is also treated as part of the paragraph around or above the list, and should not be independently numbered. Paragraph or section headers (titles), whether abutting the left margin or centered on the page, are not considered paragraphs and should not be numbered.
However, you will notice that this provision uses "may" and "should" pretty consistently. This reflects that paragraph numbering is considered a recommendation, rather than a mandate.
For provisional applications, you may well choose to include paragraph numbers, since there are no disadvantages to doing so. But there are no formality requirements for provisional applications anyway, so you are doubly insulated from any need for paragraph numbering.
