In my spreadsheet I have the function “=DATE(2020,1,19)” in Cell A2. In Cell C2 I have the function “=MONTH($A$2)”. This returns the result “1899-12-31”. I would expect the result “1”. Any idea what is going on?
Did you try formatting C2 as number? 
That works, thanks. A2 was formatted with the Default style and I had not changed that. What still puzzles me is that Cell B2 has the Function “Year($A$2)” andD2 has the Function Day($A$2)". Both are also formatted with the Default style and both give the expected result.
Your month cell was formatted as date, not default.