What is wrong with this IF Statement?

It’s missing an opening parenthesis, and it’s got an an unparsed date string.
You need to use DATETIME_PARSE() to parse the string into a DateTime object to compare with your Date field.

Also, you may want to use the IS_AFTER() date comparison function.

I think this should be your equivalent formula:

IF(
   IS_AFTER(
      {purchase-date},
      DATETIME_PARSE("02/01/2020", 'MM/DD/YYYY')
   ),
   "Yes",
   "No"
)