Postgres is strange. If you make a query
select min(column_with_index) from table;
the database performs a sequential scan – you can only imagine how long it takes on a 10M record database. This seems to be a feature (!@!#!@), but indices can will used if you use the following workaround:
select column_with_index from table order by 1 (desc) limit 1;
This trick is explained here.