Either of the two samples below will work:
SELECT MAX(date_columns) AS max_date
FROM ( (SELECT date1 AS date_columns
FROM data_table )
UNION
( SELECT date2 AS date_columns
FROM data_table
)
UNION
( SELECT date3 AS date_columns
FROM data_table
)
) AS date_query
The second is an add-on to lassevk's answer.
SELECT MAX(MostRecentDate)
FROM ( SELECT CASE WHEN date1 >= date2
AND date1 >= date3 THEN date1
WHEN date2 >= date1
AND date2 >= date3 THEN date2
WHEN date3 >= date1
AND date3 >= date2 THEN date3
ELSE date1
END AS MostRecentDate
FROM data_table
) AS date_query