What you're talking about are known as Arabic or Hindu numerals, which use positional notation (so the columnar location matters and can be taken advantage of). They derive from methods developed originally in India, but migrated, diffused, and built-upon by scholars in Persia and the Arabian peninsula, especially during the Abbasid Empire (750-1250CE, the "Islamic Golden Age"). These involve using early versions of the numerals you are familiar with today, stacking them in columns, algebra, etc. None of our modern techniques were invented once in one place, but were developed over centuries, and spread to Europe during the Middle Ages, where it (very slowly) displaced both the abacus and Roman numerals.