A HISTORY OF MATHEMATICAL NOTATIONS
CONTENTS PART 1 NUMERALS ? CURIOUS BEGINNINGS * * CERTAIN ANCIENT NUMBER SYSTEMS ?? * SILK AND ROYAL ROADS *? ? TE INDIAN GIF *? ? ARRIVAL IN EUROPE ?? ? TE ARAB GIF ?? ? LIBER ABBACI ?? ? REFUTING ORIGINS ?* PART 2 ALGEBRA ? SANS SYMBOLS ?? ?? DIOPHANTUS’S ARITHMETICA ?* ?? TE GREAT ART ??? ?* SYMBOL INFANCY ??? ?* TE TIMID SYMBOL ?*? ?? HIERARCHIES OF DIGNITY ?** ?? VOWELS AND CONSONANTS ??? ?? TE EXPLOSION ??? ?? A CATALOGUE OF SYMBOLS ??? ?? TE SYMBOL MASTER ??? ?? TE LAST OF THE MAGICIANS ??? PART 3 THE POWER OF SYMBOLS *? RENDEZVOUS IN THE MIND ??? *? TE GOOD SYMBOL ??? ** INVISIBLE GORILLAS ??* ** MENTAL PICTURES *?? *? CONCLUSION *?? PART NUMERALS SIGNI?CANT MANUSCRIPTS AND INITIATORS BAKHSHÂLÎ MANUSCRIPT (DATE IN DISPUTE: ???–???) INDIAN SHOWS THAT THE INDIANS HAD A PLACE-VALUE SYSTEM IN PLACE BEFORE ???AD BISHOP SEVERUS SEBOKHT (CA ???–CA ???) SYRIAN SCIENCE AND PHILOSOPHY WRITER AUTHOR OF THE EARLIEST KNOWN EXTANT REFERENCE TO HINDU-ARABIC NUMERALS OUTSIDE OF INDIA BRAHMAGUPTA (???–???) INDIAN MATHEMATICIAN-ASTRONOMER HIS BRAHMASPHUTASIDDHANTA (?*?) HAS THE ?RST KNOWN USE OF ZERO (A SMALL BLACK DOT) AS A NUMBER, NOT JUST AS A PLACEHOLDER HARUN AL-RASHID (?TH CENTURY) PERSIAN CALIPH FOUNDED THE HOUSE OF WISDOM IN BAGHDAD, A LIBRARY AND TRANSLATION CENTER THAT CONTAINED MANUSCRIPTS OF MATHEMATICS AND PHILOSOPHY TRANSLATED INTO ARABIC FROM MANY OTHER LANGUAGES AL-KHW¯ARIZM¯I (CA ???–CA ???) PERSIAN MATHEMATICIAN-ASTRONOMER-GEOGRAPHER SCHOLAR IN THE HOUSE OF WISDOM WROTE THE COMPENDIOUS BOOK ON CALCULATION BY COMPLETION AND BALANCING (ALGEBRA), ?*?AD MAS’ÚDÌ (ABU’L-HASAN ‘ALI) (CA ???–???) MESOPOTAMIAN ARAB HISTORIAN, ADVENTURER