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Posts Tagged ‘division sign

“Those who wish to know the art of calculating, its subtleties and ingenuities, must know computing with hand figures”*…

Scholars at an Abbasid library. Maqamat of al-Hariri Illustration by Yahyá al-Wasiti, 1237 [source]

The House of Wisdom sounds a bit like make believe: no trace remains of this ancient library, destroyed in the 13th Century, so we cannot be sure exactly where it was located or what it looked like.

But this prestigious academy was in fact a major intellectual powerhouse in Baghdad during the Islamic Golden Age, and the birthplace of mathematical concepts as transformative as the common zero and our modern-day “Arabic” numerals.

Founded as a private collection for caliph Harun Al-Rashid in the late 8th Century then converted to a public academy some 30 years later, the House of Wisdom appears to have pulled scientists from all over the world towards Baghdad, drawn as they were by the city’s vibrant intellectual curiosity and freedom of expression (Muslim, Jewish and Christian scholars were all allowed to study there).

An archive as formidable in size as the present-day British Library in London or the Bibliothèque Nationale of Paris, the House of Wisdom eventually became an unrivalled centre for the study of humanities and sciences, including mathematics, astronomy, medicine, chemistry, geography, philosophy, literature and the arts – as well as some more dubious subjects such as alchemy and astrology.

To conjure this great monument thus requires a leap of imagination (think the Citadel in Westeros, or the library at Hogwarts), but one thing is certain: the academy ushered in a cultural Renaissance that would entirely alter the course of mathematics.

The House of Wisdom was destroyed in the Mongol Siege of Baghdad in 1258 (according to legend, so many manuscripts were tossed into the River Tigris that its waters turned black from ink), but the discoveries made there introduced a powerful, abstract mathematical language that would later be adopted by the Islamic empire, Europe, and ultimately, the entire world.

Tracing the House of Wisdom’s mathematical legacy involves a bit of time travel back to the future, as it were. For hundreds of years until the ebb of the Italian Renaissance, one name was synonymous with mathematics in Europe: Leonardo da Pisa, known posthumously as Fibonacci. Born in Pisa in 1170, the Italian mathematician received his primary instruction in Bugia, a trading enclave located on the Barbary coast of Africa (coastal North Africa). In his early 20s, Fibonacci traveled to the Middle East, captivated by ideas that had come west from India through Persia. When he returned to Italy, Fibonacci published Liber Abbaci, one of the first Western works to describe the Hindu-Arabic numeric system.

When Liber Abbaci first appeared in 1202, Hindu-Arabic numerals were known to only a few intellectuals; European tradesmen and scholars were still clinging to Roman numerals, which made multiplication and division extremely cumbersome (try multiplying MXCI by LVII!). Fibonacci’s book demonstrated numerals’ use in arithmetic operations – techniques which could be applied to practical problems like profit margin, money changing, weight conversion, barter and interest…

Fibonacci’s great genius was not just his creativity as a mathematician, however, but his keen understanding of the advantages known to Muslim scientists for centuries: their calculating formulas, their decimal place system, their algebra. In fact, Liber Abbaci relied almost exclusively on the algorithms of 9th-Century mathematician Al-Khwarizmi. His revolutionary treatise presented, for the first time, a systematic way of solving quadratic equations. Because of his discoveries in the field, Al-Khwarizmi is often referred to as the father of algebra – a word we owe to him, from the Arabic al-jabr, “the restoring of broken parts”—and in 821 he was appointed astronomer and head librarian of the House of Wisdom…

Centuries ago, a prestigious Islamic library (tragically burned in the the Siege of Baghdad) brought Arabic numerals to the world; its mathematical revolution changed our world: “How modern mathematics emerged from a lost Islamic library.”

For more on The House of Wisdom– and the sad stories of other libraries and archives that have been destroyed through the ages– see Richard Ovenden‘s remarkable new Burning the Books- a History of the Deliberate Destruction of Knowledge.

* Leonardo da Pisa, known posthumously as Fibonacci [see here]

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As we count our blessings, we might spare a thought for John Pell; he died on this date in 1685.  An English mathematician, he is perhaps best remembered for having introduced the “division sign”– the “obelus,” a short line with dots above and below– into use in English.  It was first used in German by Johann Rahn in 1659 in Teutsche Algebra; Pell’s translation brought the symbol to English-speaking mathematicians.  But Pell was an important influence on Rahn, and edited his book– so may well have been, many scholars believe, the originator of the symbol for this use.  (In any case the symbol wasn’t new to them:  the obelus [derived from the word for “roasting spit” in Greek] had already been used to mark passages in writings that were considered dubious, corrupt or spurious…. a use that surely seems only too appropriate to legions of second and third grade math students.)

source

Teach your children well…

Your correspondent is headed again across the Dateline (where he loses all track of what day it actually is), thus (R)D will be in abeyance until March 9 or 10, when “service” will resume again.

In the meantime, a message from the past to the future…

In 1959, philosopher, logician, mathematician, historian, and social critic Bertrand Russell appeared on the BBC interview program Face-to-Face.  As the program came to its final two minutes, he was asked a valedictory question: “What would you tell a generation living 1,000 years from now about the life you’ve lived and the lessons you’ve learned?”…

[TotH to Open Culture]

As we do our level best to take good advice, we might recall that it was on this date in 1611 (81 years before the beginning of a case Russell might have cited, the Salem Witch Trials, on this date in 1692) that John Pell was born.  An English mathematician of accomplishment, he is perhaps most remembered for having introduced the “division sign”– the obelus: a short line with dots above and below– into use in English.  It was first used in German by Johann Rahn in 1659 in Teutsche Algebra; Pell’s translation brought the symbol to English-speaking mathematicians.  Indeed, Pell was an important influence on Rahn, and edited his book– so may well have been, many scholars believe, the originator of the symbol for this use.  (In any case the symbol wasn’t new to them:  the obelus [derived from the word for “roasting spit” in Greek] had already been used to mark passages in writings that were considered dubious, corrupt or spurious…. a use that surely seems only too familiar to legions of second and third grade math students.)

John Pell (source)

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