Until the advent of materialism and 19th c. dogma, Western Civilisation was superior to anything Islam had developed. Islam has not aided in the development of the modern world; in fact civilisation has only been created in spite of Islam. Proof of this resides in the 'modern' world and the unending political-economic and spiritual poverty of Muslim states and regions. Squatting on richer civilisations is not 'progress'. Islam is pagan, totalitarian, and irrational.
Imagine a world without numbers and double-ledger accounting. Accurate financial reporting, profits, losses, even taxes would be impossible. Trade and commerce would decline. Corporations would be unable to seek capital from public or private markets. The ideas of wealth, equity, the burden of debt, current assets and receivables outpacing those of current liabilities, would be known, but hard to measure and control.
Accounting was invented, premised on new mathematical ideas, in the 15th century – the supposed 'dark ages' which never existed. Italy was rife with commerce, long-distance trade, banks, ledgers and higher math and science from 900-1400. A system which could record all aspects of business, and monitor the health of commerce and industrial affairs was long overdue by the late 15th century. It is unsurprising that a workable, elegant and direct system was authored in Italy.
Modern accounting is premised on the innovations and genius of Luca Pacioli who in 1494 [summary of his life here], in Venice, published the opus, “Summa de Arithmetica, Geometria, Proportioni et Proportionalita” [google book link here]. It is not an exaggeration to state that Pacioli's book is one of the most important documents on mathematics in history. Its impact has been monumental. For instance we find in Section 9 of this book or the chapter, "particularis de Coputis et Scripturis," a treatise about double entry bookkeeping. [source]
The demands of modern capitalism and commerce, first developed in Catholic Europe starting circa 900 AD, birthed accounting. Pacioli states in the first chapter of his book: "We will here adopt the method employed in Venice which among others is certainly to be recommended, for with it one can carry with any other method." In other words, Venetian 'counting houses' were employing double-entry methods to manage their finances.
In this regard Pacioli’s monumental contribution is part of a creative process which endured over many centuries. You cannot go from Roman numerals to balance sheet accounting over the long-weekend. But, as with so many other inventions, only in Medieval Europe do we see accounting developed and used. Why ? The historian of accounting A. C. Littleton describes seven "key ingredients" which led to its creation [see here his history of accounting]
Capital: By 1000 AD Europe was the richest area on the globe, and this 'excess' wealth was being deployed into a variety of industries and commercial enterprises.
Commerce:.European trade patterns were long, complex and high in volume. Commerce demands an ability to keep proper accounts, records and documentation.
Private property: Without property rights and contractual law, capitalism cannot arise.
Credit:.Using current credit against future cash flows, or as a lien against a current asset such as property, is a necessity for longer-term planning, investment and business cycles.
Writing: Or more accurately a common language. Vernacular language expresses contracts, obligations and laws, all of which you need to develop capitalism.
Money: The "common denominator" for exchanges, since there is no need for bookkeeping except as it reduces transactions to a set of monetary values.
Arithmetic: A method of computing is necessary, as is a general literacy about math, money and commerce.
Why did accounting develop in the Medieval period ? In one word – Capitalism. The framework of trade and commerce, which includes legal, moral, and cultural factors did not arise in Protestant Holland, or a functionary's office in Venice. It was a complex development starting before 900 AD which occurred throughout much of Medieval Europe. Italy, a major intersection of north-south; and east-west commercial activity, ran riot with commerce throughout the Medieval period. Venice, as seat of a commercial empire, is a logical place one would expect to locate the invention of accounting. But the antecedents to this seminal creation were long in the making.