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Eurocentrism in Mathematics
The history of mathematics has a murky past due to the reason that it cannot be directly traced back to any certain type of people or continent. However, mathematics is often attributed to white European men, even with evidence of the development of mathematics rooting from all continents across the world. This bias is due to the effects of Eurocentrism in mathematics. Eurocentrism is a worldview and idolization of anything European. Eurocentrism is prevalent in mathematics simply because the contribution of non-European people are overlooked in the academic world of mathematics. For example, when learning about mathematics, famous mathematicians such as Isaac Newton and Leonhard Euler are mentioned far more than mathematicians from non-European backgrounds. Consequently, Eurocentrism in mathematics is due to the fact that mathematical contributions from Islamicate sources in are often overshadowed and under-represented compared to European mathematical sources. Islamicate contributions to mathematics has been paramount in shaping the mathematics that we know today.

Algebra
The founding of algebra can accredited to the Muslims. The word algebra stems from the Arabic word al-jabr, which means ‘restoration’. Algebra was established by mathematician and astronomer Muhammad ibn Musa al-Khwarizmi (whose name originated ‘algorithm’).

It was under the patronage of Abu al-Abbas Abdallah ibn Harun al-Rashid, better known as al-Ma'mun the seventh Abbasid Caliph, in which he formulated his book, The Compendious Book on Calculation by Completion and Balancing in which he proposed solutions to problems by ‘al-jabr’ and ‘al-muqabala’. The common meaning of jabr in math is the adding of equal terms to both sides of the equation to remove negative terms. The other less common meaning of jabr is to multiply both sides of the equation by one to remove fractions. The common meaning of muqabala is the reduction of positives by subtracting equal amounts from both sides of the equation.

The combination of both jabr and muqabala is used to mean performing algebraic operations. With the terms of al-jabr and al-muqabala, al-Khwarizmi’s book is also known as The Compendious Book on Calculation by al-jabr and al-muqabala. In al-Khwarizmi’s book, he explains that all linear and quadratic equations can be reduced to six types in which he provides rules for solving.


 * 1) $$ax^2 = bx$$
 * 2) $$ax^2 = c$$
 * 3) $$ax = b$$
 * 4) $$ax^2 + c = bx$$
 * 5) $$ax^2 + c = bx$$
 * 6) $$ax^2 = bx + c$$

Mathematical Induction
The history of mathematical induction is debated by historians in where it first originated. It’s commonly thought to originate from Blaise Pascal in Traité du triangle arithmétique, but according to Georges Vacca in Bulletin of the American Mathematical Society, it was Francesco Maurolico, not Pascal, who was the first to formulate mathematical induction. Even further, there are works of Jacques Bernoulli and Levi ben Gershon to possibly be the originators of mathematical induction.

Before Maurolico or even Pascal, works of Abu Bakr Muhammed Al-Karaji were found to utilize methods of mathematical induction for proving the binomial theorem.

Series
In contribution of number theory of series and exponential growth, Abu Rayhan Al-Biruni came up with the famous chessboard problem. It is a problem in mathematics that shows how quickly exponential series grow. The problem that Al-Biruni posited to his king was to be given the amount of grains of rice on the chessboard, but with the caveat that the first square have one grain, the second have two grains, the third square having four grains, and repeating pattern all the way up to the sixty-fourth square. This resulted in an accumulation of 18,466,744,073,709,551,615 grains of rice.

The modern representation of the problem would be:

$$\sum^{64} 2^{n-1} = 2^{64} - 1$$

Decimal System
The decimal system in which we write our numbers today was first used by Muslim mathematicians. They were the mathematicians who began the numeration system with two characteristics that hold true today.


 * 1) The numbers from one to nine are represented by nine digits, all easily made by one or two strokes.
 * 2) The right-most digit of a numerical counts the number of units, and a unit in any place is ten of that to its right. Thus the digit in the second place counts the number of tens, that in the third place the number of hundreds (which is ten tens), and so on. A special mark, the zero, is used to indicate that a given place is empty.

The two characteristics describe the system that we use today when writing numbers. It was the Hindus who were the first to use a cipherized, decimal, and positional system. But, it was the Muslims who were the ones to extend the system to represent the units by decimal fractions, therefore the system is "Hindu-Arabic".