The Mathematics of the Quran

"The sun and the moon [move] are calculated" (Quran 55 :5)

This verse highlights the sun and moon because all universal life depends on their precisely calculated orbital movements. These celestial bodies maintain perfect sequences according to divine mathematical principles, never deviating even by fractions of seconds across billions of years of cosmic history. This astronomical precision inspired Islamic mathematicians during the Golden Age (8th-12th centuries) to develop sophisticated mathematical tools for understanding and predicting celestial phenomena, recognizing mathematics as the language through which Allah's cosmic design becomes comprehensible to human intellect. "He Who created the seven heavens one above another: No want of proportion wilt thou see in the Creation of (Allah) Most Gracious. So turn thy vision again: sees thou any flaw? (Quran 67:3)

Since the universe operates through precise divine calculations, the Quran naturally employs mathematical principles in its very structure. Allah's challenge to produce anything resembling the Quran extends beyond literary beauty to include its mathematical architecture. Quranic verses demonstrate intricate numerical relationships and word patterns that create a mathematical matrix underlying the text's spiritual message. This mathematical dimension provides additional evidence of divine authorship, as such complex numerical relationships could not result from human composition. An example of this is the number 19, which appears only once in the entire Quran which is the chapter 74 (Al Mudhateer), while talking about the angels of punishment, and that there are 19 angels in charge of the fire of Hell, the Blessed and Exalted says: "There are nineteen of them "(Quran 74:30). Why did Allah (SWT) make their number nineteen, neither more nor less? The verse following this one answers this question and confirms that this number has a great secret behind it. It is a trial for the disbelievers, and at the same time, it is a means to increase the faith of the believers. Therefore, Allah (SWT) says: "And We did not make their number except as a trial for those who disbelieved" (Quran 74:31). Then He mentioned to us the other goal, saying: "And those who believe will increase in faith" (Quran 74: 31). Then Allah (SWT) confirmed that this number is a means of remembrance and a reminder to humanity that the Quran is the truth. Therefore, He said: "And it is only a reminder to mankind." (Quran 74: 31). After that, Allah (SWT) swore that this number represents one of the greatest miracles. Therefore, He said after that: "Indeed, it is one of the greatest" (Quran 74: 35).

Another miracle is that the number of Surah Al-Muddaththir is 74, and that the miracle of the number 19 was discovered in 1974. It was discovered that the entire structure of the Quran is mathematically composed of the symbol number 19. Some examples of how the Holy Quran is coded with the number 19 are:

1. First, the number of Quranic verses in the Quran is 114 = 19 x 6.
2. The number of verses in the Quran is 6,346 = 19 x 334.
3. The number of times the word Allah is mentioned in the Quran is 2,698 = 19 x 142.
4. If we count all the verses where the word Allah occurs that number is 118,123 = 19 x 6,217.
5. The Basmala (bismi ʾllāhi ʾr-raḥmāni ʾr-raḥīmi), the Quranic opening formula, which, with one exception, is at the beginning of every Surah of the Quran, consists of exactly 19 letters.
6. The first word of the Basmala, Ism (name), without contraction, occurs 19 times in the Quran (19x1). [Also, no plural forms, or those with pronoun endings]
7. The second word of the Basmala, Allah (God), occurs 2698 times (19x142).
8. The third word of the Basmala, Rahman (Gracious), occurs 57 times (19x3).
9. The fourth word of the Basmala, Rahim (Merciful), occurs 114 times (19x6).
10. The multiplication factors of the words of the Basmala (1+142+3+6) give 152 (19x8).
11. The Basmala appears 114 times (despite its absence in chapter 9, it appears twice in chapter 27); 114 is 19x6.
12. From the missing Basmala in chapter 9 to the additional Basmala in chapter 27, there are exactly 19 chapters.
13. The occurrence of the additional Basmala is in Quranic verse 27:30. Adding this chapter number and the verse number gives 57 (19x3).

1. The word "Salawat" (prayers) is mentioned 5 times in the Quran, and the number of daily prayers mandatory for every Muslim is A- Subh, A-Duhr, Al-Asr, Al-Maghrib, Al-Isha.
2. The Word "Shahr" (month) is mentioned 12 times in the Quran, just as the number of months there are in a year.
3. The word "Yawn" (day), in the singular, is mentioned 365 times in the Quran, just as the number of days there are in a year.
4. The word "Ayyam" (days), in the plural, is mentioned 30 times in the Quran, just as the number of days there are in a month.

Based on this Quranic verse, some pairs are also mentioned equally in the Holy Quran:

1. "Al Hayat" (life) and "Al Mawt" (death) are both mentioned 145 times.
2. "Al-Dunya" (mundane life) and "al Akhira" (the afterlife): both 115 times.
3. "Malaika" (angels) and "Shayatin" (demons): both mentioned 88 times.
4. "Ar Rajul (man) and "Al Mar'a (woman): are both mentioned 24 times.
5. "Ar Raghba (wish) and "al Khauf (fear): are both mentioned 8 times.
6. As Salihat (good deeds) and "As Sayyi'at" (wrongdoings), both mentioned 167 times.
7. "An Nafaa" (benefit) and "Al Fasad (corruption): both are mentioned 50 times.

Now, when the Prophet (SAW) was asked by the people of Quraish about Allah (SWT), the answer came directly from Him in the form of Chapter 112 of the Noble Quran, which is considered the essence of the unity or the motto of Allah (SWT) 's Oneness (Al Tawheed). This is one of the shortest Chapter of the Holy Quran. Its number of verses is only 4. Let's check the mathematical balance in this Chapter:

1. It has 15 Arabic words. 7 words at the beginning, 7 words at the end, a word in the middle- balance!
2. The number of letters in the first 7 words is 22. The number of letters in the last 7 words is 22! -Balance again!
3. The middle word has three letters. The middle letter is 'lam', which is the 23rd letter of the Arabic alphabet. And there are exactly 23 letters before and after the letter 'lam'! That is, balance!
4. There is another balance! At the end of the first verse, there is the word 'Ahad', and at the end of the last verse, there is also the word 'Ahad'. The word 'Ahad' means the oneness of God.
5. In the middle of the surah, there are words about giving birth. Giving birth is a human characteristic. That means the two sides of the surah are the attributes of Allah (SWT), and the middle is the attributes of humans.
6. As we saw, the middle letter of the Surah is 'Lam' which is the 23rd letter of the Arabic alphabet, and there are exactly 23 letters before and after the 'Lam'. So, the question is, why are there 23 in the middle? The importance of the number 23 is that the number of human chromosomes is 23 pairs, and the middle of the surah deals with the human characteristics of giving birth.

Muslim Mathematicians

This verse calls Muslim scientists to study celestial bodies for calculating time periods essential to Islamic practice. Mathematics became crucial for determining prayer times, identifying Ramadan's beginning, and coordinating pilgrimage schedules. During Islam's Golden Age, mathematical sciences flourished as scholars recognized their instrumental role in fulfilling religious obligations while advancing human knowledge. Islamic mathematicians viewed their work as both a practical necessity and a spiritual service. Muslim mathematicians were able to draw on and fuse together the mathematical developments of both Greece and India. Indeed, just after the founding of the House of Wisdom in Baghdad around 810, work started on translating the major Greek and Indian mathematical and astronomy works into Arabic language. Moreover, in the field of geometry, one consequence of the Islamic prohibition on depicting the human form was the extensive use of complex geometric patterns to decorate their buildings, raising mathematics to the form of an art. Over time, Muslim Mathematicians discovered all the different forms of symmetry that can be depicted on a 2-dimensional surface. From the large number of Muslim Mathematicians of the Golden Age, Muhammad ibn Musa al-Khwarizmi (c. 780-850 CE) earned recognition as the 'Father of Algebra' through groundbreaking mathematical innovations. As director of Baghdad's House of Wisdom, he revolutionized mathematics by:

Advocating the Hindu-Arabic numeral system (0-9): He recognized these numerals' computational power and efficiency, leading to their adoption throughout the Islamic world and later Europe.

Developing algebra: His work, 'Hisab al-Jabr wa'l-Muqabalah', introduced systematic methods for solving polynomial equations, giving algebra its name from 'al-jabr' (restoration/completion).

Discovering zero's significance: Al-Khwarizmi elevated zero from a mere placeholder to a full numeral, enabling negative numbers and advanced calculations impossible under previous systems.

His mathematical innovations transformed computation from cumbersome procedures into elegant, systematic methods that remain foundational to modern mathematics.

Another Muslim mathematician, Omar Khayyam (1048-1131 AD), excelled in mathematics, and among his most prominent achievements in it are the following:

1. He found a method for extracting roots of the third degree.
2. He solved cubic equations by calculating conic sections.
3. He studied Euclid's parallel postulates.
4. He developed Euclid's theory regarding rational numbers by solving the problem of irrational numbers, as he imagined that the number system is broader.

Moreover, the 13th-century Muslim astronomer, scientist, and mathematician Nasir Al-Din Al-Tusi was perhaps the first to treat trigonometry as a separate mathematical discipline, distinct from astronomy. Building on earlier work by Greek mathematicians such as Menelaus of Alexandria and Indian work on the sine function, he gave the first extensive exposition of spherical trigonometry, including listing the six distinct cases of a right triangle in spherical trigonometry. One of his major mathematical contributions was the formulation of the famous law of sines for plane triangles.

Furthermore, one of the most remarkable Muslim mathematicians was Ghiyath Al-Din Al- Kashani, who thrived in the late 14th Century. His focus was on the theory of numbers and the techniques of computations. In 1424, he astounded the mathematical world by calculating a value of 2π to an unprecedented sixteen decimal digits of accuracy, a feat that still stands as a testament to his mathematical precision. He achieved this by using an approximation of the circle with 805306368-sided polygons. His magnum opus, "Miftah-Ul-Hissab" or "The Calculator's Key", introduced an algorithm for finding the fifth root of any number. This groundbreaking book was a staple in Persian schools until the 17th Century. Kashani's contributions also extended to trigonometry, where he devised a method to approximate the function "sin" by solving a cubic equation with remarkable precision.