Mathematical Thinking

“Mathematics is the music of reason.” James Joseph Sylvester.¹⁾

“Mathematical thinking is a lot more than just being able to do arithmetic or solve algebra problems. It is a whole way of looking at things, stripping them down to their essentials, whether it’s numerical, structural or logical and then analyzing the underlying patterns.”²⁾

“The seventh of the attributes of the inheritors (of the Earth) is mathematical thinking. In the past the people in Central Asia and later on in the West achieved their renaissances by means of the laws of mathematical thinking. Man discovered and brought to light many uncertain and unknown things in the mysterious world of numbers. Without going to the extremes of the Hurufis, what we say is that without mathematics it is not possible to understand the relations of humanity and objects with one another. It illuminates our roads like light on the line that stretches from the universe to life; it indicates to us what is beyond the human horizon, even the depths of the world of contingencies, which is very difficult to think upon; and it makes us meet with our ideals.”³⁾

“… being mathematical does not mean knowing everything related to mathematics. It is to think mathematically, to think within mathematical laws, and to be aware that it permeates everything from man’s thoughts to the depths of existence, from physics to metaphysics, from matter to energy; from body to soul, from law to Sufism. In order to comprehend existence completely, we have to accept a dual method of Sufi thinking and scientific research. The West essentially lacks essence, and has tried to compensate for this loss, as far as it can, by taking refuge in mysticism. In our world, which has always been intimate with the soul of Islam, there is no need to look for anything strange or foreign, or to take refuge in anything. We have all our sources of power within our system of thought and faith. That suffices as long as we comprehend that source and spirit with its original richness. Then we will see some of the mysterious relations in existence, how harmoniously such relations run, and reach a different knowledge of observing and taking pleasure in everything.”⁴⁾

“Failure to observe the conditions and means of our age is against the ‘Qur’anic reasoning.’ You may want to light the torches of others with it the torch in your hand before it burns out, but you must look for alternative ways to do it without a failure and take the means into account.”⁵⁾

“‘Being mathematical’ can be achieved not by learning mathematics, but by getting used to thinking in terms of mathematical laws, and by assimilating the great framework of Greek thought, which has been ingrained in Europe for centuries, which considers sensibility as a false and incomplete tool in the comprehension of reality. What has kept us in the Middle Ages to this day is our lack of knowledge and discipline of mathematics, especially the latter. Europe, which shows some anti-rationalist tendencies today, perhaps needs to enrich an essence; but for the East, whose mystical spirit is saturated, nothing remains to be added to this essence. However, provided that they preserve this spirit in its original richness, if they have a mathematical mind, they will be able to open a great cultural era. In Poincaré’s words: If we have an intuition in the mathematical order, this feeling that makes us discover secret correlations and harmonies will fill the missing part of an uncontrolled, suspicious and defective intuition with the magnificent glow of the intellect.”⁶⁾

“Mathematical thinking, precise thinking is the privilege of the European.”⁷⁾

“Two groups stand out in terms of metaphysical thought: One of them is the Peripatetic people whose leader is Aristotle and who use thinking as a method, and the other is the Illuminists, who use both the methods of purification of the soul and the mathematical thinking. Those on this second path are Socrates and Plato from the former ones, and Al-Ghazali and Suhrawardi from the latter. These are the people of Sufism who have attained spiritual discoveries and pleasures, and have achieved significant success.”⁸⁾

“According to the modern scientific research methodology, mathematics is an ‘objective’ method for scientific studies. It is also the most objective tool for generalizing the results obtained. In the background of science and technology, there is mathematics, which is the expression of the Knowledge of God Almighty, and this is often overlooked. The mathematical thinking and features that Muslim scholars noticed in the Middle Ages were emphasized in the works of hundreds of scholars, from Al-Ghazali to Al-Biruni, from Nasiruddin Tusi to Abu-Mahmud Khojandi and Al-Khwarizmi.”⁹⁾

Comprehension

Free-thinking

John Mason, Leone Burton, Kaye Stacey, Thinking Mathematically: Thinking Mathematically

Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

Kaye Stacey, “What Is Mathematical Thinking and Why Is It Important?”

Keith Devlin, Introduction to Mathematical Thinking

M. Fethullah Gülen, “The Statue of Our Souls”

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