The Collatz Conjecture and a Lesson on Faith
“We will show them Our signs in the horizons and within themselves until it becomes clear to them that it is the truth.” (Qur'an, Fussilat, 53)
In the world of mathematics, there is a problem so simple yet profoundly deep that it has captivated the greatest minds for decades. This problem is known as the Collatz conjecture or simply 3x+1.
The rule is straightforward: take any positive integer. If it's even, divide it by two; if it's odd, multiply it by three and add one. Repeat this process with each subsequent number. Astonishingly, no matter which number you start with, you always seem to end up in the same infinite loop: 4, 2, 1, 4, 2, 1…
Thousands of mathematicians have tested billions of numbers. In fact, the largest number mathematicians have reached using incredibly powerful computers is approximately 2682^{68}268 (about 2.95 × 10²⁰), a number with 21 digits. No one has found a single number that breaks this pattern. Yet, despite extensive efforts, the Collatz conjecture still lacks a formal mathematical proof.
Mathematicians believe it to be true, not because they have formal proof, but because everything observed thus far points in that direction. Their belief in the validity of this conjecture is not based on blind faith, but rather on careful observation of order and harmony.
Isn't this similar to our understanding of faith?
Just as the Collatz conjecture demonstrates perfect order despite the lack of a formal proof, our belief in Allah, the Most High, does not depend on experimental evidence but rather on the insight into the order, harmony, and laws of the universe around us, as well as the peace and clarity we feel in our hearts. Allah shows us signs of His power everywhere, in the precision of the laws of physics, in the perfection of biological processes, and even within our souls that find peace when we remember Him.
Yet some people demand experimental proof of God's existence, saying: "Prove to me that He exists." But just as even the brightest sunlight cannot help one who chooses to keep their eyes closed, neither can proof benefit one who decides to close their heart. Whoever desires to see, already sees, and that is enough.
Being Honest with Ourselves
Perhaps we should be more honest with ourselves. If we can believe in a mathematical statement that hasn't been formally proven but is confirmed everywhere by experience, why wouldn't we place even deeper trust in the One whose signs are evident not just in numbers, but in every aspect of our lives, from hope and love to tranquility and repentance?
How Much is the Search for Truth Worth?
And this is what amazes us most, generations of mathematicians have devoted their entire lives to a single conjecture. They spared neither time nor effort, not for material reward or fame, but because they believe that behind this simple rule lies a deeper truth. If people are willing to invest so much for the sake of a single number, how much more should we be willing to invest in knowing the One who created all numbers, all laws, our minds, and our hearts? Their dedication testifies to human persistence, but our quest for the truth about Allah, the Most High, should be even stronger, more sincere, and lifelong, because our ultimate goal is not just to understand, but to achieve the eternal pleasure of the One who has given us understanding.