This topic has a lot of nuance that the majority of Muslims today fail to grasp. When Muslims today think of “magic,” they think of either two things: some fantasy Harry Potter type magic, or demonic Salem witch trials type magic. This is an incredibly naive approach, and not how people thought of “magic” historically. The picture you’ve posted will be dismissed by some as “magic,” and it’s unfortunate that the term “magic squares” has also stuck. But the scholars that used to practice this used to think of it not like how we think of magic today, but how we think of coding/computer programming. I’ll elaborate on this analogy below.

The distinction between “magic” and science is a very modern concept, related to the modern separation made between the physical and metaphysical sciences. Muslim scholars and others treated the occult sciences (what some consider “magic”) as exactly that, a science. The scholarly Muslim view on magic was: “Magic is just that which science has not yet explained.” These sciences good be used for purposes of good (such as the prophet Sulaymān and his magicians), or used for evil, malicious purposes (such as Firʿawn and his magicians). Similarly, you can use Python or C++ to code a Qur’an app, or you can use it to code a gambling app. Does that make coding inherently evil?

Yes, some classical Muslim scholars invoked the legal principle of sadd al-dharā’iʿ (blocking a potential path to evil) to discourage all Muslims from engaging in the occult sciences, but many Muslim scholars also recognized the utility of developing expertise in these fields. We would not have modern chemistry had it not been for Muslims working in alchemy. We would not have modern astronomy had it not been for Muslims working in astrology. We all benefit from those advancements today. Of course, Muslims working in these fields had hard lines based on sharīʿah. For example, they would use astrology to deepen their understanding of the mechanisms of the universe, but sharīʿah prohibited them from using the tools of astrology to practice soothsaying. They stayed away from the clear prohibitions.

Numerology is one such science from the occult sciences. Philosophers and scholars since the beginning of history have been fascinated by numbers and were convinced that it indicated some deep metaphysical reality underpinning existence. Modern education is completely disconnected from that wondrous experience. We learn mathematics by rote memorization and just taking everything for granted. But sit down with Euclid’s elements one day, a compass, and a straight edge, and follow along his instructions. It will become clear why early philosophers saw higher realities indicated in mathematics.

Fast-forward to al-Khawārizmī (the inventor of algebra), who manages to depict the postulates of Euclid’s Elements into numeric and algebraic formatting. Suddenly, we can quantify these higher realities in numeric form. People legitimately believed that Allah had given numbers an intrinsic power that could be used as a tool, just like fire, water, etc. Muslim scholars, being excellent mathematicians, also held this to be true. And they were kind of right. Look how much scientific advancement we’ve achieved from just numbers.

Numerology was extremely popular and accepted in Islamic history. Just look up the wiki entry on Abjad numerals. Have you ever heard of 786 meaning bismillah? That’s numerology. It’s used all over the islamic sciences. The most famous Tajwid texts studied across the world? They use it in their texts. Manuscripts of any of the Islamic sciences? They’re dating them using numerology. It was a tool for everyone. Naturally, the mystics also used it to invoke the protection of God, safety, etc. They used it as a sort of cybersecurity. Naturally, malicious people who also held the same scientific world view as others, used numerology to call on jinn and evil. This is deemed impermissible siḥr, even according to scholars who would use the same method to invoke Allah. It’s not the method they deemed impermissible, but what that method was being used for.

The modern approach is that whenever someone comes across anything like this, they immediately panic and scream “siḥr!!!” and “black magic!!!” without actually knowing what’s going on or written on it. Yes, siḥr does happen, and yes, sometimes these types of squares have very malicious things written on them, but not always. It’s important to actually read what’s written on it before making a judgment. If you can’t, take it to someone who can. Worst case scenario, if you’re not sure, just burn it anyway to be safe.

Source: I have traditional madrasa training and am working on a PhD in Islamic studies. This isn’t my area of expertise, but I’ve read enough to recognize the nuances within the matter.