A Call to Correct Mathematical Principles for Future Generations.

The Zero Given by Sanskrit It’s different from what you think. Sanskrit gave zero in mathematics. Sanskrit also showed the method of multiplication in mathematics. Mathematicians like Aryabhata, Brahmagupta, and Bhaskaracharya developed essential arithmetic, algebra, and number systems theories. These were spread to Western countries through Islamic scholars. Along with that, Western countries also used the multiplication method from Sanskrit sources.

To understand the definition of multiplication in mathematics, it’s essential to look at the definitions available in famous dictionaries.

According to the Merriam-Webster Dictionary, multiplication is repeatedly adding a number to zero. According to mathematical rules, this applies to other numbers (such as complex numbers, vectors, and matrices.

According to the Oxford Learner's Dictionary, multiplication is one of the basic operations in arithmetic needed in various mathematical contexts where numbers are multiplied. As per the Britannica Dictionary, multiplication is repeatedly adding a number to itself.

It is also used to show growth or increase, like the uncontrolled growth of cancer cells. The Cambridge Dictionary defines multiplication as the process of adding a number to itself several times.

For example, multiplying five by five means adding 5 to itself five times, which equals 25. Similarly, multiplying -5 by -5 means adding -5 to itself five times. This is believed to give +25 because multiplying a minus by a minus provides a plus. However, current mathematics does not explain how this becomes a plus.

In science, multiplying a minus by a minus to get a plus does not match the dictionary definitions either.

Because when -5 is added five times, like -5 + (-5) + (-5) + (-5) + (-5), it equals -25. But it is considered +25. Since we cannot find the answer straight through calculation, some Western mathematicians have tried to explain this spiritually.

They say that when multiplying negative numbers, there are different directional changes compared to multiplying positive numbers. This repeated addition process leads to a positive result instead of a negative one. However, it is not stated in the definition.

If that’s the case, the concept of directional changes when multiplying -5 by -5 does not match the definition of multiplication. If -5 is multiplied by +5, it represents a directional change. How is a directional change possible when multiplying -3 by -5, as they are different numbers?

If the definition doesn’t match everywhere in mathematics, then it cannot be considered the correct definition. This means we are not even learning the proper definition of multiplication in schools today. This is not just one country's situation; it's the condition of schools worldwide.

Since Sanskrit gave concepts like zero, infinity, and multiplication to mathematics, let’s now try to understand the concept of multiplication in Sanskrit.

Brahmagupta’s text "Brahmasphutasiddhanta" mentions a rule about zero and multiplication.

"?????? ??????? ????? ????? ???????? ???????"

This translates to: "Multiplying zero by zero or any other number always results in zero." This verse explains the basic rule of multiplication related to zero, which became an important concept in mathematics.

In the Mandukya Upanishad, Mandukya Karika, verses 3.46 and 3.47 state:

"??? ? ????? ?????? ? ? ??????????? ?????

?????????????? ????????? ?????? ??????? ???"

"??????? ?????? ?????????????? ????????????

?????? ??????? ???????? ?????????? ???"

Verse 46 says that when the mind is not distracted by worldly activities and does not wander away from desires, it becomes peaceful. It experiences no visible form. At that moment, the mind merges with Brahman.

According to verse 47, the mind that merges with Brahman is considered to have attained the highest joy from realising the self. This is called liberation. Its form cannot be described and is unborn.

This is called the all-knowing Brahman because it exists in nothingness and merges with the soul. It is something that is sought and attained through knowledge.

Verse 46 says that when the mind is disciplined, it neither falls into a deep sleep where everything is forgotten nor gets distracted by external objects. This means the mind is calm.

When placed in a windless area, the flame of a lamp reflects on an object and forms an image in our retina, allowing us to see the object. But if the object is black and does not reflect light, we cannot see it. Similarly, when our mind is calm, it cannot be disturbed by external activities and desires awakened through the senses.

At that moment, the mind merges with Brahman.

Verse 46 explains that merging the mind with Brahman is the highest reality of joy, which can only be experienced and recognized through self-knowledge. It is a state of complete peace, where all sufferings end. This is liberation. It cannot be described in words. Since it is entirely different from all things, it can only be experienced. Because it is attained through experiential knowledge, it is called unborn.

Concepts like zero ????? and void (?ūnyāti?ūnya ?????????????) have been used in Shaiva texts to explain this state.

In "Vijnana Bhairava Tantra," the characteristics of the ultimate reality of voidness are mentioned.

Lord Shiva's form as Bhairava, representing the ultimate void, is beyond the senses and the mind. It remains unaffected by the tools of the senses. It is depicted in "Vijnana Bhairava Tantra ?????????????????" as the state of voidness (zero) from the mind's perspective and the state of fullness (infinity) from the perspective of reality.

In Vedic spiritual and metaphysical traditions, ?ūnyāti?ūnya is a philosophical concept formed by combining two words. "?ūnya" means emptiness or void. "Ati?ūnya" means beyond the void or supreme void, which can be understood as the realization of infinity. Combining these gives "?ūnyāti?ūnya," meaning "the state beyond emptiness" or "supreme void."

This concept points to a transcendental state beyond ordinary emptiness or void, where even the concept of voidness dissolves. Not just existence and non-existence, but all distinctions related to void and fullness become meaningless. Duality ends ??????.

The "Brahmasphutasiddhanta," written around 628 CE by Brahmagupta, contains verses related to algebra in its 18th chapter. It says:

"????? ?? ???? ????? ?? ????? ?? ??? ?? ?????

?? ??? ?? ???? ????? ?? ???????? ??? ?? ???????"

"Samai? kha?" means that adding a positive number to zero keeps the number unchanged (for example, a + 0 = a).

"Sama kha? kha? eka?" means adding zero to zero always results in zero (0 + 0 = 0).

Brahmagupta established that adding zero to any number leaves the number unchanged. Adding zero to zero always results in zero.

The 18th chapter of "Brahmasphutasiddhanta" also states:

?????? ??????? ?????? ?????? – Adding zero to zero equals zero.

?????? ??????? ?????? ?????? – Multiplying zero by zero equals zero.

?????? ??????? ??????? ?????? – Separating zero from zero always leaves zero.

?????? ??????? ?????? ?????? – Subtracting zero from zero equals zero.

In "Brahmasphutasiddhanta," it is written:

?????????????????? ????????????? ??????? ???

???????? ? ??????????????? ???????? ???????

This means:

?????????? – Adding positive to positive equals positive.

??????? – Adding negative to negative equals negative.

????????????? – Adding positive to negative equals the difference between the two.

??????? ??? – When positive and negative are equal, it results in zero.

???????? ? – Adding positive to positive gives positive.

?????????????? – Adding negative to negative gives negative.

???????? ??????? – Adding zero to zero gives zero.

This means that the sum of two equal but opposite things, positive and negative, is zero. When your positive and negative are equal, zero is present.

In mathematics, zero satisfies Maharishi Kanada's Vaisheshika Sutras (Newton’s third law), which states that for every action, there is an equal and opposite reaction. For each positive number, process, or elemental particle, there must be a negative counterpart to balance the system.

Thus, the meaning of zero is perfect balance rather than nothingness or void.

This means zero is not something nonexistent. It is the state of balance between positive and negative, action and reaction. In health, it is the state of balance between Kapha, Pitta, and Vata. In mathematics, it is the state of coexistence between every positive and negative number.

This includes (+0 and -0), (+X and -X), (+Y and -Y), (+∞ and -∞).

When you talk about plus and minus, you must add your number to zero each time to multiply.

When you multiply +5 by +5, you multiply (0+5) and (0+5). You end up with two +5s. The multiplication of 5 and 5, according to the multiplication rules, gives 25.

However, when you enter the area of multiplying negative numbers, you cannot follow the definition of Western multiplication because the definition does not specify what to do when both numbers are negative.

Because even though it is not mentioned in the definition, the new claim by Western mathematicians is that minus means direction change.

While subtracting -5 from -5, due to the directional change, the first subtraction results in zero, the second in -5, and so on.

After five cycles, it becomes -5.

However, Western mathematicians argue that it should result in 25 because, practically, 25 is the answer. They say, "Minus times minus equals plus."

But how? They don’t have an answer.

The answer lies with the Sanskrit scholars who initially identified this multiplication.

According to the mathematical principle above, you had no problem with +5. It seemed that the Western definition of multiplication applied there.

The real challenge comes when you multiply -5 from -5.

According to Sanskrit scholars, subtracting or adding means completing that number by adding it to zero.

As per the definition, adding +5 to zero gives +5. There is no problem with multiplication there.

When subtracting negative from zero or negativity from nothingness, it’s essential to understand the philosophical or conceptual side of the definition.

In the case of 5, zero comprises +5 and -5.

When you subtract -5 from zero, it means removing -5 from both +5 and -5.

That leaves +5 behind.

So when you do 0 - (-5), it results in +5.

Therefore, when you multiply -5 by -5, the result is like multiplying +5 by +5, which gives +25.

In this way, Sanskrit's definition of multiplication applies to both positive and negative numbers.

This indicates that When Western mathematicians took the concept of zero and multiplication from Sanskrit, in their haste to make it their own, they couldn’t understand its core elements. Let alone other matters; their definition couldn’t handle the results even in basic calculations. They couldn’t confirm the practical results either. They also failed to incorporate those results into a coherent definition.

There needed to be more skill in presenting the hidden aspects in a way the world could believe.

The ability to present the hidden aspects to the world convincingly needed to be improved. The clear answer lies in Sanskrit.

The world must take this concept and teach students the correct mathematical principles by fixing their shortcomings. This shows how much pride we can take in our tradition and history.