"Metior"

Adrien mumbled, causing the tip of his wand to glimmer with light blue light. The next moment, he felt magical energy coursing through his body, after which a mist of blue light erupted from the tip of his wand and coalesced into the number '36,386' in front of him.

'Excellent....works perfectly. Never expected the Patronus charm to be so helpful. This saves me a lot of time. I'll be able to commence my investigations into the applications of Arithmancy to combative magic earlier than expected.'

He grinned triumphantly, looking at the now-fading number in front of him with a thrilled expression. 

The spell he had just cast was the last spell that needed testing in the Metric Series, a series of magic spells designed to quantify everything about magical energy in association with wizards.

From how much of it was present in spells to a wizard's magical energy capacity, The Metric Series could precisely measure it all.

'Should catalog these results...'

"Accio Diary."

He twirled his wand and muttered, and, the next moment, a pitch-black diary - from seemingly nowhere- flew gracefully into his hands.

He softly stroked the dairy's spine and pointed his wand at its cover. 

"Aparecium"

He muttered, instantaneously causing the diary's color to turn brown and revealing a string of texts on its surface.

'The Magic Series Codex'

The crux of all of Adrien's theories on how Mathematics could be applied to Arithmancy relied on two things: the ability to accurately understand how exactly numbers could affect magical energy, and, a complete understanding of the way wizards interacted with the mystical energy.

Without fully comprehending these two things, his theories would be rendered void, no different from gibberish spouted by a toddler, and Adrien understood this very well.

For no underlying reason, he decided to investigate the relationship between numbers and magical energy first, and what he found blew his mind. 

Every numeral - i.e., numbers 0-9 - invoked the activity of magical energy particles in subtle and specific ways.

Initially, he commenced his investigation into the matter using the number '7'. In the canon, and even in this world, it was widely recognized as the most magical number, so he mused that observing it would be the easiest.

Thus, he wrote the number '7' repeatedly on parchment and visualized any magical energy fluctuations around the number using his Truth Eyes. 

He observed that the number '7' caused the magical energy particles around it to become restless and move about in zig-zag patterns. 

The discovery shocked him to his core, and he couldn't help but remember some of the words Pythagoras, the Greek Philosopher and Mathematician, left in his scripts back on Earth.

'Number rules the universe.'

'Number is within all things.'

'Number is the ruler of forms and ideas, and the cause of gods and demons.'

When he first came across these texts back on Earth, he had scoffed at them and written them off as pure gibberish. Pythagoras had implied that numbers had spiritual properties, and Adrien, being the pragmatic modern man he was, sneered at the seemingly ludicrous notion.

All his life, he was taught that Mathematics was merely a tool for understanding the world around him. Just that, nothing more. It was designed to rely on pure logic and realism and, thus, could not have any mystical connotations.

Seeing that numbers could be more than that with his own two eyes shook Adrien. 

Clearly, numbers were more than just inputs to equations; they hummed with the music of the universe.

The magical properties of numbers were innate, and Adrien wondered whether it was the same back on Earth or just due to the laws of J.K. Rowling's Harry Potter Universe.

Nonetheless, he was elated at the discovery. He also inwardly thanked his stars for being born with the Truth Eyes; without them, precisely observing the magical properties of numbers would be near impossible.

He didn't stop at just writing the number '7' on parchment; he even went as far as saying it out loud and writing it on different surfaces, air included. He needed to understand every way in which the number affected magical particles.

He found that every way he represented the number '7', whether saying it aloud or writing it, caused magical energy particles to behave in the same zig-zag pattern he observed earlier. 

After recording the discovery in The Magic Series Codex, he proceeded to investigate the magical properties of the other numerals. 

Some of them required him to zoom into the air very closely to observe the magical energy fluctuations they caused - they were too subtle and minute to observe normally.

Like that, he recorded the magical properties of every numeral in The Magic Series Codex in detail. However, one number was extraordinary...way more than Adrien had anticipated. 

It was the number 0.

At first, when he tried to observe its magical properties, he couldn't detect anything, even after zooming in. He became confused seeing that. Did 0 not have any magical properties?

Adrien, being the astute scientist he was, refused to conclude such without researching extensively. Thus, he persisted in investigating the number, and luckily for him, this would prove to be fruitful.

He made the groundbreaking discovery when he tried writing the number in the air while Aella was flying around his study.

Magical energy particles are permutable, meaning they can change forms depending on the circumstance, which can be seen when casting spells.

Their natural form, which is to say the form in which they exist in nature, is what Adrien calls the neutral state.

For example, when the spell 'Bombarda' is cast, magical energy particles transmute into particles imbued with the fire elemental attribute. When the spell 'Lumos' is cast, they transmute into particles imbued with the light elemental attribute.

When Aella flies, she creates lightning sparks, which simply arise due to the transmutation of neutral magical energy particles into lightning-attributed ones.

When Adrien wrote the number 0 in the air while Aella flew past him, he observed the lightning sparks around her reduce significantly.

The discovery nearly caused him to fall over in disbelief. He tried it multiple times and observed the same phenomenon occur. 

Doing that, and observing the phenomenon with his Truth Eyes, led him to one conclusion.

The number 0 reverts all magical energy particles to their neutral or' origin' state. 

The revelation was mind-boggling. Adrien couldn't believe that the number had such a powerful property. He was astounded that it had remained undiscovered. Its applications were simply limitless. 

In fact, it was even the basis of his investigations into the combative use of Arithmancy.

After analyzing the individual magical properties of numbers, Adrien investigated their collective properties - as in combined, for numbers like 11, 25, etc.

He found that when identical numbers were combined, -for example, numbers 11, 22, 33, and so on- their individual effects were amplified.  

For different numbers combined, their individual effects merely blended together.

He fought the urge to observe the magical properties of the number '666' out of fear of dying out of the blue.

In Christian theology, the number had sinister connotations and was widely known to be related to the devil. Adrien had no way of knowing what sort of magical effect the number had and didn't want to take any chances on something that could potentially endanger his life, so he brushed it off.

After all, the HP universe and Earth's universe were strikingly similar. It was plausible to think that the same connotations applied on Earth could be used in this world. 

He wasn't trying to die young; he had already done that.

Once he understood how numbers affected magical energy, he began his inquiry into the way wizards interacted with magical energy. Similar to his discoveries with numbers, what he found was eye-opening.

J.K. Rowling never went into detail on the mechanism by which wizards cast spells. In the books, it was simply stated that magic was done either through wands or wandlessly.

Adrien wanted to understand this mechanism in greater detail. He already knew that wizards did not store magical energy and only channeled it through their bodies whenever they used spells. 

However, he wondered how exactly it was channeled. Where did the magical energy particles go upon absorption into the human body?

He started his investigation by confirming what was already known. Using his skin cells as a sample and his advanced microscopes, he identified the biological determinant of wizardkind - the magic gene.

DNA analysis revealed that the gene had its locus on chromosome 15 of the human genome, and that the gene was covered in golden scribbles - something that Adrien speculated to be some universal runic language. 

Because he could not decode the runes, he could not sequence the magic gene and determine all the parts of the human body the gene affected.  

Additionally, there was no book about wizardkind anatomy, so he couldn't find what he was looking for.

Thus, he changed his approach and decided to experiment on the human body directly. There was a problem, though. Where was he going to get a wizard's body to experiment on?

He couldn't leave the vicinity of his home, so his options were limited. After much delibration, he decided to take drastic measures and experimented on fresh corpses of wizards in the cemetery in Godric's Hollow.

It was an odious decision, but he was willing to take it. He didn't have the luxury of being nitpicky, and he didn't have time to waste...certainly not enough time to be concerned about the ethics of his actions.

So, under the guise of going to play outside, he left the Dumbledore Family home - briefcase in tow - and absconded to the cemetery in Godric's Hollow, where he dug up the corpses of wizards who had recently died for experimentation.

To ensure he couldn't be seen, he made sure to go when it was getting dark and casted a Muggle-repelling charm, and Fidelius charm around his excavation sites. His Fidelius charm was shoddy at best, though it still sufficed.

Fortunately for him, there were quite a few to pick from, though he chose the bodies of wizards who did not belong to prominent wizarding houses just to be safe.

He dissected the bodies inside the lab in his briefcase. It was a hellish experience - mostly due to the noxious smell the bodies emitted- but he persevered. Unexpectedly, his biology lessons in high school and college proved to be useful. 

It was a stretch to call his operation a dissection since he thoroughly disfigured the bodies, though he called it one nonetheless. 

From their bodies, he discovered that every wizard possessed magical energy channels of varying width underneath their blood vessels - something that wasn't present in muggles. 

At first, he hypothesized that the width of the channels was related to the talent of a wizard. However, this hypothesis got debunked once he noticed a peculiar pattern.

He noticed that older wizards had wider magical energy channels than younger wizards. It made him wonder, was the channel width correlated with how powerful a wizard was instead?

It was a reasonable line of thought mainly because, on average, the older the wizard, the more powerful they were expected to be - due to using magic longer than younger ones.

He decided to test his new hypothesis by forcefully channeling magical energy particles through the channels of a younger wizard to see whether the channel's width increased.

Because he was experimenting on a corpse, he speculated that he would observe no increase in channel width, but, despite that, the channel width increased slightly after about 4 months of continuous forceful channeling.

To solidify his now-confirmed hypothesis, he tried to forcefully channel magical energy through the channels of all the corpses he dissected and see whether they experienced an increase in width. 

Surely enough, they did after continuous forceful channeling, with some taking significantly longer than others.

With that experiment, Adrien was able to conclude the following,

1. All wizards possess a magic gene that alters their anatomy in multiple ways, one of which being the creation of vessel-like conduits called magical energy channels.

2. When a wizard casts a spell, he/she effectively absorbs magical energy particles from their surroundings and directs them through these channels.

3. The channels dictate how much magical energy a wizard can conduct at any given time.

4. The more magical energy a wizard can conduct, the greater his magical capacity and power.

 

These two major discoveries served as the first piece Adrien would need for his eventual creation of The Metric Series...