I Created Scientific Magic

Chapter 77: Chapter 69: How Many Math Olympiad Problems Did You Do to Achieve Today’s Success (Please Follow)

Lynn’s brief two sentences struck Ailoke from heaven down to hell, sending a shiver through all the apprentices present,

“Advanced Mathematics is an extremely precise course. We need to sift through a plethora of complex data operations to discern patterns, then summarize them into corresponding formulas, thereby simplifying the algorithms and enhancing the overall computational efficiency.” Lynn surveyed everyone in the classroom, paused for a moment, and then spoke again.

“The patterns Ailoke summarized aren’t wrong, but their applicability is too limited. If the exponential increase within a square can be dual, it can equally be triple, fivefold, tenfold! With this, the pattern becomes inapplicable…”

“And this exponential summation formula is applicable to all exponential increases that meet the conditions!” Lynn snapped his fingers, and under a surge of magic power, the complex formula reappeared before everyone.

When q≠1, Sn=a1(1-q^n)/(1-q)

Johnny, Pearce, and others stared at the so-called exponential summation formula, pondering deeply. Soon, they picked up their quill pens and began to calculate, listing the sequences for double, triple, quadruple multipliers to discern patterns, then trying to substitute them into the formula.

With Ailoke’s previous summary and deduction through q≠1, Pearce quickly realized that this symbol likely represented the magnitude of the multiplier. But why subtract one?

Pearce bit his thumb, inserting the initial dual growth square game and ignoring the later part (1-q), directly performing the calculations to find it works perfectly, albeit the result was the exact opposite—a negative number.

Meaning, the purpose of the latter part of the formula is to turn a negative number into a positive number?

However, if switched to triple exponential growth, the amounts were completely incorrect…

Pearce’s brain spun rapidly, almost grasping that answer, just a bit more, just a bit!

But what could it be?

In the classroom, many others like Pearce were deeply engrossed in their work, either tugging at their hair or scratching their heads, but no one chose to slack or give up.

Was the atmosphere at Yiyeta Magic Academy always so intense?

Lynn was somewhat puzzled; these people really loved learning…

As the class session neared its end, just as Lynn believed no further progress would be made today, a hand shot up.

“Professor Lynn, I have some ideas!”

The speaker was Johnny, who, after being acknowledged, stood up and said, “In the summation formula, a1 should refer to the quantity placed in the first square, q to the multiplier, and n corresponds to the number of squares, right, Professor?”

“Roughly correct. After class, you may go to the academy’s entrance to claim your reward!” Lynn nodded in response; Johnny’s explanation was quite vague, but it was indeed precise.

Pearce couldn’t help but beat his chest in frustration. With Johnny’s hint, he quickly understood as well. Why was he just a bit short? He was about to solve it!

After gesturing for Johnny to sit, Lynn then began to explain to all the apprentices present what a geometric sequence was, along with its general term and summation formulas, continuing until he described how each formula was derived.

The Wizard Apprentices below took their quill pens very seriously, recording every word Lynn said on paper, then attempting to vary the initial term and the multiplier to perform repeated validations. The desktops quickly filled with various drafts…

It must be said, with the general term and summation formulas at hand, the speed of computation was not just times faster, and the more complex the equations, the faster the improvement.

Seeing these students solving problems with such zeal, Lynn could not help but exclaim, how easy his role as a professor was!

If schools in the Federation all shared this scene, why worry about technological and academic decline?

…

The second session of Advanced Mathematics soon ended, and Ailoke and others, still eager, left the classroom, endlessly discussing the derivations of the summation formula…

“Johnny, from last night till now, how much has your control over magic power increased?” A dark-haired Wizard Apprentice hastened up, patting Johnny on the shoulder and asking curiously.

“About ten percent?” the silver-haired girl pondered for a moment before replying casually. Nôv(el)B\\jnn

“That’s just a bit more than mine.” The dark-haired Wizard Apprentice pouted but showed no envy.

Rumor had it that Ailoke had been calculating all night without sleep, and the next day, he found that his control over the magic had increased by about twenty percent, which was the news that had ignited the entire Yiyeta Magic Academy.

So this morning, every Wizard Apprentice who was not in class had come, eager to witness the so-called magical power of this Advanced Mathematics class, and she was no exception.

The conclusion was very clear; the complex, intricate computations of Advanced Mathematics effectively exercised their mental faculties. This process of logical deduction and cracking numerical patterns was equally fascinating, certainly more interesting than the monotonous meditation.

Johnny paid no heed to the dark-haired Wizard’s words, glancing back towards the classroom, silently contemplating how many Advanced Mathematics problems Lynn had solved within the Secret Magic Society over the past six months to achieve his current accomplishments…

…

“Doing math problems can actually enhance a wizard’s control over magic power?”

Lynn, of course, heard every word of the pupils’ discussion clearly and felt somewhat surprised.

But upon reflection, it seemed quite natural. The reason his strength had increased significantly through the psychic linkage with the AI was because the overload mode greatly enhanced his computing power, or rather, spiritual power.

This was incredibly important for wizards, as the extent of their control over magic power closely depended on the strength of the wizard’s own spiritual power. Lynn felt somewhat helpless that this was precisely his blind spot.

At least, the process of forming a magic spell was somewhat similar to repeatedly practicing a movement to form muscle memory.

For instance, picking up a drinking glass from the table to take a sip, if performed by an artificial intelligence, would require determining the distance, calculating the correct angle and force to pick up the glass, and then analyzing the most natural arc to bring the glass to the lips.

Such a complex process can be instantly executed under subconscious control without the slightest obstruction. The same was true for a magic spell; with long-term practice, a complex spell could be released with just a thought.

There was just one caveat; the wizard’s spiritual power had to be strong, able to provide sufficient computing power, otherwise the casting process would be prolonged, exposing vulnerabilities.

Considering this, Lynn stroked his chin, pondering whether to set himself some advanced math problems to solve…

It might really be useful, mightn’t it?