The scholars whispered among themselves, their eyes flickering between Elara and me.

  "A spell without an incantation? Without a medium?" one of them muttered.

  "Preposterous," another scoffed.

  But I had already expected this reaction.

  After all, in this world, magic was thought to be inseparable from ritual.

  A mage needed incantations, gestures, runes, or artifacts to channel their will into reality. That was the absolute law of magic here.

  But I knew better.

  Because I had created this world.

  And I knew the one thing no one else did—magic wasn’t bound by tradition.

  It was bound by logic.

  Elara and I stepped onto the spell-testing platform. The stone beneath our feet pulsed with faint blue light, activating the mana-detection runes.

  "This platform will measure all magical output," one of the scholars explained. "If you attempt deception, we will know."

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  I smirked.

  "We wouldn’t dream of it."

  A different scholar adjusted his spectacles. "You claim to be able to cast a spell without a medium. Very well—show us a practical application."

  I turned to Elara. "Ready?"

  She nodded.

  We had already planned this out.

  Our goal wasn’t just to prove that magic could be cast without traditional methods—we had to demonstrate complete control.

  That meant not just summoning energy, but shaping it freely.

  The Spell Begins

  I closed my eyes.

  I wasn’t just trying to cast a spell—I was solving an equation.

  Mana wasn’t some mystical force. It followed laws—just unknown ones.

  And right now, I was about to prove those laws existed.

  I took a deep breath, mentally visualizing the spell not as words or gestures—but as a function.

  M(x) = ∫ f(x) dx

  Where:

  M(x) represented mana flow over time.

  f(x) represented spell intensity as a variable function.

  a to b defined the controlled boundaries of the energy.

  The problem with magic in this world was that mages couldn’t predict energy fluctuations. They relied on instinct, leading to unstable casting.

  But I had a formula.

  And formulas always worked.

  I opened my eyes.

  Mana gathered around me—not wild and chaotic like a normal spell, but precise, flowing in a controlled pattern.

  A soft golden light shimmered at my fingertips.

  Gasps erupted from the scholars.

  "Impossible," one of them whispered.

  I kept going.

  By tweaking the integral function’s upper and lower bounds, I adjusted the mana’s output—compressing it into a single, stable shape.

  A perfectly formed sphere of light.

  No words. No gestures. No catalysts.

  Just pure mathematical control.

  Elara stepped forward. She had spent the last few days studying my equations, and now she followed the same principles.

  She raised her hand, shaping a thin blade of wind—not with an incantation, but by altering the mana flow density using derived formulas.

  A scholar stood up.

  "This… this breaks every known magical law!"

  I turned to him, still holding my controlled sphere of mana.

  "No," I corrected. "It proves magic always had laws—you just never discovered them."

  Silence.

  Then, a slow clap echoed through the chamber.

  The lead scholar, the one who had been the most skeptical, now wore a stunned expression.

  "You two… have just rewritten history."

  We passed the test.

  Not because of talent.

  But because we had the knowledge that no one else did.

  And with that knowledge, we now had access to the Royal Archives.

  Where the Forbidden Grimoire awaited.

  Idk why but equation was not showing properly. So here is proper version of Mana Flow Equation:

  M(x) = ∫ f(x) dx

  M(x) represents the total mana flow over time.

  f(x) is the intensity of the spell as a variable function.

  the stronger the function f(x), the greater the total mana output.