Abstract: Revolutionary Breakthroughs in Number Theory, Complex Analysis, and the Riemann Hypothesis, shattering the Foundations of Mathematics, Breaking the Boundaries of Infinity In this revolutionary work, we demolish long-standing mathematical barriers and reconstruct the very fabric of number theory, complex analysis, and infinity itself. The old mathematical world is gone. Welcome to the new. I present an entirely original mathematical framework that overturns conventional understanding of numbers, infinity, and complex analysis. Through groundbreaking definitions and proofs, this work achieves what was previously deemed impossible: *The Birth of a Universal Absorbent Element Redefining Algebraic Structures We introduce a groundbreaking absorbent mathematical element that revolutionizes the concept of algebraic annihilation. Like zero’s dominance in multiplication This research revolutionizes the foundations of transcendental functions by defining a provable, consistent solution to the previously undefined expression log(0), hence : log(0)= 2 - ∏2 /6 ≈ 0,356733333 *The Collapse of Infinite Products – Demonstrating that any non-unit complex number (S ≠ ±1), when multiplied by itself infinitely, converges to zero: S×S×S×⋯=0(e.g., π×π×⋯=0, 8×8×⋯=0).S×S×S×⋯=0(e.g., π×π×⋯=0, 8×8×⋯=0). *All Infinite Sums Lead to the Same Door – No matter the number (8, π, √2…), adding it infinitely converges to a universal constant log(0) : S+S+S+S+……..= log(0) , 8+8+8+8+8+ ….= log(0) , √2+√2+√2+…..= log(0) , π+ π+ π+…..= log(0) *Redefining the Impossible – A Rigorous Framework for Z(1) This research overturns centuries of mathematical consensus by proving that the Riemann zeta function at s=1s=1—previously considered divergent—converges to an exact finite value: Z(1) = ∏2 /6 + 1/12 *The Negative Prime Product Paradox – A Groundbreaking Reformulation of Infinite Prime Products We resolve one of the most counterintuitive problems in analytic number theory by proving the exact evaluation of the infinite product of negative primes: (-2)*(-3)*(-5)*(-7)*(-11)*(-13)*(-17)*………………….. = - 2∏2 -1 = - (2∏2 +1) *The Emptiness Paradigm : A Radical Reconstruction of the Complex Plane This work overturns 200 years of complex analysis by demonstrating the fundamental incompleteness of the Argand plane. We introduce new complex plane with emptiness space that looks like black hole