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The Mathematical Proof: Logical Reasoning & The Language of Mathematics

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The Mathematical Proof: Logical Reasoning & The Language of Mathematics

4.85 93,241 ratings · 7,830 reviews
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Overview: The mathematical proof is one of the best tools that science has to produce facts and truths on which we base our civilization. The road to current day mathematics started in South Africa, over 70,000 years ago, when someone scratched geometric patterns into rocks. It took another 40,000 years until prehistoric humans tried to quantify time. Another 10,000 years passed until archaeology produced the remnants of some of the first attempts to 'play' with numbers. This is where the timeline of mathematics starts to accelerate in its representation of accomplishments. Around 3,400 BC, the Sumerians are credited with the first form of number system. As the field of mathematics evolved it became clear that this 'language' transcended culture, geography, mythology and even religious beliefs. Algebra originated in the Mideast as did the mathematician Muhammad Al-Karaji whose work brought algebra into the next stage. He introduced the 'Theory of Algebraic Calculus. It was by using this method that arguably the first 'proof by mathematical induction' was performed in the 10th century. This began a whole new era for math, logic, philosophy, reasoning, debate and physics. A 'Golden Age of Math' so to speak had begun. This book summarizes most of the formalities of mathematics that have been produced from this era. - Paul F. Kisak

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Published December 8, 2014
ISBN 26546930
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Paul F. Kisak
About the Author
Paul F. Kisak
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Paul F. Kisak is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Paul F. Kisak can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Jennifer Hall
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Kevin White
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Christopher Garcia
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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Charles Parker November 02, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Steven Harris
Steven Harris July 21, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Lisa Diaz
Lisa Diaz March 27, 2024
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Betty Hernandez
Betty Hernandez September 27, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Dorothy Miller
Dorothy Miller November 11, 2024
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Laura Rivera
Laura Rivera May 23, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Margaret Green
Margaret Green January 31, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Eric Ramirez
Eric Ramirez October 15, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Jacob Gonzalez
Jacob Gonzalez January 31, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Lisa White
Lisa White November 16, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Donna Hill
Donna Hill July 05, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Stephanie Hall
Stephanie Hall April 12, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Christopher Garcia
Christopher Garcia December 31, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Carol Smith
Carol Smith April 19, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Joseph Hernandez
Joseph Hernandez July 04, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Joseph Jones
Joseph Jones September 29, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Lisa Mitchell
Lisa Mitchell December 21, 2025
Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
Sarah Green
Sarah Green October 21, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Lisa Thomas
Lisa Thomas November 21, 2025
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
Jennifer Nelson
Jennifer Nelson March 24, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Ashley Campbell
Ashley Campbell July 07, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Stephanie Robinson
Stephanie Robinson August 19, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Richard King
Richard King April 05, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Donald Harris
Donald Harris January 09, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Mark White
Mark White November 14, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Jacob Williams
Jacob Williams February 21, 2025
Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
Richard Campbell
Richard Campbell June 20, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Robert Adams
Robert Adams March 31, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Donna Campbell
Donna Campbell November 13, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Michael Thompson
Michael Thompson September 06, 2024
I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
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