The Language of The Mathematical Proof: "The Logical Reasoning of Mathematics"

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The Language of The Mathematical Proof: "The Logical Reasoning of Mathematics"

Written by Paul F. Kisak
4.85 55,316 ratings
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About this ebook:
In South Africa, over 70,000 years ago, someone scratched geometric patterns into rocks. It took another 40,000 years until prehistoric humans tried to quantify time. Another 10,000 years pass until archaeology produces the remnants of some of the first attempts to 'play' with numbers. This is where the timeline of mathematics starts to accelerate in it 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 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.

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Published August 26, 2015
ISBN 26589618
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Paul F. Kisak
About the Author
Paul F. Kisak

After spending years working in the corporate world, Paul F. Kisak finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Sandra Nelson
Sandra Nelson October 25, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Jessica Lopez
Jessica Lopez August 24, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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James Jones October 10, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Kimberly Clark
Kimberly Clark March 17, 2024
I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
William Gonzalez
William Gonzalez December 24, 2025
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.
Mark Jones
Mark Jones December 04, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Stephanie Cruz
Stephanie Cruz June 13, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Donna Turner
Donna Turner December 24, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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Brian Green August 04, 2024
A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
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Christopher Nelson October 02, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Eric Smith
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A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Such a rich narrative. 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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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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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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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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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.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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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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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Such a rich narrative. 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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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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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.
William Gonzalez
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Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Rebecca Nelson
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Eric Garcia
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Brian Gomez
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
George Lee
George Lee January 10, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Thomas Brown
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Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Charles Torres
Charles Torres February 11, 2025
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
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James Scott January 27, 2024
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Emily Taylor
Emily Taylor February 03, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Barbara Baker
Barbara Baker July 14, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Robert Wilson
Robert Wilson June 12, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Karen Wright
Karen Wright January 29, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Amanda Carter
Amanda Carter February 25, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Nicholas Evans
Nicholas Evans August 15, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
George Lee
George Lee September 05, 2024
It was adequate. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
David Collins
David Collins May 24, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Kenneth Mitchell
Kenneth Mitchell July 14, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Thomas Allen
Thomas Allen November 08, 2024
I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
Sandra Brown
Sandra Brown September 05, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Charles Martin
Charles Martin October 26, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Margaret Evans
Margaret Evans December 16, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Kimberly Clark
Kimberly Clark July 14, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Thomas Rivera
Thomas Rivera March 25, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Kenneth Scott
Kenneth Scott December 20, 2024
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.
Barbara Mitchell
Barbara Mitchell July 14, 2025
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Carol Lopez
Carol Lopez March 05, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Mark Jackson
Mark Jackson July 08, 2024
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
Daniel Johnson
Daniel Johnson April 09, 2024
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Matthew Walker
Matthew Walker November 26, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Christopher Lee
Christopher Lee April 01, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Mary Miller
Mary Miller April 11, 2025
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
Richard Allen
Richard Allen May 26, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Deborah Carter
Deborah Carter July 11, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Michael Martin
Michael Martin October 05, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Deborah Martin
Deborah Martin July 23, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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