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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 83,901 ratings · 2,380 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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Book details & editions

ISBN
26546930
Publication date
December 8, 2014
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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About the Author
Paul F. Kisak
11,317 Followers

Paul F. Kisak writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Paul F. Kisak lives with their spouse and a very vocal rescue cat.

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Carol Wilson
Carol Wilson December 21, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Amanda Evans
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I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Christopher Collins
Christopher Collins September 10, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Stephanie Diaz November 04, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Rebecca Collins
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. 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. I am now a lifelong fan of this author.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
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Dorothy Davis December 25, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Karen Adams
Karen Adams May 31, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Donald Reyes
Donald Reyes February 02, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Melissa Miller
Melissa Miller October 22, 2024
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
Christopher Allen
Christopher Allen January 28, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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Ashley Green October 16, 2024
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
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Margaret Young March 08, 2025
A decent, if standard, experience. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Jessica Gonzalez
Jessica Gonzalez July 31, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Karen Lee
Karen Lee March 21, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Mary Carter
Mary Carter September 24, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Andrew  Parker
Andrew Parker November 13, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Michelle Lewis
Michelle Lewis May 06, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Anthony Wright
Anthony Wright December 08, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Joseph Lopez
Joseph Lopez January 14, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Jacob Miller
Jacob Miller June 18, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Carol Anderson
Carol Anderson May 24, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Paul Reyes
Paul Reyes June 30, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Jacob King
Jacob King April 10, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Robert Anderson
Robert Anderson June 19, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Nancy Miller
Nancy Miller September 08, 2024
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.
Jennifer Allen
Jennifer Allen February 26, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Edward Gonzalez
Edward Gonzalez July 21, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Donna Reyes
Donna Reyes December 13, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Mary Clark
Mary Clark April 12, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Mary Carter
Mary Carter September 21, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Joseph Jones
Joseph Jones December 08, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Emily Carter
Emily Carter October 09, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Michael Walker
Michael Walker March 21, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Susan Campbell
Susan Campbell April 22, 2024
A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
William Wright
William Wright July 20, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Sandra Wright
Sandra Wright December 29, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Dorothy Hall
Dorothy Hall November 23, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
John Moore
John Moore July 12, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Michelle Edwards
Michelle Edwards October 24, 2025
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.
Sandra Ramirez
Sandra Ramirez September 13, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Eric Johnson
Eric Johnson November 04, 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.
Donald Adams
Donald Adams April 14, 2025
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Karen Adams
Karen Adams May 29, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Joseph Smith
Joseph Smith July 16, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Jessica Wright
Jessica Wright October 06, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Andrew King
Andrew King June 29, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Jennifer Clark
Jennifer Clark December 10, 2025
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.
Barbara Jackson
Barbara Jackson June 10, 2024
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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