The Mathematical Proof: Logical Reasoning & The Language of Mathematics

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