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Mathematical Milestones


Clement E. Falbo

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This is an expository book emphasizing the progress of mathematics and its uses. Concentrating on the last four centuries and acknowledging worldwide historical beginnings, I want the reader to experience number theory problems of 400 BCE right on up to Artificial Intelligence problems of today. Come with me and learn about the practical problems solved over the centuries by matrices. Marvel at the invention of non-Euclidean geometries and abstract algebras. Sense the emotions on a rollercoaster ride from Hamilton’s jubilance when he found the missing piece for his quaternions to Frege’s agony on the receipt of Russell’s letter.

I believe the beauty and the power of mathematics shines through from the stories and applications I have written about here. I rejoice in equations, because I can, and do, explain them, and because they are the most eloquent way to express ideas in mathematics. I establish, early, the fact that equations are sentences.