İmkansızın İspatı: özülemeyen Matematik Problemlerinin 2000 Yıllık Serüveni

by David S. Richeson

Matematik tarihinin en bilinen dört probleminin, ilham verici, ilginç ve sıradışı hikâyesini dinlemeye hazırlanın.

David Richeson İmkânsızın İspatı’nda, Antik Yunanlılar tarafından ortaya atılan ve iki bin yıl boyunca neredeyse tüm matematikçilerin uykularını kaçıran bu cetvel ve pergel problemlerinin ispatlarının, matematiğin zaman içindeki gelişimine bağlı olduğunu ve sanılanın aksine sadece pergel ve cetvel ile çözülmelerinin mümkün olmadığını ortaya koyarken, okurunu matematik tarihinde ufuk açıcı bir yolculuğa çıkartıyor.

İmkânsızın İspatı ile sözü edilen imkânsız problemlerin izini sürerken matematiğe dair temel ve ileri seviyede bilgiler edinecek; Öklid, Arşimet, Descartes, Newton ve Gauss gibi önemli matematikçilerin bu antik problemleri anlamak için verdiklerini emeğe ortak olacaksınız. Kendileri geometriye dayansa da çözümleri karmaşık sayılar, analitik geometri, cebir ve kalkülüs bilgisi gerektiren problemlerin; neden 19. yüzyıla değin ispatlanamadıklarını anlayacak, Pierre Wantzel ve Ferdinand von Lindermann isimli az tanınan iki matematikçinin π üzerine yaptıkları çalışmaların imkânsızın ispatını ortaya koyarak yüzlerce yıldır süren bu serüveni sonlandırışlarına tanıklık edeceksiniz.

David Richeson’ın yoğun bilgiyi anlaşılır bir dille aktardığı çalışması, matematik tarihine ilişkin derli toplu bir bakış sunmasının yanında imkânsızın ispatına değin geçen süreçte, problemleri çözdüğüne fazlasıyla emin olan matematik delilerinin, saplantılıların çılgın hikâyelerini de yer vererek son derece eğlenceli bir okuma deneyimi vadediyor.

“Richeson’ın İmkânsızın İspatı kitabını okurken büyük keyif aldım. Klasik olmayı hak ediyor ve şiddetle tavsiye ediyorum.”
Robin Wilson, Times Higher Education

“Kitabın tamamı hem bilgilendirici hem de oldukça eğlenceli. Okunması muhakkak önerilmeli.” Adhemar Bulteel, Avrupa Matematik Derneği

Genres: Mathematics, Science, History, Nonfiction, Stem

488 pages, Paperback

First published October 8, 2019

About the author

David Richeson is a professor of mathematics at Dickinson College and the editor of Math Horizons, the undergraduate magazine of the Mathematical Association of America. He received his undergraduate degree from Hamilton College and his masters and PhD from Northwestern University. He lives with his wife and two children in Carlisle, Pennsylvania.

Reviews

[Jake Hunt · Rating 5 out of 5]

This is the first math history book I’ve ever read (gift from Max). This book clarified and unified the field of mathematics in my mind so eloquently and even inspired me to buy a set of basic geometry tools (compass and straightedge).

The content is rewarding while not being too proof-heavy, and for one with limited [pure] mathematics background such as myself, I can say that I merely had to digest the material more slowly than a modern-day Euclid, Archimedes, or Gauss might. In summary, this book gives a robust history of the field of synthetic geometry, and the necessary algebra and additionals fields of math required to prove the impossibility of the following 4 problems of antiquity:

1. Squaring the Circle
2. Doubling the Cube
3. Trisecting the Angle
4. Constructing all regular n-gons

These problems are indeed impossible to perform using the classical Euclidean construction tools. In spite of this fact, they have continuously captured and inspired the minds of countless individuals in the past and I count myself lucky to count myself among them.

[John Gunerli · Rating 4 out of 5]

I'm not big brain enough to understand this

[Eric Goodill · Rating 4 out of 5]

I enjoyed the book, but I'm not much of a review writer. However, I wanted to mention that the Kindle edition's footnotes are not hyperlinked, so it's quite tedious to visit them as you encounter them while reading the main text.

[Fernando Pestana da Costa · Rating 5 out of 5]

This is a really excellent book. Its starting point are the classical geometrical problems of Antiquity: the squaring of the circle, the trisection of a general angle, the doubling of the cube, and the construction of a general n-gon (a polygon with sides) using only a compass and an unmarked straight edge. The problems are stated with precision (and the reader is alerted to the crucial importance to state problems with precision!), and then the wonderful history of the effort of countless persons, some of the major genius of humankind among them, throughout more than two millennia to solve them and, in the end, to prove them impossible! Actually, part of this fascinating story is that, in the process of trying to solve them as the ancient Greeks stated them (with compass and straight edge) a whole new set of techniques were developed, and constructions using conics other than the circle, or using marked straight edge, or origami type techniques, were proved successful for some of the problems. Other proved a really harder nut to crack, such as the construction of the general n-gon (which required the intervention of complex numbers and was only completely settled by Pierre Wantzel in 1837) and, of course, the squaring of the circle, which boiled out to the proof of the transcendence of pi, achieved in the famous 1882 paper by Ferdinand von Lindemann, who used a slight adaptation of an earlier argument by Charles Hermite. In this long, two millennia process, we see some of the great human minds struggle with problems, invent techniques, develop concepts, creating new branches of Mathematics (such as Algebra and Analysis), refining and greatly expanding others (such as Geometry and Number Theory) and ultimately achieving the point where we have a sophisticated enough machinery to settle the problem for good! This is really a wonderful book telling a tremendous story! An example that sometimes the problem is really much more important than the solution...

[Laura van Rhee · Rating 4 out of 5]

Gelezen voor research seminar. Leuk om geometrie weer eens op te halen, en om de historie te volgen van hoe ze bij calculus kwamen (functies met x enzo komt dus ook vanuit geometrie, ik leerde ze alleen ‚geisoleerd‘ in assenstelsels etc). Hij kan goed wiskunde populariseren en uitleggen voor amateurs zoals ik. Wel had hij het einde kunnen inkorten en het is geen historicus.

[Steve Gross · Rating 4 out of 5]

More than you ever wanted to know about the three/four classic problems of antiquity. Touches on many other areas of mathematics.

[Dave · Rating 3 out of 5]

Decent book, but it did not captivate me like Euler's Gem.

[Yossi Khebzou · Rating 4 out of 5]

I enjoyed this book because I think the most beautiful and exceptional area of Mathematics is proofs. However, I’m personally not very emotionally fond of Euclidean Geometry, which takes a good part of the book. Anyhow, it’s still a great read about the development of impossible problems, the history of Mathematics and the advancements that were made trying to solve these problems.

[A J · Rating 5 out of 5]

math is good