Proofs from the book is a math book that is filled with mathematical proofs. Written by Martin Aigner, this book is also a guide as well as a tribute to the mathematician, Paul Erdos. The famous mathematician would refer to “The Book” and he said that this is the one book in which God keeps all the secrets of the proofs of mathematical theorems.

## Proofs from the Book Pdf Review:

The book is divided into 32 sections and in each section, a single theorem is mentioned. The fifth edition has 44 sections. The sections are comprised of a single theorem but multiple proofs are mentioned for those theorems and the results of these proofs. There are a lot of topics mentioned in the book, including number theory, graphs, and analysis of mathematical data. The book also has illustrations which were done by Karl Hofmann. Till date, five editions have been published and the book has been translated into many languages including German, French, Persian, Chinese and Portuguese and so many others. ## Proofs from the Book Pdf Features:

• There are many proofs in the book such as the proof of why e is irrational.
• Also, proofs for how other related numbers are irrational are also mentioned.

Number Theory: 1. Six proofs of the infinity of primes.-

1. Bertrand’s postulate.-
2. Binomial coefficients are (almost) never powers.-
3. Representing numbers as sums of two squares.-
4. The law of quadratic reciprocity.-
5. Every finite division ring is a field.-
6. The spectral theorem and Hadamard’s determinant problem.-
7. Some irrational numbers.-
8. Three times π2/6.-

Geometry: 10. Hilbert’s third problem: decomposing polyhedral.-

1. Lines in the plane and decompositions of graphs.-
2. The slope problem.-
3. Three applications of Euler’s formula.- 14. Cauchy’s rigidity theorem.-
4. The Borromean rings don’t exist.-
5. Touching simplices.-
6. Every large point set has an obtuse angle.-
7. Borsuk’s conjecture.-

Analysis: 19. Sets, functions, and the continuum hypothesis.-

1. In praise of inequalities.-
2. The fundamental theorem of algebra.- 22. One square and an odd number of triangles.-
3. A theorem of Pólya on polynomials.- 24. On a lemma of Littlewood and Offord.- 25. Cotangent and the Herglotz trick.

– 26. Buffon’s needle problem.-