Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who...

literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement of...

the OEIS). Many proofs of Cayley's tree formula are known. One classical proof of the formula uses Kirchhoff's matrix tree theorem, a formula for the...

paper proofs or electronically marked on electronic proofs by the author, editor, and proofreaders. The compositor, typesetter, or printer receives the edited...

Proofs from THE BOOK, Springer-Verlag, pp. 141–146, ISBN 3-540-40460-0. Benjamin, Arthur T.; Quinn, Jennifer J. (2003), Proofs that Really Count: The...

I'm always saying that the SF has this transfinite Book that contains the best proofs of all mathematical theorems, proofs that are elegant and perfect...

which God maintains the most elegant proofs of mathematical theorems and which inspired Proofs from THE BOOK The Book (short story), an unfinished, fragmentary...

Martin; Ziegler, Günter M. (2018). "Chapter 15: The Borromean Rings Don't Exist". Proofs from THE BOOK (6th ed.). Springer. pp. 99–106. doi:10.1007/978-3-662-57265-8_15...

not suffer from the same problems of concurrent execution. Another variant of zero-knowledge proofs are non-interactive zero-knowledge proofs. Blum, Feldman...

mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction...

ironically by speaking of "The Book", a supposed divine collection of the most beautiful proofs. The 1998 book Proofs from THE BOOK, inspired by Erdős, is...

prove a result, as the first proof that is found can often be improved. The theorem for which the greatest number of different proofs have been discovered...

(1998), Proofs from THE BOOK, Springer-Verlag. Double counting is described as a general principle on page 126; Pitman's double counting proof of Cayley's...

interval [0, π/2], see Proofs of trigonometric identities). For non-geometrical proofs using only tools of calculus, one may use directly the differential equations...

Reverse Mathematics: Proofs from the Inside Out is a book by John Stillwell on reverse mathematics, the process of examining proofs in mathematics to determine...

produced two other proofs in 1816 and another incomplete version of his original proof in 1849. The first textbook containing a proof of the theorem was Cauchy's...

(2018). "Three applications of Euler's formula: Pick's theorem". Proofs from THE BOOK (6th ed.). Springer. pp. 93–94. doi:10.1007/978-3-662-57265-8....

Birkhäuser. pp. 129–133. Aigner, Martin; Ziegler, Günter M. (1998). Proofs from THE BOOK (4th ed.). Berlin, New York: Springer-Verlag. pp. 27–36. doi:10...

ISBN 3-540-90376-3; ) (with Günter M. Ziegler) Proofs from THE BOOK Aigner, Martin (2001). Proofs from the book. Günter M. Ziegler (2nd ed.). Berlin: Springer...

the number of simplices is a multiple of n!. Aigner, Martin; Ziegler, Günter M. (2010). "One square and an odd number of triangles". Proofs from The Book...

Bunder & Tognetti (2010). Aigner, Martin; Ziegler, Günter M. (2004), Proofs from THE BOOK (3rd ed.), Berlin; New York: Springer, pp. 94–97, ISBN 978-3-540-40460-6...

Martin; Ziegler, Günter M. (2018), "Chapter 15: The Borromean Rings Don't Exist", Proofs from THE BOOK (6th ed.), Springer, pp. 99–106, doi:10.1007/978-3-662-57265-8_15...

Divine move (game of Go) Proofs from THE BOOK Rubik's Cube group Solved game Paul Anthony Jones, Jedburgh Justice and Kentish Fire: The Origins of English in...

S2CID 3319306. Further reading Aigner, Martin; Ziegler, Günter (2009), Proofs from THE BOOK (4th ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-642-00855-9...

Invalid proofs. Invalid proofs at Cut-the-knot (including literature references) Classic fallacies with some discussion More invalid proofs from AhaJokes...

MathWorld. Example 3. Martin Aigner & Gunter M. Ziegler (1998) Proofs from THE BOOK, § 3 Analysis: Sets and functions, Springer books MR1723092, fifth...

well-known results from Graph theory. Steve Fisk's proof is so short and elegant that it was chosen for inclusion in Proofs from THE BOOK. The proof goes as follows:...

Frege. While the above-mentioned correspondence says that proofs in a theory translate to sequences of short proofs in the corresponding proof system, a...

set theory. Erdős' proof is so short and elegant that it is considered to be one of the Proofs from THE BOOK. In the case that the continuum hypothesis...

Gorenstein for his book Finite Simple Groups, An Introduction to their Classification (Plenum Press, 1982); and his two survey articles The Classification...