Springer Verlag Publishes ‘Proof’ of Goldbach’s Conjecture
Posted by John Baez
The ‘big three’ science publishers — Elsevier, Springer, and Wiley–Blackwell — like to argue that their high prices pay for high quality. Recent events cast a tinge of doubt on this. We all know about the case of El Naschie, and Elsevier’s fake medical journals. Now Springer has published a book that purports to contain elementary proofs of Fermat’s Last Theorem and Goldbach’s Conjecture!
Here it is:
- Nico F. Benschop, Associative Digital Network Theory: An Associative Algebra Approach to Logic, Arithmetic and State Machines, Springer Verlag, 2009. ISBN: 978-1-4020-9828-4.
The author recently posted about his book on the newsgroup sci.math.research. Here is the post, with a comment by the newgroup’s moderator:
Please notice that my book “Associative Digital Network Theory” was just released by Springer Verlag, see:
http://www.springer.com/computer/communications/book/978-1-4020-9828-4
It is about the use of function composition (semigroup theory) as binding principle for the three main levels of functions applied in computer engineering : State-machines, Arithmetic and (Boolean) logic, corresponding to a hiërarchy of associative algebra’s : non-commutative, commutative, and idempotent,respectively : $a(b c) = (a b ) c =a b c, a b = b a , a a = a$.
In Chapter 2 the five basic state machines are derived, and the decomposition of permutation machines with a non-trivial simple group as closure is in Ch.3 (e.g. group A5 of order 60 as coupled network of cyclic groups of order 2 [twice] , 3, 5). Ch.4 discusses the general decompositon of finite semigroups / statemachines, as (possibly coupled) network of the five basic statemachine types, including the two non-commutative memory types: branch- and set/reset machines.
‘Planar Boolean Logic’ (Ch.5) is defined as practically related to symmetric Boolean functions, with a proof that all $BF_n$ of n<5 inputs are planar. Also various forms of fault tolerant logic designs are treated and compared.
Moreover, proofs of FLT and Goldbach’s Conjecture (Ch.8, 9) are given, both using a ‘residue-and-carry’ method (with proper choice of modulus), as well as a result of “Waring for residues” (Ch.10) for prime power moduli: each residue mod $p^k$ [$k>0$] is the sum of at most 4 p-th power residues.
Log-arithmetic (Ch.11) over double base 2 and 3 is discussed , using : each odd residue mod $2^k$ is a unique signed power of 3, as well as over single base 2 (a 32-bit VLSI implementation as an Euro ‘Esprit’ project).
—–
dr. Nico F. Benschop, Geldrop (NL) – Amspade Research —- nfbensc…@onsbrabantnet.nl
[mod note. Springer have clearly published this book by Benschop. Furthermore, this book claims to give elementary proofs of FLT and of Goldbach’s conjecture. Benschop has posted proofs of such things in the past—for example chapter 8 of this book appears to the moderator to be largely the same as the proof of Goldbach’s conjecture announced at
http://arxiv.org/abs/math/0103091
in 2001. As far as the moderator knows, the mathematical community has not yet accepted the proof described in this paper. Furthermore, viewers with access to math. reviews might want to see review number MR1831809, which appears to the moderator to pertain to another chapter of this book. The moderator wants to make it clear that acceptance of this sci.math.research post is nothing more than *acknowledgement of the statement that Springer has published the book*, which the moderator believes to be of independent interest, and does not imply that the moderator has read, or believes, any of the stronger claims made in the book.]
Re: Springer Verlag Publishes ‘Proof’ of Goldbach’s Conjecture
Springer has also recently published
Farming Human Pathogens
Ecological Resilience
and Evolutionary Process
By Rodrick Wallace · Deborah Wallace ·
Robert G. Wallace
Have a look and tell me if the comparison between the two books is unfair.