Customer Reviews

Mathematics and the Divine: A Historical Study

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The majority of the chapters in this book read like random notes arbitrarily pasted together without any discernible goal other than the creation of a chapter-length chunk of text. Historically, many beautiful things have been written on the connection between mathematics and the divine, but unfortunately these old ideas are obscured by exceedingly poor presentation in this book. The following sentence---which is quite typical in terms of opacity, though extreme with respect to incompetence---illustrates my point:

"For Anatolius, quoted by Ps. Jamblichus, the Number Seven, the only number that is not generated by any of the first numbers except the unity, and the only one that does not generate any other number, is likened to Athena, the virgin motherless goddess." (p. 129)

The basic idea that 7=Athena is very clever indeed, but unfortunately the presentation it receives here is far from divine.

First of all there are elementary editorial shortcomings. For example, we are given no page reference so apparently we must read through Jamblichus's entire book (100 pages of classical Greek) if we want to see the original passage in question. Also, the term "generated" is never defined or used elsewhere, so we have no idea what the sentence even means. It must also be understood that the vague phrase "the first numbers" refers to the first TEN numbers.

But worse still are the blatant mathematical errors which show that the author really has no idea what he is talking about. For in fact "generation" is here intended in the sense of multiplication, which means that almost everything in the sentence above is wrong:
--7 is NOT generated by 1.
--7 is NOT the only number not generated (2, 3 and 5 are not generated either).
--7 is NOT the only number that does not generate others (neither does any of 6 through 10).

Thus if you want to read about the beautiful idea that 7=Athena from an author who is not mathematically incompetent you are better off ignoring this book in favour of classical sources themselves, such as this:

"Since the number 7 neither generates nor is generated by any of the numbers in the decad, they identified it with Athene. For the number 2 generates 4, 3 generates 9, and 6, 4 generates 8, and 5 generates 10, and 4, 6, 8, 9, and 10 are also themselves generated, but 7 neither generates any number nor is generated from any; and so too Athene was motherless and ever-virgin." (Aristotle, fragment 203, not cited in the book under review)

This book contains 35 articles by mostly European authors. It is quickly evident that most of them were not fluent in English. Too many non-idiomatic phrases and invented words make it a difficult read. Many paragraphs of the originals are given in the footnotes in German, Dutch or French. The reader must be prepared to be frustrated in trying to make sense of such poor English. The text abounds in high sounding phrases, artificially hyphenated words and latin phrases which do not add any value to the story. I cannot be sure if the editor was trying to sound scholarly or was unable to translate effectively.
I had hoped that there would be some philosophical insight and critical commentary, but I was disappointed. The book is a collection of episodes from history trying to shed light on the attitude toward mathematics by influential thinkers.

Most articles have a bibliography. There is an Author and Subject index at the end. The book is 701 pages long.
The personal email of most of the authors is given with their article. There are many B&W and color illustrations. Some articles contain college level math, but that should not deter anyone. The book is listed for over $300 and I do not believe worth buying. I do not know if the articles are available separately on the web.

I was happy to find a decent foto of Gerritt Mannoury and a color painting of Nicholas of Cusa.

The Title, author and country of origin of each article is given below.

Introduction - Teun Koetsier and Luc Bergmans - Netherlands / France
1. Chinese number mysticism - Ho Peng-Yoke - UK
2. Derivation and revelation: The legitimacy of mathematical models in Indian cosmology - Kim Plofker - Netherlands
3. The Pythagoreans - Reviel Netz - US
4. Mathematics and the Divine in Plato - Ian Mueller - US
5. Nicomachus of Gerasa and the arithmetic scale of the Divine - Jean-Francois Mattéi - France
6. Geometry and the Divine in Proclus - Dominic J. O'Meara - Switzerland
7. Religious architecture and mathematics during the late antiquity - Marie-Pierre Terrien - France
8. The sacred geography of Islam - David A. King - Germany
9. "Number Mystique" in early medieval computus texts - Faith Wallis - Canada
10. Is the Universe of the Divine Dividable? - Maurice-Ruben Hayoun - France
11. Mathematics and the Divine: Ramon Lull - Charles Lohr - Germany
12. Odd numbers and their theological potential. Exploring and redescribing the arithmetical poetics of the paintings on the ceiling of St. Martin's Church in Zillis - Hugue Garcia - Switzerland
13. Swester Katrei& Gregory of Rimini: Angels,God,and Mathematics in the fourteenth century - Edith Dudley Sylla - US
14. Mathematics and the Divine in Nicholas of Cusa - J.-M. Counet - Belgium
15. Michael Stifel and his numerology - Teun Koetsier and Karin Reich - Neth. / Germany
16. Between Rosicrucians and Cabbala-Johannes Faulhaber's mathematics of Biblical numbers - Ivo Schneider - Germany
17. Mathematics and the Divine: Athanasius Kircher - Eberhard Knobloch - Germany
18. Galileo, God and Mathematics - Volker R. Remmert - Germany
19. The mathematical model of Creation according to Kepler - Andre Charrak - France
20. The mathematical analogy in the proof of God's Existence by Descartes - Jean-Marie Nicolle - France
21. Pascal's views on mathematics and the Divine - Donald Adamson - UK
22. Spinoza and the geometrical way of proof - Ger Harmsen - Netherlands
23. John Wallis (1616-1703): Mathematician and Divine - Philip Beeley and Siegmund Probst - Germany
24. An ocean of truth - Cornelis de Pater - Netherlands
25. God and Mathematics in Leibniz's thought - Herbert Breger - Germany
26. Berkeley's defence of the infinite God in contrast to the infinite in mathematics - Wolfgang Breidert - Germany
27. Leonhard Euler(1707-1783) - Rudiger Thiele - Germany
28. Georg Cantor (1845-1918) - Rudiger Thiele - Germany
29. Gerrit Mannoury and his fellow significians on mathematics and mysticism - Luc Bergmans - France
30. Arthur Schopenhauer and L.E.J. Brouwer: A comparison - Teun Koetsier - Netherlands
31. On the road to a unified world view: Priest Pavel Florensky- theologian, philosopher and scientist - Sergei S. Demidov & Charles E. Ford - Russia / US
32. Husserl and impossible numbers: A sceptical experience - Francois De Gandt - France
33. Symbol and space according to René Gudnon - Bruno Pinchard - France
34. Eddington, science and the unseen world - Teun Koetsier - Netherlands
35. The Divined Proportion - Albert van der Schoot - Netherlands