Perfect colouring of isonemal fabrics by thin and thick striping of warp and weft with more than two colours is examined where the cells with warps and wefts of the same colour do not appear along diagonal lines (not twilly redundancy). In species 33 to 39, all fabrics of specific orders (linear periods) can be perfectly coloured by thin striping with satin redundancy. In fewer species, all fabrics of specific orders can be perfectly coloured by thick striping in two different ways with doubled satin redundancy. The isonemal fabric 6-1-1 can be used as a redundancy configuration. All these colourings allow the coloured weaving of flat tori and – a few of them – cubes.

Journal Article Carl Posy and Yemima Ben-Menahem, eds. Mathematical Objects, Knowledge and Applications: Essays in Memory of Mark Steiner. Jerusalem Studies in Philosophy and History of Science Get access Carl Posy Yemima Ben-Menahem, eds. Mathematical Objects, Knowledge and Applications: Essays in Memory of Mark Steiner. Jerusalem Studies in Philosophy and History of Science. Springer, 2023. Pp. xxii + 393. ISBN 978-3-031-21654-1 (hbk); 978-3-031-21657-2 (pbk); 978-3-031-21655-8 (e-book). DOI: https://doi.org/10.1007/978-3-031-21655-8. Robert S D Thomas Robert S D Thomas Robert.thomas@umanitoba.ca Search for other works by this author on: Oxford Academic Google Scholar Philosophia Mathematica, nkad012, https://doi.org/10.1093/philmat/nkad012 Published: 23 June 2023

I investigate with examples limitations that mathematicians accept in research: aesthetic, scientific, and practical, in particular, on what bases such choices are made. Discussion is partly in terms of the ideal agents that Philip Kitcher and Brian Rotman used to analyse mathematical writing.

Originally published in 1996, this book contains a translation and study of Euclid's Phaenomena, a work which once formed part of the mathematical training of astronomers from Central Asia to Western Europe. Included is an introduction that sets Euclid's geometry of the celestial sphere, and its application to the astronomy of his day, into its historical context for readers not already familiar with it. So no knowledge of astronomy or advanced mathematics is necessary for an understanding of the work. The book shows mathematical astronomy shortly before the invention of trigonometry, which allowed the calculation of exact results and the subsequent composition of Ptolemy's Almagest. This work and the (roughly) contemporaneous treatises of Autolycus and Aristarchos form a corpus of the oldest extant works on mathematical astronomy. Together with Euclid's Optics one has the beginnings of the history of science as an application of mathematics.

The first three books of Euclid’s Elements provide the charming classical introduction to deductive mathematics with the geometry of the blackboard. A blackboard with straightedge and a pair of com...

My journal article abbreviation of Euclid’s Phenomena with Len Berggren shows what the book says to those that don’t need or want the whole treatise. Its most important part is a list of the enunciations of the theorems as the obvious way to express the contents. This is a summary of the Spherics of Theodosios for “those that don’t need or want the whole treatise”. That summary is the second long section of this paper. The first section explains why, with examples, the summary cannot be just “a list of the enunciations of the theorems”.

Aesthetics in philosophy of mathematics is too narrowly construed. Beauty is not the only feature in mathematics that is arguably aesthetic. While not the highest aesthetic value, being interesting is a sine qua non for publishability. Of the many ways to be interesting, being explanatory has recently been discussed. The motivational power of what is interesting is important for both directing research and stimulating education. The scientific satisfaction of curiosity and the artistic desire for beautiful results are complementary but both aesthetic.

Having criticized the analogies between mathematical proofs and narrative fiction in 2000 and between mathematics and playing abstract games in 2008, I want to put forward an analogy of my own for criticism. It is between how the mathematical community accepts a new result put forward by a mathematician and the proceedings of a law court trying a civil suit leading to a verdict. Because it is only an analogy, I do not attempt to draw any philosophical conclusions from it.

Perfect colouring of isonemal fabrics by thin striping of warp and weft with more than two colours is examined. Examples of thin striping in all possible species with no redundancy and with redundant cells arranged as twills are given. Colouring woven flat tori is discussed.

The Viewpoint column offers readers of The Mathematical Intelligencer opportunity to write about any issue of interest to the international mathematical community. Disagreement and controversy are welcome. The views and opinions expressed here, however, are exclusively those of the author, and the publisher and editors-in-chief do not endorse them or accept responsibility for them. Viewpoint should be submitted to one of the editors-in-chief, Chandler Davis and Marjorie Senechal.

This notice is not an attempt to do any sort of justice to the nine essays in the journal issue listed at the end, the seventeen essays in the first book, listed at vol. 18 (2010), pp. 367–368, or the contents of the second book. It is intended to do no more than to make note of them and of such unity as they have. They were produced under the auspices of the scientific network ‘Philosophy of Mathematics: Sociological Aspects and Mathematical Practice’ (PhiMSAMP) (2006–2010). The journal issue comprises the selective proceedings of its first workshop in Berlin 2006 9 14–16. The first book comprises two different kinds of document. Eight essays are collaborative efforts written mostly by more than one author and worked on by the network: Buldt/Schlimm, De Cruz/Neth/Schlimm, François/Van Kerkhove, Geist/Löwe/Van Kerkhove, Lengnink/Leufer, Lengnink/Schlimm, Löwe/Müller, and Ramharter. The other nine are selective proceedings of the third workshop...

Darwin’s theory is generally reduced to a single book, On the Origin of Species, and to a single slogan: descent with modification by means of natural selection. However, such a reading is a caricature of Darwin’s thought. It is possible to distinguish three main periods in the elaboration of Darwin’s theory of descent. The diachronic period, preceding the reading of Malthus’ Essay on Population in September 1838, is mainly concerned with a transformist theory based on the causes and laws of variation. The synchronic period, represented by the Origin, corresponds to the unification of Darwin’s transformism around the principle of natural selection. The panchronic period, developed in The Descent of Man, conciliates the diachronic principles with synchrony, and particularly with natural selection. Three different theories of instinct correspond to the three main periods of Darwin’s thought. The diachronic theory is perfectly Lamarckian, while the synchronic theory denies any instance of Lamarckism. Both Darwin’s manuscripts and published works show that the conversion to synchronism does not forbid an ever-present panchronic tendency. I propose to discuss the different theories of instinct, concentrating on both the synchronic conversion and the persistency of panchrony. This approach could be considered as part of a renewal of the Darwinian studies, emphasising problematics treated by the English naturalist but eclipsed by the caricatural interpretation of his thought that the orientation of modern science confirms. Contact Information of Corresponding author: ATINER CONFERENCE PAPER SERIES No: PHI2012-0097