Dirk Huylebrouck

Similarities in Irrationality Proofs for π, ln2, ζ(2), and ζ(3)

The irrationality of π dominated a good 2000 years of mathematical history, starting with the closely related circle-squaring problem of the ancient Greeks. In 1761 Lambert proved the irrationality of π (Lindemann would complete the transcendence proof in 1882 [2, pp. 52 and 172]). The interest in π’s younger brother ζ(3) started only a few centuries ago, but the number resisted until 1978, when R. Apéry presented his ‘miraculous’ proof [14]. Even after Apéry’s lecture, scepticism remained general, until Beukers’ simplified version confirmed it [3]. The character of the ζ -numbers still fascinates the mathematical community, and even very recently it was upset by results of Tanguy Rivoal (communication J. Van Geel, University of Ghent). Essential in the simplified proofs are the representations of ζ(2) and ζ(3) as integrals. Since ∫∫ 1

Observations about Leonardo's drawings for Luca Pacioli

Three versions of Luca Paciolis ‘De divina proportione’ remain: a manuscript held in Milan, another in Geneva and a printed version edited in Venice. A recent book, ‘Antologia della divina proporzione’, has all three in one volume, allowing an easy comparison of the different versions. The present paper proposes some observations about these drawings, generally said to be of Leonardo da Vincis hand.

Alphabetic magic square in a medieval Church

Does your home town have any mathematical tourist attractions such as statues, plaques, graves, the café where the famous conjecture was made, the desk where the famous initials are scratched, birthplaces, houses, or memorials? Have you encountered a mathematical sight on your travels? If so, we invite you to submit to this column a picture, a description of its mathematical significance, and either a map or directions so that others may follow in your tracks.

In Memoriam: Slavik Jablan 1952–2015

After a long and brave battle with a serious illness, our dear friend and colleague Slavik Jablan passed away on 26 February 2015. [...]

Mathematical tourist: A mathematics treasure in California

directions so that others may follow in your tracks. A lthough James Stirling enjoyed a substantial reputation as a mathematician among his contemporaries in Britain and in some other European countries, he published remarkably little after his book Methodus Differentialis: sive Tractatus de Summatione et Interpolatione Serierum Infinitarum in 1730. An article with valuable information on the achievements of James Stirling during his time as mine manager in Scotland appeared in the Glasgow Herald of August 3, 1886, see [8]. The Herald article was reprinted in Mitchell’s The Old Glasgow Essays of 1905 [7]. Detailed accounts of Stirling’s mathematical achievements and correspondences with his contemporaries can be found in [12, 13], and [14].

Can Art Save Mathematics

“Can art save the world?” is a well-known catchphrase in art circles. As most participants to the ICME are mathematicians, the title of this DG was reformulated more modestly as: “Can art save mathematics?” Indeed, some call mathematics a supreme art form as it enjoys total freedom, unrestricted by material limitations. An art form with the “collateral advantage” of having many real life applications, sure.

Renaissance Area-Fillings in the City Hall of Augsburg

The catapult that Archimedes built, the gambling-houses that Descartes frequented in his dissolute youth, the field where Galois fought his duel, the bridge where Hamilton carved quaternions-not all of these monuments to mathematical history survive today, but the mathematician on vacation can still find many reminders of our subjects glorious and inglorious past: statues, plaques, graves, the card where the famous conjecture was made, the desk where the famous initials are scratched, birthplaces, houses, memorials. Does your hometown have a mathematical tourist attraction? Have you encountered a mathematical sight on your travels? If so, we invite you to submit to this column a picture, a description of its mathematical significance, and either a map or directions so that others may follow in your tracks. Please send all submissions to the Mathematical Tourist Editor, Ian Stewart.