Page 35 - Textos de Matemática Vol. 44

NATA´LIA BEBIANO’S LEGACY 25
‘Pastimes and other Times’, ‘The Primes’, ‘The Imaginary Numbers’ , ‘The Di- vine Proportion’, ‘The Harmony of the Spheres’, ‘Galileu and Einstein’ ‘From euclidean to curved Space’ and ‘Symmetry’.
Each of these chapters, after an introduction, has a number of subtitles. Chapter 1 for example, after recounting some stories about Fermat, tells us about Algebra in Alexander’s time - Diophant, diophantine equations, Hilbert’s 10th problem and decidability, the Shimura-Taniyama-Weil conjecture, Weier- strass parametrization, elliptic curves, the ABC conjecture, Frey’s curve. These pages do not shun neither formulas nor figures and everywhere skillfully inter- weave history and some technical details; for example it explains the attractive ABC conjecture of Oesterl´e and Masser in 1980 in enough detail to understand the importance of its (possible) very recent proof in 2012.
As is the case with her biographical articles, the book is replete with fitting dictums. Thus chapter 3 on Euclides’ elements begins with a citation found in Dostoievskys ‘The Brothers Karamazov’: [...] if God exists, and really created the world, then he did it according to Euclides’. It goes then on to speak about the Elements, asks ‘what is an axiom? tells about axiomatic systems, consis- tency, completeness, and independence, the parallel postulate and attempts to prove it, Lambert and Sacheri, etc.
The poetic side of Piet Hein, the danish multi-talent and predecessor of John Nash as an inventor of Hex is appreciated more recently in [BCN10] where some of Hein’s ‘grooks’ are interpreted.1
Together these endeavours - and others more like a book entitled ‘1+1=11’, her fine lecture notes on Complex Analysis enriched with coloured Mathematica⃝c graphics and suggestions to experiment with this software (a book i suggested to the students when i gave the course), an imaginative booklet ‘The Mystery of the meandering Ring’ written for her children and printed 1993 in the same collection in which a number of portuguese translations of books by Enid Bly- ton and Alfred Hitchcock appeared, her scientific articles, her supervisions of Master’s and Ph.D. theses, the biographies - all this shows an impressive range of intellectual skills that make Nat´alia a worthy follower of the “HuMen” of culture she so well describes.
*
All of the above was written before the writer - not having internet on his type setting computer, and no fan of navigating the net - even opened Nat´alias home page
http://www.mat.uc.pt/~bebiano
1The writer had only available a portuguese preliminary version of this article