The poet and the pendulum

Looking upward, I surveyed the ceiling of my prison. It was some thirty or forty feet overhead, and constructed much as the side walls. In one of its panels a very singular figure riveted my whole attention. It was the painted figure of Time as he is commonly represented, save that, in lieu of a scythe, he held what, at a casual glance, I supposed to be the pictured image of a huge pendulum, such as we see on antique clocks. There was something, however, in the appearance of this machine which caused me to regard it more attentively. While I gazed directly upward at it, (for its position was immediately over my own,) I fancied that I saw it in motion. In an instant afterward the fancy was confirmed. Its sweep was brief, and of course slow. I watched it for some minutes, somewhat in fear, but more in wonder.
- from The pit and the pendulum by Edgar Allan Poe
After the abandonment of Tarja Turunen, the Nightwish engaged Anette Olzon as a female voice for five years, from 2007 to 2012. Again the separation it was not the best, but the fact is that Anette, despite the apparent sympathy, certainly did not enter the hearts of the fans, evidently still loving Turunen. His place was then taken by the dutch Floor Jansen, who turned out to be a worthy substitute for Turunen, but in the meantime Olzon sang one of Tuomas Holopainen's most interesting and inspired songs, evidently inspired by Edgar Allan Poe and to his mystical story The pit and the pendulum:

Gerbert's satanic signs

In the history of numbers, Gerbert of Aurillac, better known as Sylvester II, the 139th Pope of the Catholic Church, takes on a curious role.
He was an eclectic character: enthusiast about science and mathematics, it is handed down that he was the introducer of the Arabic numbers in Europe:
Gerbert was a figure of utmost importance as a religious, politician and scientist, who could not be ignored by his successors to the papal throne. He was considered the greatest intellectual exponent of the 10th century and one of the most important of the Middle Ages, a multifaceted and profound connoisseur of the arts of trivium and quadrivium. Thanks to his contact with the most advanced Islamic culture, Gerbert introduced in Europe the use of the clock, of a siren running on water vapor, and was the inventor of complicated musical and astronomical instruments. He used these inventions in Reims for teaching in the cathedral school. For example, Gerbert had built a complex system of celestial spheres designed to calculate the distances between the planets and, again in astronomy, asked in a letter of 984 to Lupito of Barcelona for the translation of an Arabic astronomy treaty, the Sententiae Astrolabii. Always in Reims he had a hydraulic organ built that excelled on all the previously known instruments, in which the air had to be pumped manually, and that in the sixteenth century was still visible in Ravenna. In the field of mathematics, the introduction of Arabic numerals in Europe has long been attributed to Gerbert, a merit of difficult attribution: surely the young aquitan knew them at the Hatto's school in Vich, but nothing authorizes us to think that he then made them know in the old continent. Certainly, Gerbert had the great merit of contributing to the studies on the astrolabe and of reintroducing the abacus in Europe, of which, according to an ancient chronicle, he would have learned the use by the Arabs.
The Arabic numbers were then considered demonic signs, so it should not be surprising that Pope Innocent X, in 1648, decided to resume the body with the aim of finding out if there was any trace of these sings on his predecessor. The exhumation was thus narrated by Cesare Rasponi:
When we dug under the portico, the body of Sylvester II was found intact, lying in a marble sepulcher at a depth of twelve palms. He was dressed in pontifical ornaments, his arms crossed over his chest, his head covered by the sacred tiara; the pastoral cross still hung from his neck and the ring finger of his right hand carried the papal ring. But in a moment that body dissolved in the air, which still remained impregnated with the sweet perfumes placed in the urn; nothing else remained but the silver cross and the pastoral ring.
The Arabic numbers derive from the Indian Brahmi symbols probably dating back to 300 BC and were spread mainly by the Arab mathematicians al-Khwārizmī and al-Kindi. Despite the meritorious work of introduction of Gerbert, it was only with Leonardo Fibonacci that, at the turn of the 1200s, the Arabic numbers were adopted in Europe in a systematic and widespread manner.

The Riemann Prize to Terence Tao

Excuse me for the delay, but I read the press release only today. So I proceed to publish:
Terence Tao, a world renowned mathematician based at the University of California in Los Angeles, USA, has been announced as the first recipient of the Riemann Prize in Mathematics, awarded by the Riemann International School of Mathematics (RISM).
Terence Chi-Shen Tao is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, geometric combinatorics, arithmetic combinatorics, analytic number theory, compressed sensing, and algebraic combinatorics. Tao was a recipient of the 2006 Fields Medal and the 2015 Breakthrough Prize in Mathematics. This prolific mathematician has been the author or co-author of 275 research papers, his most impressive results being those on three-dimensional Navier-Stokes existence and smoothness.

Maths in Europe: The ultimate question

If you are a reader of the Hitchhiker's guide to the galaxy, you probably know that 42 is the answer to the Ultimate Question of Life, the Universe, and Everything. The choice of the number by Douglas Adams was quite random, excluding the simple fact that the number liked the writer. Yet the 42 was the protagonist of a recent news related to one of the open problems of mathematics:
Is there a number that is not 4 or 5 modulo 9 and that cannot be expressed as a sum of three cubes?
To find an answer to this question, mathematicians used numerical methods. In particular, Andreas-Stephan Elsenhans and Jorg Jahnel using a particular vector space, searched solutions of the following diophantine equation:
Continue on Mathematics in Europe

A primordial flash

The primordial universe continues to reveal its mysteries to us: a research group led by Christina Williams from the Steward Observatory of the University of the Arizona, using the 66 antennas that constitute the ALMA radiotelescope in Chile, has revealed a weak emission in radio frequencies, probably dued to the dust generated by stellar formation inside a giant primordial galaxy, about 12.5 billion years away from us, just more than a billion year after the initial expansion of the spacetime (the Big Bang).
Williams, C. C., Labbe, I., Spilker, J., Stefanon, M., Leja, J., Whitaker, K., ... & Weiner, B. (2019). Discovery of a Dark, Massive, ALMA-only Galaxy at z∼ 5–6 in a Tiny 3 mm Survey. The Astrophysical Journal, 884(2), 154. doi:10.3847/1538-4357/ab44aa (arXiv)

We know we don't know

A few days ago on Nature Astronomy it was published a paper by a team of italian researchers with an unequivocal title: Planck evidence for closed Universe and a possible crisis for cosmology(6). We can consider it as one of the first scientific articles that seriously takes into consideration a situation that it is becoming increasingly pressing: a crisis in cosmology.
The standard cosmological model, based on cosmic inflation(2) and on empirical constants that evaluate unknown physical quantities as dark matter and dark energy, although very well verified, has not yet passed the last step: the detection of gravitational waves in cosmic microwave background (CMB). One of the fundamental points of this model, but also of many of the surviving competing models, is the accelerated expansion of spacetime at speed greater than that of light which explains the flatness of the early universe.
This flatness emerges in particular when studying the cosmic microwave background, the residual energy of the initial expansion of spacetime. This radiation has come down to us from the point where it was produced, a little less than 14 billion years ago, crossing the whole universe. This means that in the signal detected there must also be gravitational lens effects(1) due to the amount of matter, usual and dark, present in the universe. These effects have long been known and calculated(4) and can already be seen in the image produced by Planck(5).