Mathematics is a very lively science, and the blood that animates it are the problems whose solution we still do not know. This *uncharted waters* have a very diverse geography: some regions are located very deep inside mathematics themselves, in their purest territories, but they also border on other sciences, or on technology – the Internet, for instance, is today an important source of problems for the world of mathematics. We will dedicate this section to recent mathematical discoveries, and also to exploring the *uncharted waters* of the problems that are still to be solved.

Paraphrasing Terence, one could say: “Mathematics is a human work, and nothing human is alien to it”. The purpose of these games in the working could not be more more humane: to provide a few moments of relaxation and entertainment for those who like to solve puzzles and challenges of a more or less mathematical nature. But that is not all. Faithful to Terence’s quote, each problem will be enriched with an introduction that, on the one hand, will place it in society -either now or at another historical moment- and, on the other hand, will serve to generate reflection and discussion on certain aspects of society itself. In other words, these amusements will be much more than mathematical. Because, to paraphrase again: “The brain is only the second favourite organ of mathematicians”.

Humanity has been struggling with mathematics for tens of thousands of years, and we do not exaggerate. This almost certainly makes it the oldest science. In that time, there have been surprising events, shocking facts, amazing adventures, or the funniest anecdotes. Echoing the best of these stories, including those of the 20th century, will be the purpose of this section.

I know someone who claimed that life without mathematics would be like the *2001, a space odyssey* apes, before the monolith appeared to them – both Clarke’s novel and Kubrick’s film are valid here. The purpose of this section will be to show that this sentence is not exaggerated and perhaps even falls short. We also intend to claim for mathematics part of the recognition and fame that is often attributed exclusively to physics, chemistry, biology, astronomy, technology or medicine, for discoveries and advances that, in not a few cases, are due both to the first of the sciences -mathematics- and to those that came after it. I know that this sounds like an obsession, the “I want you to come and live with me, die with me, do everything with me” that Humbert Humbert said to Lolita – to quote from another Kubrick film, or from Nabokov’s novel – what can I say! In any case, we are not the only ones obsessed, since the prince of wit already made his Don Quixote say that even knights-errant: “must know mathematics, because at every step they will be required to do so”.

Adolf Hurwitz’s first words to the audience at the first International Congress of Mathematicians (Zurich, 1897) were: “It is true that most great mathematical ideas are the offspring of silence and solitary work. No science, with the possible exception of philosophy, has generated such eremitic and isolated characters as mathematics. And, even so, in the heart of a mathematician there is always a need to communicate and collaborate with his or her colleagues. And each of us knows from our own experience how stimulating the exchange of ideas with others is. That’s what we intend to do from this section: collaborate and exchange ideas with the many fine blogs on mathematics, and science in general, which shine like stars in the virtual universe.

Alegrías are a flamenco form with the light of Cadiz. Camarón sang one that affirms with the forcefulness of a theorem: “Trust in man / you should never have”.

The lyrics of these alegrías are half surreal and have resonances as if from haiku: “With the light of the cigarette, / I saw the mill. / My cigar went out. I lost my way”.

Almost as surreal as that couplet is what we propose in this section: using mathematics as a knife, we will split reality open, be it social, political, cultural, scientific or other… and we will look to see what is inside.

“I shot in the air, sang Camarón, it fell into the sand. / There is no trust in man.”

Every worthwhile blog devotes some highly visible space to place quotes from more or less famous personalities. We could not be any less. But as we mathematicians like to play and are somewhat crooked -almost all of us-, we will incorporate all kinds of pills here: some will be poisonous and bitter, others sweet; it will be difficult to swallow more than one and others will go down like a pinch of pure ambrosia. Some will be just a placebo and others, we hope, will bring relief and recovery.

I once described mathematics as the stew that is obtained by putting together the following ingredients: searching and unveiling secrets and proving the validity of the findings; seasoning, from time to time, with a little bit of infinite pepper or computational cinnamon stick. This scheme suggests a tear, which is not uncommon in mathematics and from which a creation often emerges: it is the tear between the logical ties that rule while proving, and the pure emotion – sometimes irrational – that guides the mathematician when investigates or discovers. This makes mathematics a creative science, an art with applications, concerned with the classical dichotomy between Apollo and Dionysus, which Bertrand Russell described so well: “Many admirable things in human works carry in them an element of intoxication – mental, not alcoholic – where prudence is swept away by passion. Without the Dionysian element, life would be uninteresting; with it, it is dangerous”.

This enriching approach will be the one we apply in this blog, as we are convinced that mathematics is often as much a matter of the heart as it is of the head.

**Antonio J. Durán**

*[ We are currently translating into English the content of this Blog. Please take it easy: translating all the posts will take a while. ]*