¿Para qué sirven las matemáticas? La pregunta reaparece con insistencia sin admitir una respuesta simple. Este libro la aborda a través de las historias concretas de ideas abstractas que no siempre surgieron con un fin practico y acabaron transformando la manera de contar, medir, predecir o comunicarnos. Desde las primeras tecnicas para registrar cosechas hasta la sofisticada matematica profesional contemporanea, el recorrido muestra como conceptos aparentemente inutiles estan en el origen de muchos avances. Es el caso de los numeros primos, que tras siglos de estudio son la base de la criptografia que hoy protege nuestros intercambios digitales. Aunque Rene Thom ironizaba sobre los cazadores de dragones para criticar cierta matematica demasiado encerrada en si misma, los dragones existen: modelos matematicos que permiten diseñar farmacos, explorar el universo, comprender la incertidumbre o construir ordenadores. Y todo ello sin menoscabo de otra utilidad de las matematicas, menos inmediata y no menos importante: formar una manera de pensar rigurosa, sensible a la curiosidad, el asombro y la belleza, y libre de presiones externas. Aquella que no solo puede servir para resolver problemas conocidos, sino prepararnos para los que aun no sabemos formular. Manuel de Leon es matematico, profesor de Investigacion del CSIC y fundador del Instituto de Ciencias Matematicas (ICMAT). Agata Timon es matematica y comunicadora. Es coordinadora de la Unidad de Cultura Matematica del ICMAT.

Deep within almost every cell in your body lies a separate, ancient strand of genetics that does not come from your father. Mitochondrial DNA (mtDNA) is passed down exclusively from mother to child, perfectly preserved across generations. Originally an independent bacterium that merged with our cellular ancestors billions of years ago, these microscopic powerhouses not only generate the energy that keeps us alive but serve as an unbroken biological ledger of human history.This book traces the astonishing journey of mtDNA through the ages. It explains how geneticists used these maternal markers to map the entire migration of Homo sapiens out of Africa, leading to the discovery of "Mitochondrial Eve"the matrilineal most recent common ancestor of all living humans. The narrative also explores how defects in this cellular battery are responsible for devastating, hidden diseases.Unlock the diary written in your cells. Understand the profound evolutionary symbiosis that powers human existence and learn how a tiny, separate ring of DNA allows us to track our ancestry back to the dawn of our species.

Esse é uma obra dirigida aos estudantes de astrofísica interessados em ingressar na seara observacional, e a profissionais que queiram consultar ou sanar eventuais dúvidas. É orientada à introdução d

The human brain is a fragile, gelatinous mass of fat and neurons. Left to its own devices, its sheer weight would cause it to collapse in on itself, crushing the blood vessels at the base of the skull. Fortunately, our consciousness is literally floating. The cerebrospinal fluid (CSF) is a crystal-clear liquid that bathes the brain and spinal cord, providing a miraculous hydraulic cushion that reduces the brains net weight by 97 percent.This fascinating biological exploration delves into the mechanics of this internal ocean. It explains how CSF not only acts as a physical shock absorber against daily impacts, but also functions as the brains private waste management system, flushing out toxic metabolic byproducts while we sleep. The narrative examines what happens when this delicate fluid balance is disrupted, leading to debilitating conditions and chronic pressure shifts.Discover the silent, flowing protector of your intellect. Learn how this dynamic, constantly regenerating fluid suspends our neurology in a state of weightless grace, ensuring that human consciousness survives the physical trauma of everyday movement.