Math Philosophy

Math has a reputation for being inaccessible. People think that it requires a special gift or that comprehension is a matter of genes. Yet, the greatest mathematicians throughout history, from Rene Descartes to Alexander Grothendieck, have insisted that this is not the case.

Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: Observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria.

In A Mind for Numbers, Dr. Oakley lets us in on the secrets to learning effectively - secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions - you just need the creativity to see them.

In this engaging exploration, archaeologist Ian Hodder departs from the two prevailing modes of thought about human evolution: the older idea of constant advancement toward a civilized ideal and the newer one of a directionless process of natural selection. Instead, he proposes a theory of human evolution and history based on "entanglement," the ever-increasing mutual dependency between humans and things. 

In Consilience (a word that originally meant "jumping together"), Edward O. Wilson renews the Enlightenment's search for a unified theory of knowledge in disciplines that range from physics to biology, the social sciences and the humanities. Using the natural sciences as his model, Wilson forges dramatic links between fields. Presenting the latest findings in prose of wonderful clarity and oratorical eloquence, and synthesizing it into a dazzling whole, Consilience is science in the path-clearing traditions of Newton, Einstein, and Richard Feynman.

One of the great insights of science is that the universe has an underlying order. The supreme goal of physicists is to understand this order through laws that describe the behavior of the most basic particles and the forces between them. For centuries, we have searched for these laws by studying the results of experiments. Since the 1970s, however, experiments at the world's most powerful atom-smashers have offered few new clues. So some of the world's leading physicists have looked to a different source of insight: modern mathematics.

"It's the animal in us," we often hear when we've been bad. But why not when we're good? Primates and Philosophers tackles this question by exploring the biological foundations of one of humanity's most valued traits: morality.In this provocative book, primatologist Frans de Waal argues that modern-day evolutionary biology takes far too dim a view of the natural world, emphasizing our "selfish" genes.

Mathematics shapes almost everything we do. From building rockets to the handheld technology that governs our day-to-day lives, we are all in debt to the mathematical geniuses of the past. But the history of mathematics is warped; it looks like a sixteenth-century map that enlarges Europe at the expense of Africa, Asia and the Americas. The Secret Lives of Numbers introduces listeners to a new group of mathematical boundary-smashers, those who have been erased by history because of their race, gender or nationality.

In the 1940s and '50s, a group of eccentric geniuses - led by John von Neumann - gathered at the newly created Institute for Advanced Study in Princeton, New Jersey. Their joint project was the realization of the theoretical universal machine, an idea that had been put forth by mathematician Alan Turing. This group of brilliant engineers worked in isolation, almost entirely independent from industry and the traditional academic community. But because they relied exclusively on government funding, the government wanted its share of the results....

The fruit of the long history of John Brockman's profound engagement with the most important scientific minds who have been thinking about AI - from Alison Gopnik and David Deutsch to Frank Wilczek and Stephen Wolfram - Possible Minds is an ideal introduction to the landscape of crucial issues AI presents. The collision between opposing perspectives is salutary and exhilarating; some of these figures are deeply concerned with the threat of AI, including the existential one, while others have a very different view.   

The Crowd: A Study of the Popular Mind is a seminal work on crowd psychology by Gustave Le Bon (1841-1931), a French social psychologist. He observes that a crowd forms when an influential idea unites a number of individuals and prompts them to act towards a common goal. In a crowd, the conscious personality of the individual is submerged and dominated by the collective mind. Furthermore, every sentiment becomes contagious to a degree that individuals readily sacrifice their personal interest to the collective. 

One of the great mysteries of science is that its fundamental laws are written in the language of mathematics. Graham Farmelo's thrilling new book shows how modern maths has helped physicists to rethink gravity, space, and time. The Universe Speaks in Numbers takes us on an adventure from the Enlightenment to the present with a vibrant cast of characters, illuminating the most exciting and controversial developments in contemporary thought.

The young field of quantum mechanics holds out the promise that some of humanity's wildest dreams may be realized. Serious scientists, working off of theories first developed by Einstein and his colleagues 70 years ago, have been investigating the phenomenon known as "entanglement," one of the strangest aspects of the strange universe of quantum mechanics. New experiments suggest it does happen, and that it may lead to unbreakable codes, and even teleportation...

Do doctors really know what they are talking about when they tell us vaccines are safe? Should we take climate experts at their word when they warn us about the perils of global warming? Why should we trust science when our own politicians don't? In this landmark book, Naomi Oreskes offers a bold and compelling defense of science, revealing why the social character of scientific knowledge is its greatest strength - and the greatest reason we can trust it. 

The world hasn’t met with destruction on any of the long list of predicted doomsday dates, but the possibility may have got you thinking: has science created more problems than it has solved? What is the point of science at all? Geoffrey Gorham considers these questions and explores the social and ethical implications of science by linking them to issues facing scientists today: human extinction, extraterrestrial intelligence, space colonisation, and more.

Nicole M. Joseph investigates factors that contribute to the glaring underrepresentation of Black female students in mathematics. Joseph's account calls attention to educational structures and practices that contribute to race- and gender-based stratification in science, technology, engineering, and mathematics. In her assessment of the intersectional difficulties facing this marginalized group, Joseph offers a critical view of the existing mathematics education research, practice, and policies that have neglected Black girls and women; and then provides suggestions for reform.

El legado de los grandes filósofos puede ayudarnos enormemente en ese reto. Es un ejercicio mental que se practica a cualquier edad y que se perfecciona a medida que uno logra desprenderse de los prejuicios y malos hábitos adquiridos a lo largo de la vida. Hábitos que, en el fondo, no son otra cosa que los kilos de más que nos impiden desenvolvernos con soltura y enfrentarnos con garantías al día a día. De ese modo, tanto nuestros hijos o alumnos, como nosotros mismos gozaremos del factor determinante para llevar una vida feliz: la higiene mental.

Aristotle’s influence on western philosophy is immense. In this work, he claimed that everything that is learned in life is learned through sensory perception. He was also the first philosopher to establish the foundational principles of logic.

"Sense and Sensibilia" is one of the short treatises by Aristotle that make up the Parva Naturalia. He discusses attributes, like those that are common to all living things. They include waking and sleeping, youth and old age, inhalation and exhalation, life and death.

In TechGnosis - a cult classic now updated and reissued with a new afterword - Erik Davis argues that while the realms of the digital and the spiritual may seem worlds apart, esoteric and religious impulses have in fact always permeated (and sometimes inspired) technological communication. Davis uncovers startling connections between such seemingly disparate topics as electricity and alchemy; online roleplaying games and religious and occult practices; virtual reality and gnostic mythology; programming languages and Kabbalah.