The story of Nicolas Bourbaki, an imaginary mathematician, reveals the power of a systematic approach to abstract principles. In the 1930s, a group of French mathematicians, frustrated by the lack of a shared mathematical language, set out to create a consistent logical framework unifying every branch of mathematics. Their treatise, the "Éléments de mathématique," began with a set of simple axioms and derived more and more complex theorems that corresponded with work being done across the field. They defined functions by how they mapped elements across domains, establishing logic that could be translated in both directions. Despite their unconventional approach, Bourbaki's publications became standard references, and their influence informs much current research. By learning about systematic approaches to abstract principles, students can develop rigorous methods and expand their understanding of complex mathematical concepts.

Maps are a fundamental tool for navigation and education, but did you know that every map humans have ever made is wrong? That's because it's impossible to make a 100% accurate flat map of a spherical planet. Despite this, maps are still widely used today, including the Mercator projection, which distorts the size of land masses and bodies of water. However, maps are not just about navigation - they also shape our perception of the world. Simple changes in map design can completely shift our point of view. Learning about the different types of maps and their limitations can expand your understanding of geography and the world around you. By exploring this topic through reading, reflection, and self-directed projects, you can become an expert in cartography and gain a deeper appreciation for the power of maps.

Have you ever thought about why we use the number system we do? Did you know that there are other systems out there, like base 12, that could make math easier and more enjoyable? In a dozenal world, numbers are represented using 12 symbols instead of 10, which makes it easier to divide numbers into whole numbers. This makes it easier to use currency and measure things like fractions. Plus, some times tables work more nicely in base 12. It might seem confusing to switch to a new system, but civilizations have switched between bases throughout history. By exploring different number systems, you can expand your understanding of math and challenge yourself to think outside the box. Who knows, maybe you'll discover a new way of thinking about numbers that will make math more enjoyable for you!

Did you know that the origin of the word 'algorithm' dates back to the late 17th century? It comes from the name of a Persian mathematician, Muhammad ibn Musa al-Khwarizmi, who was born around 780 AD. His innovative contributions to mathematics, astronomy, geography, and cartography revolutionized the field. He wrote an influential book called “On the calculation with Hindu Numerals" which introduced Hindu-Arabic numerals to the West, the system we use today. His books showed how complex problems could be broken down into simpler parts and solved, which eventually gave birth to the computer age. Today, algorithms are everywhere, helping us get from A to B, driving internet searches, making recommendations of things for us to buy, watch or share, and even predicting how we vote or who we fall in love with. Learning about algorithms can give you a better understanding of how the world around you works, and it can even inspire you to create something new that could change the world.

The video clip discusses the importance of curiosity and exploration in academia. It highlights the stories of Richard Feynman, Eratosthenes, and Armand Fizeau, who made significant contributions to science by asking simple questions and investigating them further. Feynman's father's explanation of inertia sparked his interest in physics, leading him to earn degrees at MIT and Princeton, solve the Challenger disaster, and win the Nobel Prize in Physics. Eratosthenes calculated the Earth's circumference by measuring the shadows cast by the sun, and Fizeau confirmed Galileo's experiments on the speed of light. These stories demonstrate the value of asking questions and pursuing knowledge, even if the answers are not immediately clear. By exploring academic topics through reading, reflection, writing, and self-directed projects, students can develop their critical thinking skills and gain a deeper understanding of the world around them.

Historians are using machine learning to analyze historical documents, correcting distortions and drawing connections. But as machines play a greater role in the future, how much should we cede to them of the past? Discover the implications for everything from art to drug development.

Medieval texts, ice core, and tree ring data reveal how volcanic eruptions triggered the Little Ice Age. Researchers from the University of Cambridge and the University of Geneva examined hundreds of annals and chronicles from across Europe and the Middle East, in search of references to total lunar eclipses and their coloration. They found that the darkest lunar eclipses all occurred within a year or so of major volcanic eruptions, leading to cooling and other climate anomalies. Find out how the monks' records of the brightness and colour of the eclipsed moon helped narrow down when the eruptions must have happened.

Hertha Marks Ayrton was a brilliant inventor who lived in the late Victorian era. She was an incredibly hard worker and passed the Cambridge University entrance exam with honours in mathematics and English. Hertha was determined to make electric lights bright, even, and safe. She noticed that electric arc lights were volatile and poorly understood, so she put together a comprehensive set of experiments to test every possibility. Hertha invented a new kind of carbon rod coated with a copper film to stop oxygen from reaching the sides of the electrodes. This made street lights safer and sparked a new after-dark world of working, playing, shopping, and exploring. Hertha's work helped create new technologies like detonators, 3D printing, and rocket launchers for space travel. Learning about Hertha's inventions can inspire you to explore academic topics independently and spark your creativity to make a difference in the world.

Luke Howard's classification of clouds in the early 1800s revolutionized meteorology and changed humanity's understanding of the skies. Howard's simple insight based on years of observation was that clouds have few basic forms, and he introduced a series of intermediate and compound types to accommodate their essential instability. Howard's classification had an immediate international impact, and clouds became easier to understand as visible signs of otherwise invisible atmospheric processes. Understanding clouds is important in comprehending weather and climate patterns. Howard's classification also had a significant impact on art, with painters like John Constable painting clouds in the open air. Learning about clouds and meteorology can be intellectually stimulating and practically useful in comprehending weather patterns and climate change.

Unravel the mysteries of ancient texts, including a stamped clay disk, Easter Island tablets, and a 16th-century world map. Discover the secrets of the Minoan kingdom and the Voynich manuscript. Join the search for answers to these enigmatic artifacts.

Lovecraftian horror is a unique type of terror that responds to the rapid scientific progress of our era, using scientific elements to lend eerie plausibility. Rather than recognizable monsters or graphic violence, the terror in Lovecraft's fiction lies in what's not directly portrayed, but left instead to the dark depths of our imagination. Lovecraft's protagonists often stumble onto hints of the existence of the Great Old Ones, beings that exist beyond our conceptions of reality, whose true forms are as inscrutable as their motives. Even indirect glimpses of them are enough to drive them insane. The Cthulhu Mythos, named after Lovecraft's infamous blend of dragon and octopus, is a shared universe adopted by a wide variety of authors, often reimagining them from diverse perspectives that transcend the author's prejudices. Learning about Lovecraftian horror will inspire you to independently explore academic topics through reading, reflection, writing, and self-directed projects.

Effective altruism has been a cornerstone in solving global problems, relying heavily on quantitative metrics. But what about the ideas, experiences, and problems that resist quantification? Let's explore how we can create a more nuanced and inclusive framework for giving that incorporates unique passions.

Have you ever wondered how inventions come about? Sometimes it takes the willingness to question long-accepted ideas, like the belief that a vacuum couldn't exist. Aristotle and other ancient philosophers thought that a true vacuum, a space devoid of matter, couldn't exist because the surrounding matter would immediately fill it. But in the early 17th century, Gasparo Berti conducted a simple but brilliant experiment to demonstrate that a vacuum was possible. This led to Evangelista Torricelli's invention of the barometer, a key tool for measuring air pressure and predicting extreme weather events. Torricelli's willingness to think outside the box and question long-accepted dogmas about vacuums and the weight of air led to his invention, which remained one of the most common ways to measure atmospheric pressure until 2007. Learning about the history of scientific discoveries can inspire us to question long-accepted ideas and come up with our own innovative solutions.

If you're looking for a field of study that combines the beauty of mathematics with practical applications in the real world, Applied Mathematics may be just the thing for you! Applied Mathematics is the study of mathematical methods that can be used to solve problems in various fields, including science, engineering, economics, and finance. It's all about taking abstract mathematical concepts and applying them to real-world situations. One of the most exciting aspects of Applied Mathematics is its versatility. You can use it to solve problems in a wide range of fields, from predicting the weather to designing aircraft. For example, Applied Mathematics is used to study the spread of diseases, to optimize traffic flow, and to develop new materials for use in manufacturing. In recent years, Applied Mathematics has seen some fascinating research and innovations. For example, mathematicians have developed new algorithms for machine learning, which are used in everything from self-driving cars to medical diagnosis. Other researchers have used mathematical models to study the behavior of complex systems, such as the stock market or the human brain. If you're interested in studying Applied Mathematics at the undergraduate level, you can expect to take courses in calculus, linear algebra, differential equations, and probability theory. You may also have the opportunity to specialize in areas such as numerical analysis, optimization, or mathematical modeling. With a degree in Applied Mathematics, you'll be well-prepared for a variety of careers. You could work as a data analyst, a financial analyst, or a software developer. You could also work in fields such as aerospace engineering, biotechnology, or telecommunications. Some notable employers in these fields include NASA, Google, and the World Bank. To succeed in Applied Mathematics, you'll need to have a strong foundation in mathematics and an interest in applying mathematical concepts to real-world problems. You'll also need to be comfortable working with data and be able to think critically and creatively. If you're up for the challenge, Applied Mathematics could be an exciting and rewarding field of study for you!

Marine archaeologists and explorers embark on a daring mission to locate Sir Ernest Shackleton's lost ship, Endurance, trapped in the treacherous Antarctic sea-ice for over 100 years. Despite failed attempts, the fascination with Shackleton's Imperial Trans-Antarctic Expedition and the legendary escape of his men fuels the search for this elusive shipwreck. With new technology and tactics, the Endurance22 project sets out to make history and answer the question: what would it mean to find the Endurance?

Understanding the science behind climate change is crucial for high school students. Eunice Foote, a women's rights activist, discovered the greenhouse effect in 1856, but her work was buried for 150 years. Guy Stewart Callendar and Charles Keeling continued their research in the 1930s and 1950s, respectively, and proved that human activity was causing global warming. Keeling's Mauna Loa project is still the world's benchmark site for measuring CO2. By learning about the history of climate science, students can appreciate the importance of perseverance in scientific research and the impact of human activity on the environment. Understanding climate science can also help students make informed decisions about their own carbon footprint and advocate for change in their communities.

Beyond his famous paintings, Leonardo da Vinci's notebooks reveal his groundbreaking contributions to science, math, and engineering. From the Vitruvian Man to designs for machines and buildings, explore the forward-thinking insights and discoveries of this true Renaissance genius. Discover how his fascination with nature led to scientific observations and speculations that would later inform modern inventions.

Are you curious about the possibility of asteroids hitting Earth in the next 1,000 years? Well, according to a new study published in The Astronomical Journal and reported by MIT Technology Review, there's good news - none of them are expected to hit us! The study, led by Oscar Fuentes-Muñoz from the University of Colorado, Boulder, used a new method to model when asteroids are expected to come near Earth in their orbit and pushed those estimates up to 1,000 years into the future. Read on to discover more about the study's findings and what this means for our planet's future.

The study published in PLOS ONE reveals the discovery of Roman gold coins that were previously thought to be fake for over 150 years. The coins, which are now scientifically proven to be authentic, shed light on the long-lost emperor Sponsian and his reign. The coins were found in an isolated gold mining outpost in Roman Dacia, providing insight into the area's untold story.

How did Richard Feynman, a young boy with an unremarkable academic record, become a Nobel Prize-winning physicist? Can modern psychology help us understand the makings of genius? Explore the origins of brilliance and the best means of cultivating it through the Genetic Studies of Genius led by Lewis Terman. Discover the lucky combination of fortunate circumstances, grit and determination, and limitless curiosity that can pave the way for exceptional achievement.