Little Quantum App vs Millennium Problems

What is a qubit? How does superposition work? And what is entanglement good for? In the Little Quantum App, Alice and Bob guide you on an accessible journey through the fascinating world of quantum physics. Step by step, you will explore some of the most important concepts of quantum mechanics and discover how ideas that may initially seem abstract can be understood through clear explanations and visual representations. The app combines short, educational animations with interactive elements that help make complex ideas easier to grasp. As you progress through the topics, animations illustrate how quantum states change and how key phenomena of quantum physics arise. After each section, small quizzes allow you to test and deepen your understanding of what you have learned. This combination of explanation, visualization, and interaction makes learning both engaging and effective. The Little Quantum App is the result of a close collaboration between the MCQST Office (Munich Center for Quantum Science and Technology) and the research group of Prof. Steffen Glaser at the Technical University of Munich. The goal of this collaboration is to make fundamental ideas from modern quantum research accessible to a broad audience and to provide an intuitive introduction to the principles of quantum mechanics. At the heart of the app is a special visualization method that represents quantum states as colored spheres. These visual objects are called “qubit beads” and “entanglement beads.” They are based on a mathematical mapping that allows arbitrary quantum states to be displayed in a visual and intuitive way. By observing how the beads move and change, users can develop a clearer understanding of how quantum states evolve. To further support intuitive learning, the digital representations can be complemented by tangible physical models. These hands-on models make it possible to explore quantum concepts not only visually but also spatially. This combination of digital visualization and physical interaction creates a remarkably simple and engaging approach to quantum mechanics. Through this approach, the Little Quantum App opens the door to quantum physics in a playful yet scientifically accurate way. The underlying mathematical structure ensures that the visual explanations remain faithful to the physics while still being easy to understand. The app invites learners to explore the fundamentals of quantum mechanics and discover the ideas behind one of the most exciting fields of modern science.

Can you solve a problem worth $1,000,000? The Clay Mathematics Institute has offered a million-dollar prize for each of seven unsolved mathematical problems — and nobody has claimed them yet. Millennium Problems brings these mysteries to life for everyone, from curious 11-year-olds to doctoral researchers. SEVEN LEGENDARY PROBLEMS • P vs NP — Is finding as hard as checking? • Riemann Hypothesis — Where do prime numbers hide? • Yang-Mills & Mass Gap — Why do particles have mass? • Navier-Stokes — Can we predict turbulent fluids? • Hodge Conjecture — What shapes are built from algebra? • Birch & Swinnerton-Dyer — How many solutions does an equation have? • Poincaré Conjecture — The shape of the universe (SOLVED!) EVERY SKILL LEVEL Choose your grade — from Grade 6 to Graduate — and the content adapts instantly. The same problem is explained with simple analogies for a middle schooler and rigorous proofs for a PhD student. INTERACTIVE 3D VISUALISATIONS Every problem comes with a real-time Three.js visualisation. Watch elliptic curves rotate, Riemann zeros appear on the critical line, and fluid particle fields swirl — all rendered natively on your device. BUILT-IN QUIZZES Test your understanding with 5 questions per problem per grade level. Earn XP, track your streak, and collect badges as you explore. WORKS OFFLINE No account. No subscription. No ads. Everything runs locally on your device. OPTIONAL BIOMETRIC LOCK Protect your progress with Face ID, Touch ID, or fingerprint — entirely optional. Whether you're a student looking for a challenge, a teacher seeking engaging material, or a mathematician revisiting the classics, Millennium Problems meets you where you are. Clay Mathematics Institute · $7,000,000 in unclaimed prizes · Since 2000