Discover how the Raspberry Pi 5 turns into a full STEM lab with free Mathematica. From real-time sensor dashboards to image processing, neural networks and stunning math art, this guide empowers students, teachers and parents to explore, invent and visualize science and engineering like never before.

If we regard interference and entanglement as the most distinctive features of the quantum world, then “which-way” experiments lie at the heart of quantum physics, vividly illustrating the contrast between classical and quantum conceptions of nature. The idea of “which-way” experiments can be traced back to Einstein’s famous proposal of a double-slit experiment with a […]

To quantify the immune response against a rapidly evolving virus, groups routinely measure antibody inhibition against many virus variants. Over time, the variants being studied change, and there is a need for methods that infer missing interactions and distinguish between confident predictions and hallucinations. Here, we develop a matrix completion framework that uses patterns in antibody-virus inhibition to infer the value and confidence of unmeasured interactions. This same approach can combine general datasets—from drug-cell interactions to user movie preferences—that have partially overlapping features.

Comet 3I/ATLAS is the third detected interstellar visitor, identified by its hyperbolic orbit; backward integration places its origin beyond the solar system. It poses no hazard to Earth, passing no closer than about 1.8 au (~170 million miles, ~270 million km). Perihelion occurs around October 30, 2025 at roughly 1.4 au (~130 million miles, ~210 million km), just inside Mars’s orbit. Its size and physical properties are under active study worldwide. It should remain observable to ground-based telescopes through September 2025, become unobservable while near the Sun, and reappear by early December 2025 for renewed observations.

Huge congratulations to John Clarke, Michel H. Devoret and John M. Martinis on the 2025 Nobel Prize in Physics “for the discovery of macroscopic quantum mechanical tunneling and energy quantization in an electric circuit.” Their superconducting Josephson-circuit experiments made quantum effects unmistakably visible at circuit scale, discrete, anharmonic energy levels and coherent tunneling between macroscopically distinct states, laying key groundwork for modern superconducting qubits. In this short computational essay, we’ll walk through compact simulations that reproduce those signatures: a spectroscopy-style level map for the Cooper-pair box/transmon, and time-domain tunneling dynamics with realistic decoherence to mirror the original observations.

The quantum Schur transform is a unitary change of basis from the computational product basis to the so-called Schur basis, a basis labeled by the irreducible representations of the symmetric and unitary groups, based on the Schur-Weyl duality in the group representation theory. The latter basis is called the Schur basis. The quantum Schur transform […]

Hyperbolic lattices present a unique opportunity to venture beyond the conventional paradigm of crystalline many-body physics and explore correlated phenomena in negatively curved space. As a theoretical benchmark for such investigations, we extend Kitaev’s spin-1/2 honeycomb model to hyperbolic lattices and exploit their non-Euclidean space-group symmetries to solve the model exactly. In this Wolfram Mathematica notebook, we first show how to construct Kitaev models on hyperbolic lattices. Subsequently, we demonstrate how to use hyperbolic band theory to obtain the ground-state phase diagram on one of them and study the phases therein. In particular, we study the exotic compressible spin liquid with low-energy density of states dominated by non-Abelian Bloch states of Majorana fermions appearing for isotropic couplings which develops into a gapped chiral spin liquid under a time-reversal-breaking perturbation.

An advanced 3D animation of the Geneva mechanism, significantly enhancing the design of a previous, more simplified version. While the earlier animation utilized basic geometric forms like cylinders and triangular prisms, this new version introduces detailed and intricate shapes, resulting in a more realistic and visually complex representation. The animation includes refined components such as the Geneva wheel, lock wheel and driving pin, all modeled with precision. Interactive controls for parameters like the number of slots, pin radius and rotation angle provide users with the ability to explore and analyze the mechanism’s functionality dynamically. This improved animation serves as a valuable resource for engineering studies and enthusiasts interested in Geneva mechanisms.