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

Aninda Sinha presents an infinite family of new π formulas, parameterized by elasticity. In the large-elasticity limit, it recovers the Madhava series. The method also yields many new identities, readily explored with Mathematica. Professor Sinha is a 2025 Wolfram Innovator Award recipient.

We simulate a polycapillary collimator at soft X-rays. The Wolfram add-on Optica is used to trace rays (Monte Carlo) through a micro-channel assembly. The 3D beam profile fits in with experiments and an analytical model. The low divergence (7 mrad) extends the theory and enables new applications.

Formulation of the generalized agent-based model as a nested recursive function.

Extend the five-point “circle” puzzle to the complex projective plane. The die-five’s unique conic factors into two lines, projectively equivalent to the radius-zero circle x² + y² = 0. Hence the five points are complex-concyclic; we visualize this via the circular points I and J.

This talk discusses updates to Import/Export and data connections in Wolfram Language 14.3 and upcoming changes for Version 15.0. We go in depth on the new tabular, document, image, config and log formats, as well as connections to multidimensional databases.

This talk describes the Wolfram Compiler and explores its various innovative features. In particular, it looks at the advances provided in Version 14.3 of Wolfram Language. The Wolfram Compiler provides an alternative way to execute Wolfram Language programs: converting them into native machine instructions that run directly on the CPU. It uses the latest advances in compiler technology and is deeply embedded with the entirety of Wolfram Language, providing many interesting and unique features. It is used for an increasing amount of new development, such as the Data Structure library.

Large language models (LLMs) are rapidly becoming essential tools for research and development. This session presents an overview of Wolfram Language's LLM integration framework, showing how LLM functions, external model connections and structured tool-calling workflows can be used in practice. We also highlight recent developments enabling complex, multistep reasoning chains that blend LLM output with symbolic computation.

This talk introduces new features in Wolfram Language's question framework, emphasizing improved question customization, including LLM evaluation in AssessmentFunction and support for EpilogFunction in QuestionObject. Through illustrative examples, we demonstrate how QuestionObject can significantly enhance computational thinking and facilitate interactive learning experiences on the CBM teaching platform.

Labeled Graphics is now backed by LabeledGraphicsBox, for better layout and resizing. Graphics is improved with Alignment control, tighter PlotRange fitting around curves, better depth buffer precision and faster rendering of SurfaceAppearance enhanced for Depth Peeling.

Quezzio provides dynamic, reliable assessments that work the way you teach. Instructors author questions in a Wolfram Notebook. Students answer questions in a web interface. Quezzio grades students' answers using instructor-defined rules. I show how LLMs can simplify question authoring.

This talk gives an overview of the various updates on PDE modeling, including discussion of new functionality for post-processing PDE solutions. Gain more understanding of the scope of PDE modeling and start your own.

As the Neural Network framework is being migrated to a PyTorch backend, its underlying eager execution will unlock important features. We explore how this new software stack allows combining symbolic network graphs, imperative layer execution and native Wolfram Language functions, making it easy to mix custom Wolfram Language code with PyTorch-powered layers and pre-trained models.

In this talk, we discuss the formalism of bosonic second quantization. Building on recent developments in the Wolfram Quantum Framework and Wolfram Language, we explore advanced applications in quantum optics. We show how interference phenomena of light can be described in terms of “bright” and “dark” states, offering a fully quantum perspective. Symbolic methods are presented for handling the non-commuting algebra of bosonic operators, enabling alternative approaches to calculations requiring operator simplification. We also examine multi-mode phase-space representations, focusing on the joint Wigner function for two-mode systems. The emphasis is on making advanced quantum ideas more approachable through computation, bridging abstract theory and practical exploration in both learning and research.

This is a hands-on workshop exploring how to construct and customize LLM-based workflows in Wolfram Language. Starting from simple single-call applications, we work step-by-step toward full agentic pipelines that integrate multiple models, external tools and symbolic computation. Along the way, we show examples ranging from conversational data analysis and natural language model building to multistep orchestration with external APIs and hybrid symbolic–numeric research assistants.

Students from the 2025 Wolfram Summer School present the projects they completed during the program. These projects span a wide range of topics and showcase how participants applied Wolfram technologies to explore original ideas, conduct research and build creative solutions, all in just a few weeks. Support the next generation of computational innovators!

This talk discusses new and upcoming features for fluid dynamics. After briefly revisiting new features in Version 14.3, we introduce and discuss new postprocessing functions for computing fluid viscosity and stress that will be part of the next version of Wolfram Language.

Developer John Fultz discusses the future of front-end development, highlighting key features like dark mode, migration challenges and enhancements on the way in Version 15. He emphasizes the significance of color contrast, documentation and user interface improvements. New features include a side notebook and a revamped find interface, focusing on speed and efficiency.

This session discusses graphical exploration of the intricate interplay between computational randomness, pseudorandom algorithms and complexity. View how pseudorandomness emerges from deterministic computational processes, revealing fractal patterns and chaotic behaviors that challenge traditional notions of randomness. By examining the computational complexity of these systems, we highlight how simple rules can generate intricate, unpredictable outputs akin to natural phenomena. Through practical demonstrations in Wolfram Language, we showcase tools for modeling and analyzing pseudorandom systems with their applications in cryptography, simulation, complex systems research, AI and data science. This talk bridges theoretical insights from Stephen Wolfram's A New Kind of Science with practical computational techniques, offering a fresh perspective on randomness and complexity in modern computing.

UX Manager Noah Hardwicke explains the efforts in implementing dark mode within UX and front-end teams at Wolfram. He details the technical aspects and methodologies for migrating content, highlighting challenges like legibility and contrast. Tools for effective dark mode implementation are introduced, along with examples of color directives. The session wraps up with key takeaways and answers to audience questions regarding dark mode functionality and compatibility.

Promptocracy is an experimental mechanism where a group of people can achieve consensus using an AI as a moderator. In this talk, I show how this started as a Wolfram Summer School experiment and recently became a multiplayer WhatsApp-based in-person game.

The presentation summarizes the use of Mathematica for the comparison of several calculation methods to obtain the damping in structures, as well as an innovative method that avoids the use of filters in multi-degree-of-freedom systems, which can distort the results.

This study uses electronic medical record data to identify hospital-acquired pneumonia using clinical criteria and leverages Wolfram Language to build scalable predictive models to be used in a clinical trial.

We present an AI program applying the concept of the system to the data provided by the European Patent Office database.

This talk explores biodiversity data analysis through the Darwin Core Archive format, detailing the steps for importing, inspecting, and visualizing data, while highlighting the role of machine learning in studying mimicry. Munoz discusses the value of citizen science platforms like iNaturalist and geographic data in spider distribution. He encourages applying these techniques to various projects and emphasizes the potential for similar analyses across different organisms.

In this workshop, Rick Hennigan—primary developer of Wolfram Notebook Assistant—walks through what it is, why it was built and how it can help you better understand and work with complex projects.

You’ll see practical examples of how Notebook Assistant can analyze existing code, explain unfamiliar sections and accelerate the process of fixing issues or extending functionality. Rick also discusses real-world use cases, current limitations and how Notebook Assistant fits into modern development workflows alongside tools like VS Code, Cursor, and Codex.

Introduction to the quantum approximate optimization algorithm (QAOA) and QUBO formulation through the max-cut problem, using the Wolfram Quantum Framework for fully symbolic and detailed explanations accessible to audiences without a physics background, including the advanced QAOA-in-QAOA method.

In this talk, we explore common pitfalls developers encounter when building dynamic interfaces in Wolfram Language and present effective patterns to avoid them. We cover a wide range of topics, including synchronization, initialization, alignment and other frequently overlooked issues.

Carlo Giacometti highlights advancements in signal processing and the integration of fitness data with video. The presentation covers network architectures for audio separation and their role in improving audio quality and visualizing fitness data.

Mathematica graphics have support for using existing OpenGL Shading Language (GLSL) files to customize 2D/3D graphics rendering through SurfaceAppearance. Many graphics features are built on top of it. Users can also use it to have customized rendering and more advanced applications. This talk lists all-new experimental SurfaceAppearance features added recently, which benefit customized rendering of Mathematica graphics. This talk also shows how to do customized rendering with several simple and advanced examples.

Life sciences encompass diverse aspects of living organisms, from genetics and molecular biology to cellular structures and the classification of organisms. Access to organized, high-quality data and robust analytical tools is essential for research and discovery in these areas. Wolfram Language offers programmatic access to a wide range of biological datasets, including genes, variants and taxonomic classifications, along with powerful functions to analyze and visualize such data. In this talk, we will explore examples such as genomic features, biological pathways and phylogenetic classification to highlight the breadth of analyses supported by Wolfram Language.

Stephen Wolfram is the creator of Mathematica, Wolfram|Alpha and Wolfram Language; the author of A New Kind of Science; and the founder and CEO of Wolfram Research.

This study concerns modelling economic growth via a two-parameter extension of the von Bertalanffy equation with seasonality. With constant parameters, an exact hypergeometric solution is found; in the time-varying case, exact bounds and Mathematica simulations validate the results.

From a historical perspective, discover the most important modeling aspects for fighter aircraft in air combat, keeping in mind the other side of the equation: tactics and the people who bring them to life.

This presentation showcases how LLMs can enhance safety log analysis in the oil and gas industry. Partnering with a major operator, we processed 15,000 safety observations through a multi-stage pipeline, using a domain-specific framework and unsupervised learning for semantic classification.

We explore continuous cellular automata by studying perturbations under different circumstances. We classify automata according to complexity, investigate intrinsic randomness generation and sensitivity to initial condition, build computational tools for chaotic strings, and share important updates.

This talk introduces models combining entropy, infinite games, and regulation to assess survival probabilities under AI dominance. Monte Carlo simulations and dynamical feedback reveal how ethics and constraints sustain human agency.

Get a first look at the latest features and libraries coming to Wolfram System Modeler—and see how they can accelerate your modeling workflows. Explore new domain-specific libraries for modeling buildings, power grids and photovoltaic plants. Learn how enhanced tools enable you to build your own custom AI assistant for faster learning, or use SystemModelValidate to express and verify requirements directly in your models. From smarter workflows to expanded modeling capabilities, this session will highlight what’s new and how you can put it to work in your projects right away.

This talk showcases elastoplastic materials in solid mechanics, highlighting advances in simulating material behavior such as permanent deformation and hardening. With examples from metal and soil plasticity, discover the latest FEM capabilities for structural analysis and gain practical insight to apply them effectively.

This talk gives an overview of what's new in the world of cloud notebooks and beyond. It also gives a brief update on the ongoing improvements with our enterprise support, as well as custom applications built with the Wolfram Cloud and related technology.

Wireworld is a 2D cellular automaton with just four states—enough to build a real computer. In this talk, we start with the rules; show how “electrons” move; and build logic gates, adders, memory and control circuits, all in Wolfram Language, ending with a complete working computer.

Learn how to design, analyze and optimize the thermal management system of an electric vehicle using Wolfram System Modeler. This session walks through a complete modeling workflow—from building the thermal system model to simulating real-world operating conditions. See how to apply post-processing techniques to evaluate performance across scenarios, then use optimization methods to identify the best operating configurations for efficiency, safety and comfort. Whether you’re focused on extending battery life, improving cabin climate control or minimizing energy consumption, this workflow demonstrates how modeling and optimization can work together to deliver better EV designs.

This presentation demonstrates the integration of symbolic computation, numerical methods, and both built-in and paclet-based functions to compute molecular weight distributions of polymers. The methodology is applied to a class of polymeric intermediates known as polyether polyols.

Explore how Wolfram System Modeler can serve as a powerful training ground for AI. This session showcases three cutting-edge workflows that combine physics-based modeling with machine learning. First, see how reinforcement learning agents can be trained in realistic simulated environments. Next, learn how high-fidelity models can be used to generate data for neural surrogate models—enabling faster optimization. Finally, discover how neural network–based model predictive controllers can be designed to control complex physical systems. Whether your goal is faster simulations, smarter controllers or more efficient AI training, see how System Modeler bridges the gap between engineering models and intelligent algorithms.

Updates in visualization features include support for dark mode, integration of tabular data and new plotting functions. Improvements focus on interactivity, labeling and future developments like plot grids and enhanced chart styles. The emphasis is on creating user-friendly visualizations and the continuous evolution of Wolfram Language's capabilities

Deep learning is expanding Wolfram Language's capabilities in computational chemistry. This session presents recent work on local protein folding and the modeling of interatomic potentials. These advances bring new levels of accuracy and realism to molecular modeling while keeping the entire workflow seamlessly integrated into Wolfram Language.

This talk is an overview of features that help us visualize fitted data in Wolfram Language data-plotting functions. In Version 14.3, we added experimental options to our data visualization functions that can be used to plot fit curves. In this talk, we look at the PlotFit and PlotFitElements options. These options enable plots to plug into Wolfram Language's powerful data-modeling capabilities and create plots that give us more insights into our data. We also explore changes and updates to these options in upcoming versions of Wolfram Language.

This session reviews engagement with the chemistry community over the last year and chemistry projects from the Wolfram summer programs. Recent and upcoming features of Wolfram GPT, Wolfram Notebook Assistant, Wolfram|Alpha and Wolfram Language related to chemical education are also discussed. New step-by-step support in chemistry is demonstrated and recent Function Repository submissions are highlighted. The new QuantumChemistry paclet is utilized to understand bonding in carbon dioxide.

Control systems is a mature field with diverse and numerous applications, but it's primarily based on explicit system models. This talk shows how Reinforcement Learning can be used to design model-free controllers, specifically LQR controllers.

This talk introduces styling tabular data, focusing on both appearance and content-based techniques. The presentation showcases various styling options and functions for data manipulation, along with practical applications for data exploration. Key functions like RawValue, ColumnValue, and ItemValue are demonstrated, showing how to apply styles based on data conditions. The session wraps up with a Q&A on sharing notebooks, column sizing, and Excel compatibility.

Biomolecules such as proteins, RNA and DNA are the building blocks of life. Access to computable biomolecular structural data is integral to biology education and research. Wolfram Language has several functions and connections to external databases that enable computations on biomolecular structures. In this talk, bioinformatics developer Soutick Saha highlights functions for analyzing and visualizing biomolecular structures, predicting protein structures from their sequences and comparing the structures of a pair of biomolecules. He also demonstrates accessing protein structure and sequence-related information using service connections and their applications.

This talk provides a general introduction to PDE modeling in Wolfram Language. Using boiling an egg as an example, we introduce the concepts of solving PDEs with the finite element method (FEM). Attendees without prior experience in PDE modeling can gain an understanding of how to set up and solve PDE models.

Wolfram Language 14.3 makes GeoGraphics return vector maps by default, and with many new available map styles.

Molecular modeling has been supported in Wolfram Language for many years, and initial support for biomolecules (proteins and nucleic acids) was recently added. The current capabilities include importing from PDB, sequence folding with ESMAtlas, visualization and some property computation. In last year's presentation, we described the computation of protein-ligand binding energy and the prerequisite biomolecule editing need to obtain an accurate result. That editing and computation were done on the Molecule representation of the protein. In this talk, we describe the direct editing of the BioMolecule representation of proteins to support the computation of binding energy, molecular dynamics and accurate properties. Specific operations covered include supplying experimentally unobserved hydrogen atoms; adjusting the amino acid residue protonation state for acidic, neutral and basic pH; and 3D point mutation of residues. Examples and discussion of the prototype code are included.

GPUs have transformed modern computing, delivering unparalleled performance for data-intensive workloads. This talk highlights GPUArray in the Wolfram Language, showcasing how GPUs are enabling breakthroughs in high-performance computing.

In this session, we will hear from a selection of students from the Wolfram Emerging Leaders Program as they present their amazing projects. Hear about human protein-protein interaction, double pendulum hashing, functional iteration and more!

This talk presents the Sound and Vision team's service framework designed to simplify interactions with REST APIs. This framework improves user experience and resolves issues with legacy systems. It offers features for managing connections, handling credentials, and defining requests, while providing clear documentation and support for authentication methods. Future enhancements may include automatic service connection generation from OpenAPI specifications.

Mesh processing plays a crucial role in graphics engineering and 3D printing. Key techniques include mesh simplification, which reduces elements while maintaining shape, and smoothing, which eliminates noise. Re-meshed (Uniform) meshes are highlighted for their ability to create stable meshes suitable for animation and modeling. The session encourages experimentation with these techniques and references additional talks on improving 3D models.

Modeling smooth surfaces with polygons can be challenging, but subdivision surfaces provide an elegant solution. This talk explores the motivation behind subdivision surfaces and their representation in the Wolfram Language, along with workflows and practical applications that make use of them.

This project geolocates settings from the novels of Mario Vargas Llosa, Peru’s Nobel Prize–winning author, to contribute to a literary map of the country. Using Wolfram Language, it identifies and maps real-world locations to reveal Peru as portrayed in his works.

This talk introduces motion planning in robotics, explaining key concepts, challenges, and various algorithms. Keren Garcia highlights the significance of workspace and configuration space, balancing optimality with computational efficiency. Different algorithms, including graph-based and sampling-based methods, are discussed. Applications in autonomous vehicles and mobile robots are showcased, featuring a robot cleaning a living room. The session wraps up with a Q&A on real-time computations and onboard sensors.

This talk covers how to compute, analyze and visualize food and nutrition data in Wolfram Language. Students, educators, researchers, developers and everyone who loves food can be creative and productive with computable, semantic representation of food. We also explore some physical principles of cooking and baking.

Leaders in many top organizations and institutions have played a major role in using computational intelligence and pushing the boundaries of how the Wolfram technology stack is leveraged for innovation across fields and disciplines. Join us as we recognize these deserving recipients with the Wolfram Innovator Award.

As AI sophistication increases with more parameters and larger token windows, curating high-quality data is crucial. This presentation explores how to acquire web-based data using WebSession/WebExecute, focusing on using selectors effectively, and providing tips for data cleaning and verification.

Given a list of rules, we can build a multiway graph. This graph represents a set of proof spaces for many theorems. Given a theorem in this graph, we can look for every possible proof. How can we define a continuous transformation from one path to another?

“By seeing mathematics and literature as complementary parts of the same quest to understand human life and our place in the universe, we immeasurably enrich both fields,” says Dr. Sarah Hart in her book Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature. Such a coexistence of mathematics and literature is particularly evident in the work of the Ouvroir de littérature potentielle (OuLiPo), a group of writers who develop, among other creative constraints, mathematically inspired poetic forms. In this talk, an artist (and former Wolfram|Alpha developer) will share an overview of their work using the Wolfram Language in Mathematica to write mathematical poetry.

In this presentation, I describe how, during the construction and operation of Sirius—Brazil’s fourth-generation synchrotron light source—I have used Wolfram Language as a decision tool: compact physics models that make constraints explicit, expose trade-offs, and set targets that help align teams and guide instrument design and operations under tight time, budget, and risk. Dr. Westfahl is a 2025 Wolfram Innovator Award recipient.

We present the solution of the Langevin equation, which can be regarded as a half-order fractional differential equation. Calculation of quaternion and biquaternion differential equations is also presented.

Zeta functions (such as the Riemann zeta and multiple zeta values (MZVs)), together with harmonic numbers and (multiple/generalized) polylogarithms are the native language of many difficult problems, from Euler sums in analytic number theory and nested sums in combinatorics to differential equation methods for multiscale Feynman integrals (iterated integrals and Fuchsian systems). We introduce a coherent family of symbols—AlternatingHarmonicNumber, HyperHarmonicNumber, MultipleHarmonicNumber, MultipleZeta, HarmonicPolyLog, MultiplePolyLog and GeneralizedPolyLog (GPL)—with exact evaluation and high-precision numerics, shuffle/stuffle-aware simplification, branch-aware transformations and deep integration with Sum, RSolve, Integrate and DSolve. These capabilities enable users to: (i) collapse high-weight Euler sums to canonical MZV combinations; (ii) normalize mixed products of harmonic numbers/logs/polylogs for downstream Sum/Integrate; (iii) solve regular and perturbative Fuchsian systems directly in terms of GPLs; and (iv) verify results via one-line high-precision checks. The talk will open with an informal historical overview of zeta functions and then present a unified interface for Euler sums, harmonic number/polylog transforms, iterated integrals and Fuchsian systems.

Turn your design requirements into automated, verifiable checks with Wolfram System Modeler. In this session, we teach you how to translate specifications directly into the SystemModelValidate function, enabling large-scale scenario testing without manual scripting. We demonstrate how the built-in requirement specification language makes it easy to express conditions such as “for how long” or “at what time,” then automatically evaluate thousands of simulation cases to uncover failure modes. By streamlining post-processing and validation, this approach helps you catch edge-case issues early and ensure your designs meet performance and safety targets—no matter the operating conditions.

Explore how to solve Sudoku puzzles through graph coloring! By turning Sudoku grids into graphs, we can apply elegant graph theory tools to find all valid solutions, revealing hidden patterns and seeing the beauty of graph theory in action.

The new unified model framework brings together statistical modeling, machine learning and symbolic computation in a single, consistent interface. We show how diverse model families—linear, nonlinear, generalized additive, tree-based and more—fit into the same symbolic pipeline. Built for efficiency with the new Tabular object, the framework supports high-performance fitting on large datasets while preserving Wolfram Language's advantages in probability, integration and symbolic analysis.

In this session, we hear from a selection of students from the Wolfram High School Summer Research Program as they present their amazing projects. Hear about physics-based prosthetics, small-molecule protein binding, constructed languages and more!

This talk explores the crucial link between prime number generation and the strength of modern data security systems. It demonstrates how modern cryptography relies on prime numbers to ensure the security of digital communication. It also examines how the limits of RSA encryption highlight the need for more advanced and efficient methods of generating primes.

The Wolfram Neural Net Repository and neural net framework are in the process of being migrated to a PyTorch back end, bringing expanded hardware support and performance gains for both training and inference. This session takes a technical look at how PyTorch is being integrated with Wolfram Language's symbolic neural network definitions, which will enable hybrid execution and smoother workflows for researchers.

This talk explores how generative AI tools, particularly LLMs, can be scaffolded to foster critical thinking rather than replace it, especially when supplemented with Wolfram Language. Using case studies in physics problem solving, we compare student-led versus model-led prompting strategies and analyze their impact on reasoning depth. We propose a framework aligning prompting strategies like chain-of-thought and ReAct with inquiry-based pedagogies and suggest assessment rubrics that center student–AI interaction as a site of learning.

This talk covers computation augmented generation (CAG) and its role in AI products. Rick Hennigan differentiates CAG from retrieval augmented generation, focusing on how it automatically retrieves relevant information for large language models (LLMs). The introduction of Agent One, an LLM API, simplifies integration. The MCP standard is discussed for connecting applications to services. The session emphasizes understanding LLM capabilities, especially in coding, and concludes with a Q&A on CAG and MCP.

Dr. Kapadia gives an overview of upcoming features related to noncommutative algebra, multiple zeta functions, matrix computation, PDE modeling and core calculus operations. He also discusses current projects related to documentation, textbook publication and online courses.

Recent advances in Wolfram Language use neural networks to assist in solving nonlinear ordinary differential equations. This talk presents how machine learning–powered methods integrate with DSolve, enabling solutions in cases where traditional symbolic approaches struggle. We showcase example systems and highlight the hybrid symbolic–numeric approach.

Handle notes, voices, scores and more in Wolfram Language: get a glimpse into what’s coming for symbolic music in the next release!

Bayesian networks (BNs) are graphical probabilistic models that can represent multivariate probability distributions efficiently in factored form. They can be used for reasoning under uncertainty and to evaluate the effects of evidence on beliefs. This talk presents the BayesianNetwork paclet.

Mathematica 14.3 introduced new functionality for computation with noncommutative polynomials, including polynomial transformations, polynomial reduction and Groebner basis computation. Version 15.0, coming in 2026, extends this functionality to noncommutative algebras given by generators and relations, including Weyl, Clifford and Grassmann algebras. This talk presents the new functionality and shows some examples.

This talk presents an in-depth exploration of the Zassenhaus, Baker–Campbell–Hausdorff and Magnus formulas, which decompose exponentials of operator sums in noncommutative settings. We detail their derivations, applications and recent algorithmic formulations for high-degree expansions. Special attention is given to symbolic implementations in Wolfram Language, showcasing efficient computation using custom-built functions and algebraic structures. Applications to operator theory, Lie algebras and symbolic matrix analysis are discussed.

In the past few years, we've added hundreds of new formulas to Wolfram|Alpha and greatly expanded step-by-step support. Learn about the expansion of step-by-step coverage to a new range of empirical formulas, thermodynamic calculations and equations that involve temperature values. We show off new step-by-step derivations, including new diagrams and formula descriptions to provide better physical understanding of problems. Also see Wolfram|Alpha's new handling of nonphysical results to inform users of the calculators when inputs lead to values outside the physical domain.

We briefly review new matrix and linear algebra functionality that was released in Version 14.3. We then look at further new functionality and enhancements to existing functions that are scheduled for Version 15.0, coming in 2026.

In this talk, we present convenient generic formulas for the Mellin transform of the product of N FoxH functions. In the case N == 1, the value of the Mellin transform integral is expressed through a ratio of products of gamma functions. In the case N == 2, its value is expressed through a FoxH function with joined sets of parameters. In the cases N > 2, its value is represented through a multiple Mellin–Barnes integral, evaluatable through multidimensional sums of Grothendieck residues. We present examples of such integrals with 1 <= Nt <= 3 FoxH functions, along with conditions of their convergence.

This talk introduces key topics in advanced combinatorics through the computational power of Wolfram Language. We explore discrete calculus, recurrence relations and finite sums as foundational tools. Using the OEIS interface, we demonstrate how to identify and analyze integer sequences programmatically. The session also highlights the Wolfram Function Repository for combinatorial statistics, showcasing tools for Eulerian numbers, Foata transformations and permutation analysis. Finally, we examine tree-based data structures for representing and manipulating combinatorial objects such as Catalan trees and binary search structures.

We will present some possible logical inferences from 4 points in a 3-universe using Systar, a software developed in Wolfram Language for modeling, simulating and controlling systems.

Mathematical modeling plays a major role in providing insights into the development of vaccines and selection of optimal vaccination strategies to control the spread of infectious diseases. For example, mathematical compartmental models provide answers to pertinent questions relating to R&D decisions like progression through various phases of development given vaccine properties, vaccine dose level and regimen, and design of clinical trials. In this talk, I discuss use of Mathematica in the development and analysis of some of these mathematical models used to support these decisions as well as inform vaccine recommendations once a vaccine is licensed. Examples of a few vaccine-preventable diseases are used for illustrative purposes. Dr. Elbasha is a 2025 Wolfram Innovator Award recipient.