Evolence is a Sydney-based company that began providing various consulting services in January 2025. Founder Dr Ben Odgers is a Wolfram certified instructor and has been a Wolfram user since 2004. In this talk we will:

1. 1. Look at how Wolfram is being used across all Evolence functions
2. 2. Take a closer look at Evolence's 'Vanalyst' ecosystem analysis product

Astronomy has long been known as a visual science, paying homage to its beginning with the naked eye looking up to the skies. In modern times, this concept continues into computer visualisation, and Wolfram Language embraces this. With accelerated development in the field of astronomy, the latest versions of Wolfram Language provide tools to query astronomical data and visualise it.

This presentation showcases how I am currently using Mathematica and Wolfram Language to facilitate university assessment marking and administration. In particular, it focuses on my use of WebExecute to automate the process of entering marks and comments into Moodle webpages, saving countless hours of drudgery and sometimes (depending on student numbers and assessment structure) avoiding thousands of repetitive strain injury–inducing mouse movements, mouse clicks and error-prone direct keyboard actions and copy-and-paste operations.

Channeling Stephen Wolfram's concepts of the ruliad, computational irreducibility, observers like us and humans as multidirectional Markov inference LLMs, we highlight the difference between ideal resource scheduling across multi-resource tasks and quantum scheduling where the outcome is limited by human time horizon choices being made at the start of a horizon period that impact choices at the start of future horizon periods.

This presentation discusses Tutoria, an intelligent tutoring system developed to support the transition to tertiary mathematics by using Mathematica as its symbolic reasoning engine. The key idea behind the project was to move beyond the use of Mathematica as a mere computational tool and instead position it at the core of the system's evaluative and pedagogical logic. In this role, Mathematica was used to test symbolic equivalence, recognise multiple valid algebraic forms, assist with simplification logic and support adaptive progression through structured tutorial pathways.

This approach addressed a persistent weakness in conventional online mathematics platforms: the inability to distinguish between an incorrect answer and a correct answer expressed differently from a pre-stored model response. By leveraging symbolic computation, Tutoria aimed to create a more mathematically authentic interaction in which student responses could be interpreted with greater flexibility and pedagogical sensitivity.

The session will outline the educational motivation for the project, the architectural role of Mathematica within the system, examples of how symbolic checking enabled improved tutorial behaviour and reflections on the opportunities and limitations of this design. The talk will conclude by considering how the ideas underlying Tutoria anticipate current interests in combining symbolic reasoning and AI for mathematics education.

The transmission of undetected infections from organ donors to recipients is a persistent concern in transplantation medicine. Despite nucleic acid testing, some infections, especially those recently acquired, may evade detection. Our research aimed to model the effects of a critical care interval before screening on the residual risk of undetected infections in organ donors.

We showed that a typical critical care interval of 2.7 days could reduce the residual risk by 43.5% for HCV, 22.9% for HIV and 7.4% for HBV—being practically significant reductions of which clinicians and recipients should be aware.

Real-world impact of this research required deployment of a suitable online risk calculator for transplant doctors which could also produce risk reports in a form that was meaningful for potential recipients. Crucially the accessibility of Wolfram Language and the ease of online deployment allowed the creation of our calculator, whereas previous pilot options had failed longer term due to technical and maintenance overheads.

We were also able to publish our online calculator as a recognised and searchable research output.

In summary, Wolfram Mathematica was an essential ingredient in the success of this research and its promulgation.

Teaching mathematics at undergraduate level to students of varying levels of strengths and skills is a challenging yet valuable experience for university teachers. The ease with which Wolfram|Alpha is appealing to students in various courses (not just related to mathematics but to life sciences too) is noted. A variety of examples are discussed. This presentation also looks at the scope and idea of introducing an AI chatbot integration into a university's learning management system (LMS) to support student learning, with enriched understanding of the underlying concepts.

How many sample points are required to exactly integrate all polynomials up to degree 77 over the unit disk? The answer, just 1015, is fewer than a naive count of degrees of freedom would suggest and is just one of the surprises in this work.

Cubature rules generalise one-dimensional Gaussian quadrature to more dimensions. An efficiency criterion (EC) sets a target for the number of sample points needed: for degree T, ideally no more than ⌈N(T)/(d+1)⌉ points, where N(T) counts the monomials to be integrated exactly and d is the dimensionality. Gaussian quadrature exactly meets this criterion in 1D, but schemes are found to beat this target in 2D, earning the designation of super efficient. How is this possible?

The key is to exploit symmetries. For example, when samples are arranged with sixfold rotational symmetry, the Zernike polynomial decomposition of the integrand reveals that azimuthal orders not divisible by six are handled automatically. This is found to reduce the effective constraint count by more than a factor of six, opening the door to schemes that beat the EC.

Visualisation of these configurations (sometimes in a warped coordinate space) reveals striking geometric structures: spiraling arrangements reminiscent of sunflower phyllotaxis as well as reflection-symmetric solutions and Voronoi cells that transition from honeycomb patterns near the center to rings of diamonds closer to the boundary. Mathematica's visualisation and optimisation tools make this landscape irresistibly accessible to exploration. This talk presents some known super-efficient schemes varying from degrees 17 to 77 and surveys a class of open cases that stand as unsolved challenges for high-dimensional global optimisers.

Counterintuitive phenomena in modern physics often challenge students and educators alike. This presentation demonstrates how computational visualisation can transform abstract equations into intuitive, dynamic learning experiences. Using a didactic approach in Wolfram Mathematica, this work develops interactive simulations that make challenging theoretical concepts from relativity, quantum mechanics and statistical physics tangible.

Central to this work are interactive implementations of Lorentz transformations and relativistic visualisations, which clarify the non-intuitive nature of reference-frame transformations and light propagation. The same computational framework is also applied to quantum and statistical domains: squeezed-state models illustrate minimum uncertainty relations, animated atomic dipole transitions reveal photon emission and wave-packet formation, and Bose–Einstein condensation simulations depict quantum state occupation and emergent collective behaviour at low temperatures.

Together, these examples show how symbolic computation, real-time simulation and interactive deployment create a practical educational framework. Attendees will see how the Wolfram ecosystem makes complex physical concepts accessible, providing adaptable tools for high-school instruction, undergraduate courses and STEM outreach.

Wolfram Notebook Assistant transforms the way educators and researchers can interact with computational tools in physics. This presentation explores how the intelligent features of Notebook Assistant enhance productivity, foster conceptual understanding and streamline research workflows. We will showcase how the assistant's context-aware suggestions, integrated documentation and code generation empower users at all skill levels to explore complex physical phenomena interactively.

Using the Wolfram Quantum Framework as a case study, we will demonstrate how quantum mechanics concepts, such as quantum states, circuits and simulation, can be introduced and investigated within the notebook environment. Attendees will learn best practices for leveraging Notebook Assistant to create engaging learning materials, facilitate discovery-based teaching and accelerate research. Whether for classroom instruction or research, the combination of Notebook Assistant and Wolfram Language tools opens new horizons for physics exploration.