### Stephen Wolfram

Stephen Wolfram is the author of A New Kind of Science and the principal lecturer at the Summer School. He is the creator of Mathematica, the creator of Wolfram|Alpha and the founder and CEO of Wolfram Research. Having started in science as a teenager (he got his PhD at age 20), Wolfram had a highly successful early career in academia. He began his work on NKS in 1981 and spent ten years writing the NKS book, published in 2002. Over the course of 30 years, Wolfram has mentored a large number of individuals who have achieved great success in academia, business and elsewhere. Starting the NKS Summer School (now called the Wolfram Summer School) was his first formal educational undertaking in 16 years.## Directors

### Xerxes Arsiwalla

#### Fundamental Physics Director

Xerxes is a theoretical physicist. He worked on black holes and string theory during grad school. He did his postdoctoral research in computational neuroscience and complex systems. In addition to fundamental physics, he is interested in the philosophy and foundations of mathematics. He also maintains an interest in the problem of consciousness and intelligence, particularly in mathematical approaches to the mind-body problem.### Mads Bahrami

#### Science & Tech Director

Mads Bahrami joined Wolfram in 2018. He is interested in developing computational paradigm for any field of research, in particular, STEM education, religion, etc. Mads received his PhD in physical chemistry from Sharif University of Technology. His field of research is the foundation of quantum theory and quantum stochastic processes. He did his postdoctoral research in the EU under a Marie Curie fellowship and also in the US at the University of California, Riverside. Mads is also a lecturer of general chemistry, physical chemistry and quantum theory at different universities and community colleges in Los Angeles.### Hatem Elshatlawy

#### Fundamental Physics Assistant Director

Hatem joined Wolfram Research in 2020 as one of the research managers of the Wolfram Physics Project and was a participant in the Wolfram Summer School (Fundamental Physics track) in 2020. He studied theoretical physics at the University of Freiburg, the University of Vienna and RWTH Aachen University. Currently, he is based at the Munich Center for Mathematical Philosophy. In addition to fundamental physics, he is interested in the history, philosophy and foundations of mathematics.### Robert Mendelsohn

#### Science & Tech Assistant Director

Robert Mendelsohn joined Wolfram Research in 2019 and was a participant in the Wolfram Summer School in 2014. He earned a bachelor’s degree in mathematics from the University of Texas in 2019. He has worked for Heartland Payment Systems, Nokia and several defense contractors in areas related to cryptography and cybersecurity.### Paul Abbott

#### Academic Director

Paul Abbott is an adjunct professor at the University of Western Australia. He obtained his PhD in theoretical atomic physics from UWA in 1987, worked for Wolfram Research from 1989–1992 and has been a Wolfram consultant and instructor since 1997. Paul was the founding technical editor of*The Mathematical Journal*in 1990 and was a columnist until 2010. His interests range from computational physics, applied mathematics and special functions to courseware design. All of his research and teaching since 1985 has used Wolfram technologies in some way, and his work has been recognized most recently by a Wolfram Innovator Award in 2015 and an Australian University Teaching Award in 2016. In his spare time, Paul enjoys cycling, walking, swimming, photography, reading and writing.

### Jonathan Gorard

#### Physics Track Director

Jonathan Gorard is a research mathematician at the University of Cambridge, where he works on a variety of problems related to the intersection of mathematics, physics and computation; having published his first scientific paper at 17, his published work now covers topics ranging from computational complexity theory, combinatorics and cosmology to general relativity, mathematical logic and the foundations of quantum mechanics to cellular automata, complex systems and quantum computation. Since 2017, he has also worked as a mathematical consultant for Wolfram Research, Inc., leading the development of Wolfram Language’s automated theorem-proving and quantum-computing frameworks and working on various related areas, such as semantic representation of mathematics, symbolic logic, discrete-state quantum mechanics and graph theory. He is also one of the principal researchers on the Wolfram Physics Project, having made several key contributions to the mathematical formalism of the Wolfram model (particularly in regards to the derivations of general relativity and quantum mechanics and its connections to quantum information theory); he has also done extensive algorithms development work for the Physics Project, particularly in relation to multiway evolution, hypergraph isomorphism testing, causal graph computation, causal invariance testing and the application of automated theorem-proving techniques. He attended the Wolfram Summer School as a student in 2017 and has been an instructor since 2018.## Instructors

### Christian Pasquel

#### Instructors

Christian Pasquel was part of the first group to join the Wolfram Research South America team in Lima, Peru, back in 2012. He has a physics background and worked on research during his first professional years. He currently manages the South America Connectivity group, working on connecting the Wolfram Language to external services and making blockchain and cryptocurrency data computable. His interests include evolutionary biology, astrobiology, artificial intelligence, music, films, books, playing with data and everything tech related. A self-proclaimed Wolfram fan, he enjoys livecoding and works on generative art projects using Mathematica. He is a cat lover and had the main part in an official music video available online.### Christopher Wolfram

#### Instructors

Christopher Wolfram is a full-stack programmer and algorithm developer who has been programming in Wolfram Language since a young age. He has been the lead developer for several built-in Wolfram Language functions (including Nearest and Encrypt), as well as for Tweet-a-Program and several of his own apps. He has presented at SXSW, Maker Faire, livecoding.tv and other venues on topics such as machine learning, data science and IoT programming. Christopher enjoys 3D modeling, Haskell, Swift, history, tennis and traveling. He has been a mentor for the Wolfram Summer Programs for five years.### Connor Gray

#### Instructors

Connor Gray is a software developer on the Engine Connectivity Engineering team, having joined Wolfram Research in 2016 as an intern on the Wolfram Compiler project. His work is currently focused on building tooling for authoring Wolfram paclets, maintaining WSTP (Wolfram Symbolic Transfer Protocol) and developing the next-generation Wolfram Language package format. He is interested in compiler technology, software tooling and development processes, and API and user interface design. In his free time, he enjoys reading, having deeply nested conversations, improving his personal organizer system, entertaining thoughts on practical idealism and thinking about how to leverage proven communication mediums (notebooks, essays, checklists, etc.) and reliable technology in new and meaningful ways to improve effectiveness and well-being.### Jack Heimrath

#### Instructors

Jack Heimrath is a PhD candidate in pure mathematics at the Wroclaw University of Science and Technology. Before grad school, he read Part III at the University of Cambridge. His areas of interest include analytic number theory, dynamical systems and the interplay between the two. Jack was a student at the 2019 Wolfram Summer School, after which he heavily integrated Wolfram technologies into his teaching. Aside from teaching and learning mathematics, he enjoys reading comic books, bouldering, solving nonograms and studying chess endgames.### Jesse Galef

#### Instructors

Jesse Galef is a research scientist who joined the Machine Learning team at Wolfram in 2020. He got his master’s in computer science from Columbia after going through and being a TA for the General Assembly data science program in Boston. Before specializing in machine learning, Jesse worked in the nonprofit sector as a media relations professional promoting effective altruism and the reduction of global catastrophic risks.### Jofre Espigulé Pons

#### Instructors

Jofre Espigulé Pons has a background in physics. Prior to joining Wolfram, he did research on quantum physics and biophysics, in particular on the magnetoreception of birds and the limits of human vision. He was a student at the Wolfram Summer School 2015, where he used machine learning to identify species of birds based on their songs. He has a broad interest in topics ranging from computational linguistics to computational sports.### Jon Lederman

#### Instructors

Jon Lederman is a physicist with interests in quantum field theory and general relativity. He is particularly interested in the emergence of ordinary quantum mechanics and relativistic quantum mechanics in the Wolfram model. Although the Wolfram model relies on objects with minimal structure, known physics relies on mathematical structures such as continuous manifolds for special and general relativity (spacetime itself) and Hilbert spaces for quantum mechanics. To this end, Jon is focusing his theoretical research on how these fundamental mathematical structures may be defined within the Wolfram model to support the emergence of known physics within the Wolfram model. In particular, he is researching the application of category theory and topological quantum field theory to the Wolfram model building on the fundamental research of Baez and Lurie. Jon is also a tech entrepreneur. He is the founder of Spinor, a tech startup that is developing voice AI technology. He is also building a science educational platform called Physica that is aimed at creating high-caliber educational content in physics, mathematics, computer science and other fields. Prior to Spinor, Jon founded and built the technology platform SonicCloud, a venture-backed and award-winning audio technology company that has commercialized audio enhancement technology. Jon worked on his doctoral research in physics at UCLA and Brookhaven Labs. He also holds two master’s degrees in electrical engineering from Stanford and Columbia. He completed his undergraduate work at Harvard, majoring in music theory and composition. Jon is an avid musician and songwriter.### Marco Thiel

#### Instructors

Marco is an applied mathematician with training in theoretical physics and dynamical systems, which many people might know because of a subarea called chaos theory. He is full professor at the University of Aberdeen (UK). Apart from some more theoretical work in mathematics, his main area of work is mathematical modeling. He uses mathematical structures and patterns to describe a large variety of systems. Some of the applications he has worked on so far are Alzheimer’s disease, epilepsy, traffic modeling, studying the stability of our solar system, modeling the life cycle of a biological cell, population dynamics, the synchronisation of heartbeats of mother and foetus, financial and forensic mathematics, voting patterns, movement of newborns, climate modeling, whiskey making, accident reconstruction, and patterns in the mating behavior of fireflies. A lot of his work involves the analysis of data, i.e. informing and testing models with data. In 2017, Marco received the Wolfram Innovator Award; he is also an instructor for the Wolfram Language. He coordinates a data science postgraduate degree program, which is taught using the Wolfram Language, at the University of Aberdeen.### Max Piskunov

#### Instructors

Max Piskunov is a researcher and a software engineer in the Wolfram Physics Project. He has been in the project since the beginning. He is the primary developer of SetReplace, the package used to run Wolfram models, which he started developing at the beginning of 2019. Max attended the Wolfram Summer School as a student in 2014, 2015 and 2019 (each time under a different name) and is joining this year for the first time as an instructor. He got his MS in physics from Moscow State University. He started a physics PhD at Northeastern University but quit to pursue the Wolfram Physics Project. He also did an internship at Lyft’s self-driving division, where he worked on camera-to-LiDAR calibration. Max is a vegan and is involved in the animal rights movement. In his free time, he goes hiking, dabbles in flying photography drones and composes music.### Nikolay Murzin

#### Instructors

Nikolay was always into computer science, programming and hacking, but he was curious and graduated with a specialist’s degree in physics from Moscow State University. Then after trying himself as a web developer for a bit, he got into IBM as a research software engineer and data scientist, working with statistical models, computer vision and natural language processing in mostly retail and supply-chain related projects. He enjoys reading books and papers on the subjects of machine learning, math and physics and also listens to a lot of science and science fiction audiobooks. Nikolay likes to take part in competitions and hackathons, quickly dives into new technologies and continuously learns new things.### Robert Nachbar

#### Instructors

Robert Nachbar is senior project director in Wolfram Solutions, the consulting arm of Wolfram Research, where he both leads technical teams and develops custom applications for clients with Wolfram technologies. He joined Solutions in 2014 after retiring from the pharmaceutical industry, where he used Mathematica and other Wolfram technologies for drug design, data analysis and clinical research. He holds a PhD in organic chemistry from Brown University and received the Wolfram Innovator Award in 2012. His research and computational interests include chemistry, biology, discrete mathematics, optimization, simulation and interactive visualization. He has been a frequent presenter at Wolfram Technology Conferences.### Tuseeta Banerjee

#### Instructors

Tuseeta Banerjee is a Research Scientist in the Machine Learning team, focusing on applications of neural networks. She imports and implements neural net models in the Wolfram Language for various high-level functions in Mathematica and for the Wolfram Neural Net Repository. In her previous role as a technology engineer, she provided machine-learning based solutions to clients. She is also a certified Wolfram language instructor, teaching and creating various courses on Mathematica programming with a focus on statistics and deep learning. Prior to joining Wolfram, she completed her Ph.D. in 2015 from the University of Illinois at Urbana Champaign with her research work in the field of chemical physics and certification in Computational Science and Engineering. For her Ph.D. research, she used Monte Carlo-based quantum-classical path integral methods to study models that mimic chemical reactions and photosynthetic reaction centers.## Teaching Assistants

### Cameron Beetar

#### Teaching Assistants

Cameron is a mathematical physics MS student at the University of Cape Town, South Africa. He graduated with his BS in physics, mathematics and computer science at the beginning of 2020 and completed his Physics Honours at the end of 2020. He has a passion for learning and is more than happy to discuss any interesting ideas someone might have. He is currently using neural networks to probe phase transitions for some interesting quantum many-body problems and how these transitions are affected by changing the topologies of the systems. With regards to the Wolfram Physics Project (WPP), he is studying the Einstein equations from a sort of hydrodynamic perspective. Using the WPP formalism, he hopes to be able to derive higher-order corrections to Einstein’s equations. This could have incredibly interesting implications for the way we understand our universe near black holes (or near any significantly strong gravitational field). He has a growing interest in discrete differential geometry (which can also partly be attributed to his work with the WPP). Outside of physics, Cameron is a keen rock climber and a lover of mountains—he has even been to the Himalayas and summited two +6000m peaks! He also loves art and poetry (although in a more casual way than he does physics).**YEARS:**

### Carlos Muñoz

#### Teaching Assistants

Carlos Muñoz started working as a Consultant for Wolfram|Alpha in September 2019 and attended the Wolfram Summer School twice (in 2016 and 2019). His interest in systems biology led him to learn to program in the Wolfram Language, and he is currently finishing his undergraduate biology thesis on genetic regulatory networks. Besides work and his thesis, Carlos enjoys doing small science projects, making jewelry, playing video games and taking care of his pet ant colonies.### Daniel Sanchez

#### Teaching Assistants

Daniel Sanchez joined Wolfram Research as a developer for Wolfram|Alpha in June 2017. He earned a bachelor’s degree in physics from PUCP (Lima, Peru) in 2018. However, his interests now lie in the foundations of computation and the implementation and design of programming languages. These will be his research topics when he starts an MS in computer science. His hobbies—when he is not in front of a computer—are playing Super Smash Bros. Melee, studying Japanese and playing with his 15-year-old dog, Archie.### Fez Zaman

#### Teaching Assistants

Fez works full time as a lexical programmer at Wolfram|Alpha. He has a BS in cognitive science from SUNY Oswego, where he also minored in computer science and audio production and design. His work centers around music, programming, the computational arts and the philosophy of mind. He attended the Wolfram Summer School in 2016 and 2018, and after joining Wolfram|Alpha, he mentored at the Wolfram High School Summer Camp in 2019 and 2020.### Jean Du Plessis

#### Teaching Assistants

Jean is a theoretical physics student at Stellenbosch University. He has a special interest in mathematical physics, especially general relativity. He participated in the Wolfram Physics Winter School, where he got involved with the relativity side of the Wolfram Physics Project. He now loves being a junior research affiliate for the Wolfram Physics Project. His wider interests include economics, chess and math. He also loves a good discussion about interesting topics.**YEARS:**

### Julián Laverde

#### Teaching Assistants

Julián is a physics engineer from the National University of Colombia (2020) and a photonics master’s student. He focuses on modeling optical phenomena and nonlinear integrated photonics. Julián joined Wolfram in October 2020 as a consultant for the Special Projects team after assisting the Wolfram Summer School 2020. He enjoys cooking while listening to history podcasts and playing with his two cats.**YEARS:**

### Mano Namuduri

#### Teaching Assistants

Mano is a programmer in the Special Projects department of Wolfram Research and a Research Fellow with the Wolfram Physics Project. She graduated with a bachelor’s degree in physics and mathematics from Minerva Schools in 2020 and started a master’s in physics at ENS Paris in fall 2021. Having participated in the inaugural Fundamental Physics track of the Wolfram Summer School in 2020, Mano is extremely excited to continue exploring the foundations of physics, simple computational systems and mathematical logic with her mentees at this year’s Summer School.### Sam Whittington

#### Teaching Assistants

Sam Whittington is a mathematician and theoretical physicist working toward a PhD that focuses on Lorentzian Kac–Moody algebras and their uses in quantum fields and string theory. In previous research at Imperial College London, his work focused on computational simulations and searches for emergent spacetime in theories of quantum gravity. In addition to theoretical and computational physics, Sam has a keen interest in cyber security, computer science and software development and has worked on several machine-learning models and web apps. He is currently working on a project to help researchers find research relevant to their own, especially in areas of literature they may not be so familiar in.**YEARS:**