Job Description

We are looking for someone to join the team who will be instrumental in developing and implementing advanced mathematical models that drive the ToffeeX engineering design software. You will collaborate with a multidisciplinary team to solve complex engineering problems, focusing on mathematical optimization, numerical methods for partial differential equations (PDEs), and computational geometry. This role offers the opportunity to work at the intersection of advanced mathematics, engineering, and technology in a rapidly growing company.

Key Responsibilities:

Develop and refine mathematical models and algorithms to address complex engineering challenges, particularly those involved in multi-physics simulation and associated PDE-constrained optimization problems. Collaborate with engineers and software developers to integrate new features and improvements into our cloud-based platform, bringing value to customers. Contribute to all stages of the software development lifecycle, from conceptualization to deployment and maintenance. Interact with customer success engineers to understand customer needs. Innovate beyond existing literature, developing creative approaches to solve unique real-world engineering problems.

Essential Skills & Experience

Ph.D. in Applied Mathematics, Physics, Engineering, or a closely related field. Research level experiencein numerical methods for PDEs, mathematical modelling or PDE-constrained optimization. Hands-on experience in developing and implementing numerical algorithms for solving complex simulation or optimization problems. You thrive in a fast-paced, collaborative environment

Desirable Skills & Experience:

Research level experience developing FVM/FEM solvers for physical systems. Experience in numerical optimization topics such as nonconvex, robust, or Bayesian optimization. Experience with topology or shape optimization. Experience with AI/ML methods for physics or optimization problems. Experience with software development in C++, Python, or similar languages.

Company Benefits

Flexibility and support for continuous learning and professional growth. 25 days holiday per annum (plus UK bank holidays) Private Healthcare with Vitality Health
Pension Scheme with NEST Cycle to Work scheme Perks at Work - Access to 30,000+ national & local employee discounts Work From Home Friday's Frequent Team Socials Visa Sponsorship options

Available once probationary period is complete

About us:

At ToffeeX, we are revolutionizing engineering design with our innovative software. This cutting-edge tool automates the creation of mechanical components for the engineering industry, leveraging advanced artificial intelligence, numerical simulation, and sophisticated mathematical optimization techniques. By bringing these innovations to the cloud, we empower design engineers to create components that outperform existing solutions.


We are committed to integrating the latest mathematical research into practical industry applications. Our cloud platform, built on a microservice architecture, allows us to continuously deploy advanced algorithms in optimization, computational geometry, and machine learning, keeping us at the forefront of engineering design technology.


Due to our recent growth, we have moved into a new office based in Central London where the team have a great space for collaboration. We have a fantastic culture within the company where each one of our team members is dedicated to helping ToffeeX become the best in the industry. ToffeeX has recently been named in theStartups.co.uk (https://www.linkedin.com/company/14033268/admin/page-posts/published/?share=true)100 Index 2025!


If you think this role is for you, please submit your application and we look forward to hearing from you!