A PhD student in mathematics at the University of Warwick with a first-class master's degree in physics from the Uni of Manchester. I primarily teach GCSE and A-level maths, further maths and physics.

Find out more about Luke

• 1) When did you develop an interest in your chosen field and in private tutoring?

  I've always had a natural aptitude for mathematics, but my interest in physics truly took off midway through my A-Levels when I was introduced to cosmology. This newfound subject motivated me to pursue physics at university, where I explored a wide range of topics. However, it was in my final year that I discovered my real passion for statistical physics and agent-based systems, leading me to pursue a PhD in this field. My enthusiasm for tutoring began when I started teaching at university. Since then, I have thoroughly enjoyed working with students, both one-on-one and in group settings, helping them develop their understanding and confidence in mathematics and physics.

• 2) Tell us more about the subject you teach, the topics you like to discuss with students (and possibly those you like a little less).

  At A-Level, my favourite topics to teach in mathematics are integration and vectors. These concepts can be challenging for students to grasp intuitively, and I enjoy the process of breaking them down in a way that makes them more accessible. I often relate them to principles from physics to provide deeper insight. In physics, I particularly enjoy teaching astrophysics and cosmology, likely because these subjects first sparked my own passion for the field during my A-Levels. At GCSE level, I find it especially rewarding to teach the foundational ideas of set theory and probability, as well as conservation laws in physics. I also enjoy helping students recognise the relationship between mathematics and physics - two subjects that are often seen as separate at this stage but are, in reality, deeply connected. By showing how mathematical concepts underpin physical principles, I aim to bridge this gap and give students a more cohesive understanding of both subjects.

• 3) Did you have any role models; a teacher that inspired you?

  Throughout my academic journey, I've been fortunate to learn from many inspiring students, teachers, and supervisors. One lecturer who particularly stood out was the professor who taught me early universe cosmology. His passion for the subject was evident in the way he taught - he was deeply engaged and put real effort into breaking down complex ideas into clear, manageable parts. His approach showed me the importance of genuinely enjoying the subject you teach, as that enthusiasm makes a real difference in how students engage with the material.

• 4) What do you think are the qualities required to be a good tutor?

  One of the most important qualities of a tutor is recognising that students have different ways of thinking and learning. Adaptability is key-being able to break down problems in multiple ways ensures that each student can engage with the material in a way that makes sense to them. Some students grasp concepts quickly, while others may take more time, and it is essential to tailor your approach accordingly.
  
  Equally important is empathy. I remind myself that there was a time when I, too, struggled to understand the very topics I now teach. Reflecting on the support I would have found helpful allows me to be more patient and effective in guiding students through their own challenges.
  
  A common hurdle I see among students is a lack of confidence. Often, their difficulties stem not from an inability to learn but from self-doubt. As a tutor, my role extends beyond teaching concepts-I aim to instill confidence in my students, helping them believe in their abilities. This, in turn, creates a positive feedback loop, where increased confidence leads to greater engagement and improvement in the subject.

• 5) Provide a valuable anecdote related to your subject or your days at school.

  A common challenge I see at A-Level is students memorizing the integration by parts formula without truly understanding where it comes from. Yet, they already have all the tools to derive it themselves. I always remind students that it's just an application of the product rule for differentiation in reverse - if you differentiate u(x)v(x), integrate both sides, and rearrange, the formula naturally follows. Once students see this, it often clicks, and they realize they don't need to completely rely on memorisation. Instead, they develop a deeper intuition for why the method works, which helps them apply it more confidently in different contexts.

• 6) What were the difficulties or challenges you faced or still facing in your subject?

  During my PhD, one of the biggest challenges is encountering problems that don't have readily available answers. Unlike at earlier stages of education, where you can often refer to textbooks or online resources, research requires tackling problems that may not yet have a known solution. This can mean being stuck on the same problem for weeks at a time, requiring persistence, creativity, and a willingness to explore different approaches.
  
  While frustrating at times, these challenges are also what make research so rewarding. They push me to develop a deeper understanding of my field and refine my problem-solving skills. Through this process, I've learned that progress is rarely linear.

• 7) Do you have a particular passion? Is it teaching in general or an element of the subject or something completely different?

  My real passion lies in the work I do during my PhD, where I research agentic systems and apply mathematical tools to better understand them. At the same time, I find that a deep passion for learning drives everything I do. Like many other students, I enjoy immersing myself in complex problems, becoming fully engaged with a topic, and striving to understand it from every angle. Teaching is also an extension of this passion - explaining concepts to others challenges me to refine my own understanding, reinforcing what I know while helping others grasp the subject as well.

• 8) What makes you a Superprof (besides answering these interview questions :-P) ?

  What makes me a SuperProf is my ability to teach a wide range of levels across both mathematics and physics. I have experience working with students from GCSE and A-Level through to university, adapting my teaching approach to suit different learning styles and academic goals.
  
  Beyond simply covering the material, I focus on building students' confidence and helping them develop a deeper understanding of the subject. In my time teaching, I've guided many students toward achieving their target grades, and it's incredibly rewarding to see their progress. Whether it's breaking down complex university-level concepts or strengthening fundamental skills at GCSE, I strive to make learning engaging, accessible, and tailored to each student's needs.