Learning Philosophy
1707 – 1783
Leonhard Euler pioneered graph theory, introduced function notation, and popularized the constant e, making key advances in calculus, number theory, and topology. He solved complex problems in infinite series, mechanics, and applied mathematics, and his work profoundly shaped both mathematics and physics, leaving a legacy that continues to influence the field today.
“Commitment”
The best thing about math is also the worst – its an endless wealth of knowledge. As such, math has a way of making students feel like they don’t know much at all, regardless of how much they’ve learnt. The simple truth is that math is hard and even the most capable will hit a wall eventually.
“Belief”
Mathematics is about simplifying and slowing things down. It’s about dissecting a problem into its most basic components, understanding each separately, then putting them back together to reach a clear conclusion. Speed comes naturally with practice and repetition. It should not be the priority. Enjoying the process and rushing to get it done are two notions that are at odds. If you rush to solve a problem, then you’re probably going to make a mistake, then rush right past it – leading to even more mistakes which you’re unable to explain because you missed the very first.
1811 – 1832
Galois revolutionized mathematics by developing Galois theory, which links polynomial equations with group theory. He determined which equations can be solved by radicals, laying the foundation for modern abstract algebra. His groundbreaking insights, formulated in his early teens and twenties, profoundly influenced number theory, algebra, and geometry before his untimely death at 20.
300 BC
Euclid, often called the “Father of Geometry,” systematically organized the knowledge of his time into a coherent, logical framework in his seminal work, Elements. He developed the axiomatic method, proving theorems from a small set of definitions and postulates, which became the foundation of modern mathematics. His work influenced geometry, number theory, and mathematical reasoning for centuries, shaping both education and scientific thought long after his lifetime.
“Motivation”
Don’t resent math for challenging you, and please dont resent yourself for struggling with math. Sitting with a problem, thinking it through, and exploring different possibilities is 90% of what math is all about. If frustration sets in, remind yourself that trial and error is a vital part of the learning process. You will need to hit walls before you can overcome them. Please go slowly, stay focused, and practice as often as you can. Like any skill, the more you exercise the mathematical part of your brain the stronger it wil become.
“Resilience”
To get the most out of tuition, it’s strongly recommended that you attend weekly lessons, focus during lessons, take notes during lessons, attempt problems during lessons, practice consistently, and provide constructive feedback between lessons. Participation is a very efficient way for students to validate their understanding and is a necessary tool for effective tuition. Don’t be ashamed to ask questions, and during explanations please politely interject if you don’t understand something, lose track, or require a slower pace. The whole point of tuition is to follow along with your tutor and learn something new. Relax during lessons, embrace the rate at which you naturally learn, and have faith that you will improve over time.
570 – 495 BC
Pythagoras, the ancient Greek mathematician and philosopher, is best known for the Pythagorean theorem, linking the sides of right-angled triangles. He founded a school that combined mathematics, philosophy, and mysticism, emphasizing numbers as the underlying principle of the universe. His work influenced geometry, number theory, and the concept of mathematical harmony, leaving a lasting legacy that shaped both Western mathematics and philosophy for centuries.
“Perseverance”
Mathematics gives us something unique and pure that cannot be found elsewhere. It gives us incontrovertible truth. When you learn something in math it doesn’t go away, fade, or die. It’s there forever, and no one can tell you differently. This is what makes learning math so worth the effort. My strongest recommendation to you, the student, is that you stop perceiving mathematics as a bottomless pit and start viewing it as an endless ladder – everpresent for you to reach new heights.
1879 – 1955
Albert Einstein made groundbreaking contributions to both mathematics and physics, transforming our understanding of the universe. In physics, he is best known for developing the theory of relativity, which includes the special theory of relativity (1905) and the general theory of relativity (1915), fundamentally changing concepts of space, time, and gravity. His famous equation, E = mc², revealed the equivalence of mass and energy, revolutionizing energy research and nuclear physics. Beyond relativity, Einstein contributed to quantum theory, explaining the photoelectric effect, for which he won the Nobel Prize in 1921, and advancing statistical mechanics, Brownian motion studies, and theoretical cosmology. Mathematically, his work relied on sophisticated tools such as tensor calculus to describe the curvature of spacetime, bridging abstract mathematics and physical reality in ways that continue to influence modern physics.