## Our Mission and Vision

It is our goal to help you to become a better thinker by teaching you to use the most impenetrable form of reasoning available to humankind: mathematics. Our vision is to provide a transformative learning experience for students in the areas of mathematical contests and proof-writing through individual coaching and live courses.

## Our Philosophy

At the core of our pedagogical philosophy lies the following question:

*What is the interplay of intuition and rigour in mathematical activity?*

Mathematical intuition is creative freedom and mathematical rigour is structured reinforcement. Both are essential to the practice of mathematics, and indeed all analytical fields. We make an effort to emphasize both aspects of mathematics. Here are more specific details about our philosophy when it comes to teaching and learning:

- When reasoning intuitively, we use diagrams, try out examples, and do concrete computations.
- When reasoning rigorously, we always dig deep by asking ourselves “What does this mean?” and “Why is this true?”
- We try to assign work to students that is meaningful so that they will be more inspired. We avoid rote computations, which are neither intuitive nor rigorous when the associated algorithms or formulas are not explained.
- Within our proofs curriculum, we believe in both short-term problem-solving, akin to sprints, and long-term theory-building, akin to marathons.
- When needed, we prefer to communicate the main idea instead of pedantically pointing out every minor detail that the student could independently verify.
- We are as truthful as possible with our audience by clearly stating any assumptions, deficiencies or omissions, in order to give a precise picture of our level of exposition.

- Don’t avoid pattern recognition but focus on recognizing heuristics that are widely applicable instead of superficial characteristics such as formulas that apply to only niche scenarios. Examples of famous heuristics are to work on a simpler question or to work backwards.
- While some schools are pro-memorization or anti-memorization, we recommend that you gain a general sense of relevant theorems, and write up personal notes that can be consulted for the details. Some degree of memorization is needed for exams, but constant usage of theorems often results in remembering how to apply them.
- Learning is never complete and no version of a theorem or proof is the final word on it. Always be ready to be surprised by new light being shed on an old idea. Sometimes, you might even have to reformulate your entire understanding of the mathematical universe.

## Our History

We are Existsforall Academy, a private academy for the mathematically inclined. Existsforall was founded in 2021 by Samer Seraj, our Principal. The origins of Existsforall go back to Seraj’s high school years when, in the midst of undertaking preparation for the Canadian Mathematical Olympiad, he started a club for sharing his knowledge with his peers. After graduating from school, he spent four years learning higher mathematics and earned his degree in mathematics from the University of Toronto. During that time, he held two prestigious research grants, a USRA and a UTEA, and was the President of the undergraduate Mathematics Union. He then moved to San Diego, California to work at a premier education company. At this institution, he was a mathematical instructor for hundreds of students, a curriculum developer who created world-class materials that were implemented by other teachers, and the direct manager of a team of over five hundred educators. After several years of gaining experience in the industry, he returned to his hometown in the Greater Toronto Area and decided that it would be the goal of his life to elevate the worldwide state of mathematics education. Thus, Existsforall Academy was born.