“A student well versed in even one technique will naturally see corresponding points in other techniques. A upper level punch, a lower punch, a front punch and a reverse punch are all essentially the same. Looking over thirty-odd kata, he should be able to see that they are essentially variations on just a handful.” – Gichin Funakoshi
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Progressive skills and knowledge development are keys to long-term progress in the martial arts……. and similarly in mathematics, since everything that you learn is merely a preliminary foundation for the next level.
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Learning in martial arts, and mathematics, is like building a house. A solid foundation is required so that the structural integrity of the house remains intact. Similarly, practitioners need to take the time to build a solid foundation of basic skills and concepts, and constantly refine and add to this base so that they can expand their knowledge.
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There are neither concepts in martial arts, nor skills in mathematics, that can exist without foundation. Therefore, failing to develop a proper understanding of fundamental concepts and principles, prevents the student from improving and refining his skill level.
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When one learns a new martial arts technique, or a mathematics concept, he or she must incorporate the elementary principles they already know with the new knowledge in order to broaden its scope and applications.
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When it is difficult to grasp a new step or concept, a student needs to break it down
by isolating the appropriate relationships and properties, and then practice or study them separately through continuous practice and self-reflection.
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The learning process starts with the introduction of basic concepts or techniques; the instructor then gradually increases the complexity and difficulty of the material as a student advances.
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In martial arts, the student starts with learning basic punches, kicks, ‘blocks’, and stances. Once comfortable with the basics, the student learns how to put them together in kata and fighting practices. Similarly in mathematics, as the student’s knowledge grows, new ideas and concepts are introduced that build upon the previous ones.
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To become experts in both disciplines, students must not only acquire facts, but also organize their knowledge to facilitate the applications in many different and diverse situations. It is this understanding that makes one a formidable fighter…… or a mathematical expert, and enables him / her to use the knowledge or techniques creatively, flexibly, and fluently, in different settings or problems.
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Mastery in the martial arts, and in math, doesn’t just happen, you achieve mastery over time. Achieving mastery is a slow, gradual and often frustrating process. Patience is an essential quality of both martial artists and mathematicians….. And discipline is crucial since the improvement is a gradual, day-by-day process.
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Martial arts and Mathematics…. Connected art forms. 
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