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What is the proper relationship to knowledge cannot validate?

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I am student at a High School in Norway. One of my favorite subjects is math, and I have been able to skip one year due to very good results. Unfortunately, I have realized that most of what we learn is math whiteout any proper validation: A simple example is that we learnt the ABC formula and how to use it without any explanation of why it actually work. I can, of course, see that the formula work, but not understand why it do so. 

My question is, therefore: What is the proper relationship to knowledge (for example math) you cannot validate? 


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