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Why proofs are necessary in mathematics?
According to Bleiler-Baxter & Pair [22], for a mathematician, a proof serves to convince or justify that a certain statement is true. But it also helps to increase the understanding of the result and the related concepts. That is why a proof also has the role of explanation.
What is the point in learning proofs?
If you discover that something is true and want to convince other people that it is true, you have to present them with a proof, otherwise they will not believe you. Besides, constructing a proof helps you better understand the result and why it is true.
Is it possible to use only math that has been proven?
It depends what you are going to do in math. It is possible in many cases to use only math that has been proven by others. The more sophisticated math you need to use, however, the more proofs will enter into. For example, in computers, you will occasional need to prove that an algorithm completes with in a certain amount of time.
Do you need pure mathematics to use these tools?
So, in general, you don’t need the rigor of pure Mathematics to use these tools. In Math we usually don’t study proofs or proofing (Proof theory is an advance topic that not a lot of people get into) proof are a tool used to construct mathematics, we used them to illustrate the logical reasoning of why something is or isn’t.
Is it possible to self-study university level mathematics?
Self-study of university level mathematics is not an easy task, by any means. It requires a substantial level of discipline and effort to not only make the cognitive shift into “theorem and proof” mathematics, but also to do this as a full autodidact.
Should we stop trying to teach math to kids?
This math and math above it are completely useless in real life, so we should quit trying to teach it to kids and replace it with something that has a more practical application to real life. My answer to this article would have been something like, “Stop dumbing down our kids!