https://www.linkedin.com/pulse/what-does-mean-concept-well-defined-john-gabriel/

]]>Rigor is needed for precise definitions of new concepts and for checking proofs of claimed new theorems. It is also needed for precise objective(!) communication of mathematical derivations (since “intuitive derivation” is unreliable, imprecise and subjective)

]]>The curriculum for graduates needs to be broader. Why is analysis and algebra the core? There are more parts of math then this and maybe people are not interested in this area. I hate being forced to do math I don’t consider interesting. Personally I would prefer to study other areas of math rigorously not analysis and algebra. So I cant be a mathematician if I don’t learn the precise math the universities want me to. So then how do you discover new ideas? We only allow people to discover new ideas after they have a Ph.D. an did math the way the university made them do it. That way they discover ideas related to their goals.

It seems like math gets narrower and narrower in its methods, and we will converge to only doing proofs. At that point its just a game of symbols with no numbers. And we are going back over stuff that is already known and redoing it again with sets. We already know the derivative. And we don’t need sets to help with this. We need to create new ideas that are as great as the derivative instead of staying at the derivative and floating around it. Its for people who are not creative and are computers and people who memorize. The derivative is only important because it can solve problems. Math is only for solving problems. I wish I could have been a mathematician in 1600s instead of “modern” mathematics. The “modern” mathematicians want to act like they did something great but there is nothing. The derivative was the only great idea for hundreds of years.

What is also funny is we use greek and latin letters to look cool even though we don’t speak latin or greek. We should redo these symbols in English since we read and write in English. Thats what the ancient mathematicians did. The math was in their language. But we use their notation even though we use a different language. We are not doing math like they did with respect to notation. We are less intuitive. I think the way we learn mathematics at the universities is foolish and with its methods of learning will never shape minds into their best geniuses. Because this school system rejects people if they don’t do it their way. The curriculum need to meet the learning styles of everyone. So all we are doing is generating mathematicians that are robots for proofs, and they have no creativity and therefore the only creations will be derived from proof. With this in mind new definitions will probably rarely occur and the derivative will remain the greatest discovery because of the universities lack of supporting creative mathematicians over computerized mathematicians. ]]>

For those who’re just starting with higher math, this guide on higher math learning could be a first step towards a holistic experience. Math is both a scientific and artistic endeavor, and focusing one aspect of it exclusive to all others can lead to a skewed perspective on mathematics too.

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