I tend to consider mathematics the body of axioms, definitions, systems of logic, and their results. If you're not adding to this body, you're not doing mathematics.
Arithmetic, calculating, solving, and so on, just seem more like accounting than mathematics. If anything, I would call these things "calculus" after the original Latin root word, referring to a stone used for counting.
Maybe it's pedantic. But I don't think so. A lot of people who "hate math" really hate "calculus." And honestly, being good at mathematics, at constructing proofs, etc is so different from being good at working with numbers. I'm decent at the former. I'm horrible when it comes to the latter.
Hello Bawar Mohammed Faraj,
Would you kindly expand on your answer? Why shouldn't we?
Hello,
every good mathematician seems to be a good calculator, this is an observation from my experience as both a researcher and a teacher. The calculus actually develops your brain for abstract activities , altough it sounds paradoxical. Under simple calculation are fundamental mathematics, keys to many proofs.
So I conclude that you cannot really do maths when you don't see the magic of calculus.
Gabriel
> So I conclude that you cannot really do maths when you don't see the magic of calculus
I would consider myself a fairly decent mathematician. I have other friends who I would consider even better ones. Neither of us are very good at, or interested in, calculating things. I tend to avoid courses that are focused on solving, evaluating, and so on, and look for more proof centric courses. I also find that a lot of people who "hate math" really just hate number crunching and solving.
Dear Daniel Goldman, in my experience some people hate maths not due to arithmetic, calculating and solving; but due to constructing logical proofs. So I agree with you on one point that being good at constructing proofs is different from being good at working with numbers. Though, for logical proofs it is not necessary to be good at working with numbers; but being good at working with numbers accelerates your logical thinking. Again mathematics has no generally accepted definition. On the other hand many people get attracted towards mathematics because of arithmetic, calculations etc. in the early stage. So I think these should not be separated from mathematics.
I'm not sure that I agree that working with numbers, practicing arithmetic, etc in any way builds the skills necessary for understanding and constructing proofs, unless those proofs themselves involve some kind of calculus. Even something as simple as proving that infinitude of primes seems very far removed from calculating. And personally, calculus was never fun for me, nor was I ever really good at it. Yet, I am quite comfortable in the world of proofs.
It is however an interesting question, Yogesh J. Bagul: to what extent do the aptitudes and skill sets for "calculus" as I call it and "mathematics" as I define it overlap, and how well does nurturing one help with the other?
Hello Daniel,
which proofs do you work with? many of them make use of calculus... There are hidden calculations in the proof of the infinitude of primes.
Gabriel
The infinitude of primes has content that is closer to calculus, which isn't surprising, as it deals specifically with prime numbers. But even then there's little that being good at calculating will help you with there. And I suppose that my cup (or is it doughnut) of tea is topology.
arithmetic and calculations are used normally in computing the numerical solutions of many real problems. Therefore, we cannot separate them from Mathematics. Even mathematical programming need lots of calculations, without any dealing with theory, but it is also a type of Mathematics.
Ahmed Chahtou, among other things, it is frustrating that so many people believe that mathematics is all about numbers and calculations. That misconception is also unhealthy for the field.
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