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September 8th, 2014, 09:47 PM  #1 
Member Joined: Jul 2014 From: Seattle Posts: 96 Thanks: 2  Link between arithmetic and higher math ability?
I have noticed that some very talented mathematicians, physicists, engineers or just "math people" who understand many advanced concepts in mathematics have no basic arithmetical ability. I have also noticed kids who have excellent arithmetical ability get stuck when they move on to algebra. Of course there are plenty of exceptions, people who are good at arithmetic and higher math and people who are bad at both. I was just wondering, what are your opinions on the link between these two things? Has anyone else noticed this kind of link? Is there no link whatsoever and thus there are people in every category? 
September 8th, 2014, 09:48 PM  #2 
Member Joined: Jul 2014 From: Seattle Posts: 96 Thanks: 2 
Sorry moderators. This was supposed to be posted in the general math forum. I have no idea what happened. Please feel free to delete it and I'll repost if you can't move the thread.
Last edited by 3uler; September 8th, 2014 at 09:55 PM. 
September 9th, 2014, 01:15 AM  #3 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,150 Thanks: 730 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Being able to do hard things correctly and being able to do easier things quickly are generally different skills. That being said, many schools now teach arithmetic and have arithmetic tests, so I would expect most degree students to have reasonable arithmetic skills.

September 9th, 2014, 08:45 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I think that there is almost no link between the two. Sometimes studying math gives you a bit more practice with arithmetic, and doing arithmetic gives a bit of insight into the basics of algebra, but on the whole there's not much in common between the two.

September 9th, 2014, 10:02 AM  #5 
Member Joined: Jul 2014 From: Seattle Posts: 96 Thanks: 2  That was what I thought but then I thought of the likes of Euler, Gauss, Von Neumann, Alexander Aitken who were amazing mathematicians who made excellent discoveries and were amazing at arithmetic. There is of course also many "lightning calculators" who had no special talent for higher mathematics (although it is interesting that many of them were not educated so you could see their arithmetical ability as an expression of mathematical ability). I think perhaps the reason many great mathematicians may have been good at arithmetic is that they had extensive knowledge of the properties of numbers at a time when it was easier to apply those properties to find solutions (rather than just reaching for a pocket calculator as we do now). Thanks for your input. 
September 9th, 2014, 10:42 AM  #6 
Member Joined: Aug 2014 From: Somewhere between order and chaos Posts: 44 Thanks: 5 Math Focus: Set theory, abstract algebra, analysis, computer science 
I don't think there is any link. Arithmetic is simply a matter of being able to mindlessly plug numbers into an algorithm to get a result. Mathematics is a matter of being able to think logically and understand abstract concepts. The two are completely unrelated. Skill in arithmetic does not equate to actual mathematical ability, nor does it hinder it. I remember in elementary school I hated math and had a lot of difficulty with long division. Once I got to high school and learned what real mathematics is about, I fell in love with math, and that love has lasted to this day. 
September 9th, 2014, 05:40 PM  #7  
Member Joined: Jul 2014 From: Seattle Posts: 96 Thanks: 2  Quote:
I think so many more people would fall in love with math if only they got past high school math which is all procedure, it's so monotonous I'm not surprised people don't like it. I just wish people knew that isn't what math is really all about. Thanks for your input.  

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