can one be a brilliant mathematician but be poor at arithmetic skills?

Question

please help settle this friendly dispute with my friend, he is from US and only knows and understands technically operative arithmitic, where as I understand mathematics as a blissful exercise, divined sourced and philosophy etc etc, my friend thinks im ridicules, he does not understand higher order geometry and maths but is super fast at computation and thinks he is more learned than I in math. I am trying to tell him that there is another way to percieve and understand mathematics outside of mere arithmtic computations. My friend does not comprehend mathematical philosophy at all. please help

Answer 1

Being fast at arithmatic is meaningless. People often confuse this with real mathematical ability. Many of the best mathematicians I have seen at work make simple numerical errors often.

For the record (and no offense), although I agree with your stance, I cannot say outright that you are better at math than he is. Were I asked to bet this weeks paycheck on the ability of one of you, however, you would get my bet.

I would show him that many fields of mathematics barely involve numbers at all. I might show him the definition of the limit in real analysis (the epsilon/delta one). Mention, perhaps, that he can show that something is true for numbers one at a time, but that you can show that it is true for all of them (if you can).

Show him how to find the area of a circle with arbitrary radius using calculus. That should shut him up.

Answer 2

Arithmetic is not mathematics. It's really pre-mathematics. Mathematics is the study of patterns. It is a system of reasoning and a way of looking at the world. Most American schools do a poor job of teaching this, partly because many teachers do not understand this themselves.

Arithmetic is one of the really useful tools for doing mathematics, and inability to do arithmetic can hamper your ability to do and learn some other things, but you can compensate for it.

I can do arithmetic, but I'm not a lightning calculator. My wife, a music teacher, is much quicker than I am at calculating. But I'm the one with a degree in mathematics. I'm the one serving on a state Mathematics Council. I'm the one who is consulting on a textbook. Is she more learned in mathematics than me? I don't think so.

One thing your friend should realize is that there are many areas of mathematics, many of which have very little to do with numbers. It takes brilliance to understand these topics and no arithmetical skill.

And to a couple of the previous posters, Einstein was not a mathematician. He was a physicist. There's a difference. Although the theoretical physics he worked with is very mathematical, he was not discovering new mathematics. He was figuring out which existing mathematics applied to motion of objects when they go really fast.

Answer 3

I'm definatly one of those (well i'm not a brilliant mathematician but I have gradute level courses in math). Whenever I have to do "shop math" at work I always just pull out the calculator. I don't have either the time or inclination to do any but the simplist arithimatic in my head.
Your friend sounds alot like some of my family members who think that because I am a math major I am a human calculator. It is one of the sad misconceptions out there. I find that it mostly comes from the lack of intelligence of people.
I tried once to explain what exactly I study ...I was just explaining some general matrix calculations (solving linear systems) to my uncle and he really thought that I was making things up and that I was trying to fool him.

Answer 4

Mathematic savant's can do quantum physics in their mind and not even be able to tie their own shoes or dress themselves! A college professor can write down a problem in trig or calc that would take a week to process, and a savant can spout out the answer as soon as the chalk leaves the board.

There is a difference in using logic to reveal the answers through process, and being spiritually connected with the "problem" to the point of using a higher form of intellect.

Answer 5

Read about Albert Einsteins' documentary. A book which examines this great mans' entire life. He was arguably the greatest math scientist that ever lived, however, he flunked basic math in high school. Such a divine inspiration of self will and clairvoyance.

Answer 6

It's possible, but in my experience pretty rare. Those who don't have good computational skills usually are lacking in the other areas of mathematics too.

Having the ability to make a rough estimate of a result is a vital skill when solving problems, to avoid all sorts of errors in calculation.

Answer 7

take me for example , if u give me say 50 q's to me, I know that I have the confidence to get the concepts right for every question and If i get wrong answer it is only due to some arithmatical mistakes, so go ahead and kick his a** for saying that math is full of arithmatics, it is only the concepts that drive me and everybody in mathematics.

even ramanujum agrees with this ( though was extra ordinary in both the things......

Try to discuss this issue with some IIT grads and ISI prof.

Answer 8

take einstein for example, he had very poor arithmetic skills, and he still got to be one of the best mathematicians.

Answer 9

There are three types of mathematician,

Those who can count etc.....


Yes it is definitely possible.

Answer 10

ya like me.