Do mathematicians solve problems by hand?

Question

In school we are taught formulas to solve different kind of problems/equations.

Do professional mathematicians solve these problem (or from more complex fields of math) by calculating with a pen and paper or do they use advanced calculators or special software like Mathematica?

Answer 1

Hi,
I work with math ever day in my job. Right now if I look at my desk, it is covered with pieces of paper with equations all over them.

I usually write things out by hand, and then program them up (in my case in Visual Basic, but most of my colleagues use Matlab).
Sometimes I use microsoft Word and its equation editor, just to make sure I have put all of the parentheses in the right places, but I'm still doing the math in my head.

Answer 2

I would say it really depends at what level you are talking about. Yes I would say quite a bit of honest to god research mathematics are conducted with computers. However if you look at alot of the college level math going on I would say it is about 50/50. Mathematics and computer programming crosses over in so many fields that is becoming almost the same thing with just different focuses. Combinitorics, statistics, and Topology are some of the math fields that computer use is pretty much a given. (Topology it is more of a usefull tool in making presentations).
Other classes like Abstract Algebra, Group theory, and most of your Calculus courses are more of a pen and paper type of math although computers can be helpfull in those as well.
In general I would say that most of use use the pen and paper method when we are going to be doing alot of manipulation with the equations and want to be able to see step by step what we will be doing. I happen to believe that in many cases writing it all out can be faster... And there is no doubt in my mind that it helps you learn the material better.
There is a certain connectiveness to accually writing out alot of your work rather than plugging it in to a computer and watch it crank out the answer.

Answer 3

Sometimes they do. If it's a really hard problem they would do some on a calculator and some on paper. I don't know about the special software but they might use Scientific Calculators.

Answer 4

Depends where you work. If you get into engineering or such, everyone runs various computer codes. There's very few people who still do it all on paper and pen. But then again, there's the people who have to write the equations that are used to modify the codes...but in general, for research, you use paper and pen. For production in the industry, you use a computer code you created from your research, and there's quite a few of those.

Answer 5

I have a Bachelor of Science degree in Mathematics and plan on going back to school for more mathematics studies, so I thought I would try to answer your question.

Really it depends on the mathematician. There are some problems that mathematicians can do by hand. Others they do use advanced calculators and software. There are some types of problems that I actually prefer to do by hand, but that's simply out of habit and I'm kind of archaic. :)

A lot of math needs to be done by hand. When you get into college level mathematics studies, a lot of what you do is prove theorems. A theorem is a statement about something in math that can be proven. Some mathematicians work in fields of math where most of what they do is attempt to prove theorems that have not been proven yet so that they can be used. In fact, all the formulas that you use in school have a proof that goes along with them to show exactly why they work.

A lot of mathematicians also use computers. When I was in college, I used a program called MAPLE a lot. It's very helpful and does all sorts of calculations for me. It will graph three-dimensionally and animate certain things as well. It also does a lot of useful things with matrices (which was my specialty). But I was also taught how to PROGRAM computers as well. So I know how to write a program that will allow the computer to do the tricky computations for me. I think most math programs at the university level require a certain amount of proficiency in programming. We do use computers quite a bit. They are a very useful tool.

But no matter how great the computer, the brain is always the best tool.

I'm teaching mathematics now and working on my master's degree at the same time and I do not allow my students to use calculators most of the time. My feeling is that if they can do it by hand, they will understand how to do the problem better. Then when they use a computer, it will simply be a tool (what it is supposed to be) and not a crutch or the only way that they know how to do a problem. I even let them use computer software for certain activities. I teach them the formulas they need to know, but I also teach them how to DERIVE them (or where they come from). Then not only do they know how to use them, but they know WHY they can use them. These are great assets to the field of mathematics, but again, nothing is as useful or as amazing as the human mind.

Hope I answered your question.

Answer 6

What mathematicians use most is their brains. A mathematician job is not to perform calculations, but to think about problems and find solutions. When they have to compute something then, like everyone thse days, they use computers and specific programs like Mathematica, mapple, etc.

But the type of problems mathematicians deal with is not a problem of the those type that involves calculation. But some problem like deciding if there are infinitely many Mersenne primes, or deciding if a series is convergent or divergent. To do this, they usually write something on paper, just to help them think.

Answer 7

Of course they need advanced calculators or special software to solve. As the Math getting more complicated, it is impossible to just use pen and paper to calculate. Because the data is tremendous large and complicated. For example, statistics problem, 3-D mathematic model, or large matrix...

Answer 8

they were also taught in schools. they were also taught formulae to solve problems. they use formulae to solve problems cause they have practised so many times. that is why they are good in mathematics and solve problems speedily.

Answer 9

they calculate with their brains! some times when they need help, they use paper and pen

Answer 10

it depends.
generally applied math use calculators and softwarfe, oure math dont

Answer 11

Both.