# What does it mean to "do mathematics"?

• musicgold
In summary: Mathematics: From the Birth of Numbers goes into many topics in depth.The Math Book is set up in the format of the popular science books that give a page to a topic with a picture and a description of that picture.
musicgold
Homework Statement:: What does the following quote by Mathematician Paul R. Halmos mean?

"The only way to learn mathematics is to do mathematics."
Relevant Equations:: What dose he mean by "doing mathematics"?

Thanks

musicgold said:
Homework Statement:: What does the following quote by Mathematician Paul R. Halmos mean?

"The only way to learn mathematics is to do mathematics."
Relevant Equations:: What dose he mean by "doing mathematics"?

Thanks
It's not reading about mathematics -- he means solving equations or puzzles. I supposed studying theorems would qualify provided that you can use the theorems in subsequent problem solving.

musicgold and Delta2
It means actively reading a textbook, filling in all the gaps in proofs that the author left out, making up your own questions.

Examples:

Is this statement true? Can I ommit this hypothesis from the theorem? Can I maybe weaken the hypothesis? Can I find counterexamples for certain claims?

And maybe most importantly, work many examples and do many exercises.

Another quote is that someone's expertise is determined by how many examples that person worked out.

musicgold, Delta2 and troglodyte
musicgold said:
Homework Statement:: What does the following quote by Mathematician Paul R. Halmos mean?

"The only way to learn mathematics is to do mathematics."
Relevant Equations:: What dose he mean by "doing mathematics"?

Thanks

To quote or misquote Louis Armstrong: if you have to ask, you'll never know.

etotheipi and troglodyte
The only way to learn soccer is to play soccer.
The only way to learn french is to speak french.

musicgold and Delta2
musicgold said:
What dose he mean by "doing mathematics"?
Have you ever tried to learn how to ride a bicycle by reading about riding bicycles?

symbolipoint, musicgold and member 587159
PeroK said:
To quote or misquote Louis Armstrong: if you have to ask, you'll never know.

...I thought this quote was from Harry Potter, stared at it for a solid minute going "I'm pretty sure Louis Armstrong wasn't in those movies...?"

There's a Chinese proverb that covers this well:

I hear and I forget, I see and I remember, I do and I understand.

Mathematicians are self-motivated to do and to understand whereas as students hear and forget then see and remember but seldom do and understand.

Sometimes mathematicians work in isolation but more often they work in collaboration investigating a problem and extending mathematical knowledge into new areas of research.

A fun quote from the 1900's was that there were three great English mathematicians, GH Hardy, JE Littlewood, and Hardy-Littlewood and they, in turn, collaborated with Srinivasa Ramanujan.

https://en.wikipedia.org/wiki/G._H._Hardy

https://en.wikipedia.org/wiki/John_Edensor_Littlewood

https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

In contrast, Ramanujan, for the most part, worked in total isolation using textbooks that were considered second rate. It was only after his papers got to Hardy did he have a chance to collaborate with the Hardy-Littlewood team at Oxford.

Hardy wrote a book called The Mathematicians Apology which is a great read for aspiring mathematicians as is Bell's Men of Mathematics book on the lives of mathematicians which sadly doesn't cover Ramanujan.

https://plus.maths.org/content/node/6725

https://en.wikipedia.org/wiki/Men_of_Mathematics

One last book would be The Man Who Knew Infinity about Ramanujan and his life before and after being a part of the Cambridge mathematical world.

https://en.wikipedia.org/wiki/The_Man_Who_Knew_Infinity

Last edited:
musicgold
phinds said:
Have you ever tried to learn how to ride a bicycle by reading about riding bicycles?
1. I could be wrong here, but I think I learned more about mathematics by reading books than I learned in school. In school I learned how to use formulae like a robot to get the answer and hated it.
I stared enjoying mathematics and solving problems only when I came across some books that showed me how awesome this field is. Here are some of them.

The Art of Infinite by Robert Kaplan
Why do buses come in threes
Fermat's Last Theorem

2. Also found this quote by a professor explaining"doing mathematics".
“Doing mathematics” means a lot more than writing a solution to a math problem - it means thinking deeply about math, struggling with math, communicating about math, practicing math skills, and trying to figure out new mathematical ideas."

musicgold said:
In school I learned how to use formulae like a robot to get the answer and hated it.
As I think you now know, that is NOT a description of "learning math" it's just a description of rote memory learning and how to pass tests.
I stared enjoying mathematics and solving problems only when I came across some books that showed me how awesome this field is.

musicgold
musicgold

## 1. What is the definition of "doing mathematics"?

"Doing mathematics" refers to the process of using logical reasoning, critical thinking, and problem-solving skills to explore and understand mathematical concepts and principles.

## 2. What skills are required to "do mathematics"?

To "do mathematics," one must have a strong foundation in basic math concepts, as well as the ability to think abstractly, analyze data, and apply mathematical principles to real-world situations.

## 3. Is "doing mathematics" only about solving equations and problems?

No, "doing mathematics" also involves creating and proving mathematical theories, developing new mathematical ideas, and using mathematical models to understand and predict patterns and relationships in the world.

## 4. Can anyone "do mathematics" or is it only for geniuses?

Anyone can "do mathematics" with dedication, practice, and a willingness to learn. While some individuals may have a natural aptitude for math, it is a skill that can be developed and improved upon by anyone.

## 5. How is "doing mathematics" relevant in everyday life?

"Doing mathematics" is relevant in everyday life in various ways, such as managing personal finances, understanding statistics and data, making informed decisions, and solving problems in various fields, including science, technology, and engineering.

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