QED: Uncovering the Meaning Behind Math Proofs

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In summary, the abbreviation QED stands for "Quod Erat Demonstrandum," which is Latin for "Which was to be proven." It is typically used by mathematicians to signify the completion of a proof. The abbreviation has been the subject of jokes and stories, including one about a professor who claimed something was obvious but couldn't prove it, and another about a professor who couldn't find a proof for a lemma he claimed was obvious. The origin of the story is unknown, but it is often attributed to mathematician G.H. Hardy. Some students have also shared their own experiences with QED in their math classes.
  • #1
Oerg
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What does QED stand for behind every mathematical proof?

i can't seem to find out what it stands for thanks.
 
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  • #2
Quod Erat Demonstrandum (Which was to be proven)
 
  • #3
LOL
my math teacher used to exclaim <quite easily done> whenever he completed a proof and then wrote QED on the board. I refused to believe it and thought QED was something he came up with lol.
 
  • #4
I regret we don't use Q in Norwegian, so we can't crack jokes about QED's meaning like your teacher did..
 
  • #5
That reminds me of the professor who, in the middle of a long, complicated proof, said "Now, it is obvious that ...". The suddenly stopped and stared at the blackboard. He then sat down at his desk and, completely ignoring the class, wrote furiously on paper. After 10 minutes of that, he stood up and said, "Yes, it is obvious!"
 
  • #6
HallsofIvy said:
That reminds me of the professor who, in the middle of a long, complicated proof, said "Now, it is obvious that ...". The suddenly stopped and stared at the blackboard. He then sat down at his desk and, completely ignoring the class, wrote furiously on paper. After 10 minutes of that, he stood up and said, "Yes, it is obvious!"
There is another similar story about a professor who wrote down a lemma on the blackboard whose proof he said was obvious, only to have a student interrupt him and say that it was not obvious to him. The professor then attempted to prove it but failed, so he told the class he would show them the proof next time. After the lecture ended, he went to his office and tried to come up with a proof, but still couldn't. He then tried to track down the lemma in the literature, and after a long search he managed to find it in a paper, but alas the author had left the proof of the lemma as an exercise to the reader! It also didn't help that the author of the paper was the professor himself.

[I read this in the book Mathematical Apocrypha by Steven Krantz.]
 
  • #7
HallsofIvy said:
That reminds me of the professor who, in the middle of a long, complicated proof, said "Now, it is obvious that ...". The suddenly stopped and stared at the blackboard. He then sat down at his desk and, completely ignoring the class, wrote furiously on paper. After 10 minutes of that, he stood up and said, "Yes, it is obvious!"

By the way, I just wanted to let you know that I decided the first time I saw you post this story that I would quote it whenever someone says that their math book says something is obvious but they can't see it.

I haven't yet had a chance to, but I promise I will.
 
  • #8
That story is supposedly about Hardy.
 
  • #9
LukeD said:
By the way, I just wanted to let you know that I decided the first time I saw you post this story that I would quote it whenever someone says that their math book says something is obvious but they can't see it.

I haven't yet had a chance to, but I promise I will.

OMIGOD, how many times have I posted this story?
 
  • #10
Xevarion said:
That story is supposedly about Hardy.

Hmmm... Hardy has an interesting commentary on the use of the word obvious in math in his book "A Course of Pure Mathematics" (on page 130 in the 9th edition at least). I wonder if this incident had something to do with that...
 
  • #11
No idea. This is only the second I've seen you post it, but I haven't been here very long. Where did the story originate?

Edit: Who is Hardy?
 
  • #12
Ah...for most mathematical proofs...my F.math teacher just writes like 2 lines of it...draws some dots and writes the word "clearly" and then just writes the last line for the proof then puts QED and all the students are like..."how is that so clear?"
 
  • #13
LukeD said:
No idea. This is only the second I've seen you post it, but I haven't been here very long. Where did the story originate?

Edit: Who is Hardy?

G. H. Hardy
 
  • #14
This reminds of of last month, when our class was doing mathematical induction as a unit.
During one test, there were hilarious comments by our math teacher, since induction was such a 'unique' topic.

Some comments included were:
'really? i don't think so.'

'so what? what does this show?'

'NO.'

'NO.'

'There is nothing worse than saying QED when it is not'

'NO.'

'Try again, bummer'

Yes, our math teacher is great!
 
  • #15
HallsofIvy said:
That reminds me of the professor who, in the middle of a long, complicated proof, said "Now, it is obvious that ...". The suddenly stopped and stared at the blackboard. He then sat down at his desk and, completely ignoring the class, wrote furiously on paper. After 10 minutes of that, he stood up and said, "Yes, it is obvious!"

If I ever become a Professor (which I hope with all my might) that exact thing has a good chance with happening with me =] I've made up theorems that I thought existed because they were 'so obvious' to me, and when a friend said they weren't obvious to him, I tried to proof it in front of him, and instead found a counter example :(
 
  • #16
I like "Quod Errat Demonstrator" more, not a one-to-one traslation but it is something like "Where the author fails". I don't know why but it sounds so mean.
 

What is QED and why is it important?

QED stands for "quod erat demonstrandum", which is a Latin phrase meaning "thus it is demonstrated". In mathematics, it is used at the end of a proof to signify that the statement has been proven to be true. It is important because it provides a clear and concise way to conclude a proof, allowing others to easily understand and verify the validity of the proof.

How do math proofs contribute to our understanding of the world?

Math proofs are essential in providing evidence and justification for mathematical concepts and theories. They allow us to make accurate predictions and deductions about the world around us, and have practical applications in fields such as science, engineering, and economics. In addition, understanding and constructing proofs can also improve critical thinking and problem-solving skills.

What are some common misconceptions about math proofs?

One common misconception is that math proofs are only used in pure mathematics and have no real-world applications. In reality, they are used extensively in various fields and have practical implications. Another misconception is that only people with exceptional mathematical abilities can understand and create proofs. While a strong understanding of math is necessary, anyone can learn to read and construct proofs with practice and dedication.

How can one improve their ability to understand and create math proofs?

Practice is key when it comes to understanding and creating math proofs. Start by studying and analyzing existing proofs, and then try to replicate them or create your own using similar methods. It is also important to have a strong foundation in mathematical concepts and logic, as well as the ability to think critically and creatively. Seeking guidance from a teacher or mentor can also be helpful in improving one's proof-writing skills.

How has the use of technology impacted the way we approach and understand math proofs?

Technology has greatly enhanced our ability to visualize and manipulate mathematical concepts, making it easier to understand and construct proofs. Tools such as graphing calculators, computer algebra systems, and proof-assistant software have made the process of solving and verifying proofs more efficient and accurate. However, it is still important to have a strong understanding of the underlying concepts and logic behind the technology in order to fully grasp the meaning behind math proofs.

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