QED: Uncovering the Meaning Behind Math Proofs

  • Context: Mathematica 
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    Proofs Qed
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Discussion Overview

The discussion revolves around the meaning and implications of the term "QED" in mathematical proofs, exploring its historical context, humorous anecdotes related to teaching methods, and personal experiences with mathematical reasoning. The scope includes conceptual clarifications, anecdotal evidence, and reflections on teaching styles in mathematics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Meta-discussion

Main Points Raised

  • Some participants clarify that QED stands for "Quod Erat Demonstrandum," which translates to "Which was to be proven."
  • Others share humorous anecdotes about teachers and professors using QED in ways that highlight the subjective nature of what is considered "obvious" in proofs.
  • A participant recounts a story about a professor who struggled to prove a lemma he claimed was obvious, illustrating the challenges in mathematical reasoning.
  • Another participant expresses a preference for a humorous reinterpretation of QED as "Quod Errat Demonstrator," suggesting a more critical view of proofs.
  • Some participants reflect on their own experiences with teachers who provide minimal explanations in proofs, leading to confusion among students.
  • There are repeated references to a specific story about a professor, indicating its popularity and relevance in discussions about mathematical clarity.

Areas of Agreement / Disagreement

Participants share a variety of anecdotes and interpretations of QED, with no clear consensus on the implications of its use or the nature of mathematical proofs. The discussion remains largely anecdotal and subjective, with multiple competing views on what constitutes clarity in mathematics.

Contextual Notes

Some comments reflect a lack of understanding of the term "obvious" in mathematical contexts, highlighting the subjective nature of mathematical proof and the varying teaching styles that can lead to confusion.

Who May Find This Useful

This discussion may be of interest to students, educators, and anyone involved in mathematics who seeks to understand the cultural and pedagogical nuances surrounding mathematical proofs and the use of QED.

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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Quod Erat Demonstrandum (Which was to be proven)
 
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.
 
I regret we don't use Q in Norwegian, so we can't crack jokes about QED's meaning like your teacher did..
 
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!"
 
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.]
 
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.
 
That story is supposedly about Hardy.
 
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.
 

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