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.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!"
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!"
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.
Xevarion said:That story is supposedly about Hardy.
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?
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!"
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.
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.
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.
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.
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.