Do you want to see another cool math proof? Check out the FAMOUS proof th-cam.com/video/TKrxXTGMJdI/w-d-xo.htmlsi=a8ZqVpCoh8sjq35d 🎁 of the Pythagorean theorem that uses a beautiful picture with areas of simple squares and triangles! The 10 min video is super accessible and ALL you NEED for the Pythagorean theorem for high school and college math! 🥳
Hi @kennethkho7165 thank you so much for your kind and supportive comment! 😊 I really appreciate the positive feedback and it means a lot to me. I am looking forward to making more videos that you will enjoy watching! 🥳 I hope you have an amazing day/evening/night! 😊
Nice explanation! “Of course if you DON'T accept the proof, you can feel free to leave a comment below and I'm happy to discuss with you… [why you are WRONG].” Haha. For a moment, I wondered if it was an unstated assumption that p1…pk were intended to be consecutive primes starting from 2, but no… case 2 ensures that any list of primes will do.
Hi @chrysleague thank you so much for your kind and supportive comment! 😊 Yes, the point you raised is very interesting! I think there are many variations of Euclid's proof and some variations present it as "Let p_1, ..., p_k be the first k primes" which works with the same argument. (I think another popular version is a proof by contradiction: assume p_1, ..., p_k are all the primes, and then arrive at a contradiction with the same reasoning.) I think Euclid's original argument was just start with any list of primes and produce another one, and I agree it is cool that this slightly more general strategy also works! 😊 I hope you have an amazing day/evening/night! 😊
Hi @RiteshArora-s9x thanks so much for your comment! 😊 Yes, number theory is quite challenging - I'll take a look at the book. I do plan on creating more number theory videos over time but the main challenge is balancing out all the different topics I am producing videos on 😅 I hope you have an amazing day/evening/night! 😊
Math proofs are just like magic tricks. It seems really impossible to prove until you listen to the proof a 1st grader would comprehend. like a magic trick looking easy when they explain how they did it.
Hi @nidadursunoglu6663 thanks so much for your comment and sharing your thoughts! 😊 I completely agree, proofs themselves don't always lead to insight about why something is true. I often find that unless I think about something myself and try to prove it myself, I don't really feel like I fully understand the statement. I hope you have an amazing day/evening/night! 😊
Hi @AndrewLappeman-w4d thank you so much for your comment! 😊 Yes, I would love to do a group theory course! Actually, my math research is very related to group theory so I think it would be exciting! I think the main challenge for me right now is trying to balance numerous topics, levels and audiences on my channel (ranging from intro math to proof-based math and everything in between), but given your interest, I will start releasing some videos on group theory soon too! I think it is a super accessible topic that people can understand (even without knowing calculus, for example). I hope you have an amazing day/evening/night! 😊
Do you want to see another cool math proof? Check out the FAMOUS proof th-cam.com/video/TKrxXTGMJdI/w-d-xo.htmlsi=a8ZqVpCoh8sjq35d 🎁 of the Pythagorean theorem that uses a beautiful picture with areas of simple squares and triangles! The 10 min video is super accessible and ALL you NEED for the Pythagorean theorem for high school and college math! 🥳
I just discovered this channel and I love that you are focusing on classical proofs, we had enough puzzles already!
Hi @kennethkho7165 thank you so much for your kind and supportive comment! 😊 I really appreciate the positive feedback and it means a lot to me. I am looking forward to making more videos that you will enjoy watching! 🥳 I hope you have an amazing day/evening/night! 😊
It is hard to find an explanation like this on TH-cam . Your presentation is so good . I love every video of yours. I am learning a lot from you
Thank you so much!!! 😊
Loved the explanation
i didnt know dr peyam had a twin brother.
Nice explanation! “Of course if you DON'T accept the proof, you can feel free to leave a comment below and I'm happy to discuss with you… [why you are WRONG].” Haha. For a moment, I wondered if it was an unstated assumption that p1…pk were intended to be consecutive primes starting from 2, but no… case 2 ensures that any list of primes will do.
Hi @chrysleague thank you so much for your kind and supportive comment! 😊 Yes, the point you raised is very interesting! I think there are many variations of Euclid's proof and some variations present it as "Let p_1, ..., p_k be the first k primes" which works with the same argument. (I think another popular version is a proof by contradiction: assume p_1, ..., p_k are all the primes, and then arrive at a contradiction with the same reasoning.) I think Euclid's original argument was just start with any list of primes and produce another one, and I agree it is cool that this slightly more general strategy also works! 😊 I hope you have an amazing day/evening/night! 😊
I have always found problems in number theory to be hard. Esp in david burton book
Hi @RiteshArora-s9x thanks so much for your comment! 😊 Yes, number theory is quite challenging - I'll take a look at the book. I do plan on creating more number theory videos over time but the main challenge is balancing out all the different topics I am producing videos on 😅 I hope you have an amazing day/evening/night! 😊
Math proofs are just like magic tricks. It seems really impossible to prove until you listen to the proof a 1st grader would comprehend. like a magic trick looking easy when they explain how they did it.
Hi @nidadursunoglu6663 thanks so much for your comment and sharing your thoughts! 😊 I completely agree, proofs themselves don't always lead to insight about why something is true. I often find that unless I think about something myself and try to prove it myself, I don't really feel like I fully understand the statement. I hope you have an amazing day/evening/night! 😊
Group theory course?
Hi @AndrewLappeman-w4d thank you so much for your comment! 😊 Yes, I would love to do a group theory course! Actually, my math research is very related to group theory so I think it would be exciting! I think the main challenge for me right now is trying to balance numerous topics, levels and audiences on my channel (ranging from intro math to proof-based math and everything in between), but given your interest, I will start releasing some videos on group theory soon too! I think it is a super accessible topic that people can understand (even without knowing calculus, for example). I hope you have an amazing day/evening/night! 😊