Here are the timestamps. Please check out our sponsors to support this podcast. 0:00 - Introduction & sponsor mentions: - House of Macadamias: houseofmacadamias.com/lex and use code LEX to get 20% off your first order - Shopify: shopify.com/lex to get free trial - ExpressVPN: expressvpn.com/lexpod to get 3 months free 1:10 - Mathematics in the Soviet Union 11:20 - Nature of reality 22:39 - Scientific discoveries 36:00 - Observing reality 52:12 - Complex numbers 1:00:58 - Imagination 1:08:49 - Pythagoreanism 1:16:44 - AI and love 1:29:22 - Gödel's Incompleteness Theorems 1:49:48 - Beauty in mathematics 1:54:17 - Eric Weinstein 2:16:12 - Langlands Program 2:22:51 - Edward Witten 2:25:57 - String theory 2:31:25 - Theory of everything 2:40:18 - Mathematics in academia 2:45:45 - How to think 2:51:31 - Fermat's Last Theorem 3:06:22 - Eric Weinstein and Harvard 3:13:47 - Antisemitism 3:34:00 - Mortality 3:41:58 - Love
I'm just in on *the Nature of Reality and I almost came to tears, this is absolutely beautiful. Thank you both wonderful beings Alex and Edward.. I really need to get Love & Mathematics 🤍🖤
I have always been curious about the complexities regarding a creative imagination and dreams in particular... as a former fashion designer, I was always able to just close my eyes, follow my intuition and focus on evening dresses in my mind (like switching the channel on a television to escape to another dimension,) and eventually I find myself walking through an upscale fashion boutique with random mannequins shown on display, all wearing fabulous dresses that I can touch, lift up and explore the hidden details, then choose to make a mental note of a few favourite dresses. After awhile, I open my eyes and sketch them quickly and note the colorways, fabrics and any details. I could also find evening dresses when I was asleep... I would often dream that I was wondering through a fashion boutique, as a lone observer looking at various evening dresses on display. Aware that I was dreaming, I would choose to make mental notes of my favourites and then force myself to wake up to sketch a few and add notes, (Often I would find myself 'dreaming within a dream' and my mind would register the conscience state I was in and I would have to force myself to wake up from a dream state again.) Now as a designer of high-end contemporary furniture/objects of art, I am still able to just close my eyes and find myself walking through an art gallery or boutique furniture showroom and find myself choosing the furniture pieces I love the most and make a mental note of the details, materials used, colors and then choose to wake up to reality and make quick sketches and note the various colors and details of each piece. I do not understand where these random mysterious designs come from, if they are 'discovered or invented' and why they are always commercial designs suited to a very sophisticated customer. (Also strange to me is why some people are born with the ability to draw... designing and drawing are 2 separate skill sets, as many designers cannot draw. I compare it to exceptionally talented musicians that can write their own music and are also able to sing well... both skills don't usually occur together with one person.)
Am I the only one who thinks this is one of the most emotional of Lex’s interviews? Towards the end, 3 hrs onwards, Edward’s discussion of his discrimination, reconciling with his trauma, his younger self and his talk on mortality and his father is one of the most mind bending, enthralling listening experiences. Who would have thought the story of a famed mathematician would pull at the heart’s strings? Thank you Edward and thank you Lex for such great questions and allowing Edward the floor for much of this interview 🙏
What a rare combination - a genius mathematician, superior orator (in a second language) and a beautiful personality. I’m blown away by this individual! Lex, you’re ok too!
Edward Frenkel was my professor at Cal. Without a doubt the best professor I’ve had. His lectures were so well explained and captivating. He is a gift to this world!
He was my favorite math teacher at Berkeley. His explanations were always really clear, and he had a sense of humor. One time in Linear Algebra, some students were chatting in the back of the room, and he asked them "Are there some eigen spaces back there?" They immediately stopped.
It's crazy how a teacher can make such a difference. I hated math in high school because it seemed useless. The teachers I had then could not explain to me what it was for. All I wanted to know was what X was and why we give a shot about finding it!?!? Later in college I had really great math teachers who were able to really explain the practicality of what we were doing. For some reason that unlocked something for me. Knowing the why/what of math was very important to me finding joy in learning it.
This conversation is so moving that I've cried several times through it, and I barely cry for anything in life. Edward is such a gift to this world! Same for Lex.
The chemistry between these two wise, humble, eloquent people is reassuring about the future of humanity. Well worth the entire time to view and listen!
I took Calculus with Frenkel waaaaaaayyyyy back at Cal. To this day he's easily my favorite professor. He made lectures fun and his charisma was Feynman-esque. A wonderful person
I have watched 90% of your podcasts in the quest for learning and understanding. This is rhe very, very best. A humble guest who is is one of the best in the world and Lex thank you for letting him rock. This coukd be the highest intellectual you looped with. Lex thank you for doing a disciplined listening without showing your intellect. I can't thank you enough. Peace Love Light Laughter, brother
Would you have any other suggestions to watch?? This is the first full length Lex podcast I’ve watched and I thoroughly enjoyed it as well. I’ve been looking for equally good talks but nothing compares to giving this a second listen haha. Any suggestions much appreciated, Lex or other.
This is completely not what the topic is about but his vocabulary is perfect. I am from Georgia and love vocabulary but his choice of words is far above the perfect words I would have chosen. Not to mention he is brilliant and humble. I have yet to hear from a more smart, humble person in my lifetime. I never knew this type of conversation was available. I never rewatch information but I may watch this 3-5 times. Thank you Lex.
Can't agree with you more, Clay. I said elsewhere these words about Edward’s grasp of the language and his descriptive powers: ‘It is his overall intelligence and very clear thinking. And, of course, his automatic care of meaning that his thought process delivers. An example of mathematical precision in spoken language with a natural human touch. I enjoyed listening to this conversation so much!’ Just wanted to share the joy with you as you noticed his choice of words and his superior smartness… And English is his second language acquired in his adulthood, not when he was a child. Now I need to order the book. ;-))
"It is impossible to be a mathematician without being a poet in the soul." Amazing. And an amazing interview with this beautiful man. Thank you for it.
I cried at Edward's revealing of his deep trauma.....it was a purgative experience and I am grateful for your having this touching interview; while my own teenage trauma was at the hands of my parents, I can relate as despite this I went on to a fruitful career in law and now in the arts. Blessings to you and Edward.
No one mentions how insanely clear and Well produced/engineered the audio is on every episode. Your mic gain is absolutely chefs kiss and the gate levels you're using are icing on the cake!!! As an Engineer, hats off to you bc it's so sauce to enjoy these just that much more. Much love!!!!!! This episode is unreal
@@Mr88Andrew88 it’s affecting you the most then, my friend. You would not believe the nuances and the impact of properly engineered audio. When done such as Lex’s pinnacle quality, it translates to all mediums for the best and most pleasing listening experience. That goes for teeny headphones or a broken iPhone, all the way to stadium loud speakers. Engineering the sound to be actualized in clarity is the most integral and unnoticed aspect (to the laymen!) much love fam!
What a beautiful conversation. The way Edward Frenkel manages to put into words the feelings, thoughts and events that shape us and relate us to each other is so impressive! He's funny, he's charming, he's brutally honest, truthful and so.. human! Such insight, wisdom and vulnerability. This is as much a dialogue about what it means to be a human as it is about mathematics and science. A fantastic experience from start to finish! Thank you, Lex
Lex’s guests never cease to amaze me. And might I add his comment sections are equally wonderful, sincere, and genuine. The positivity is very refreshing :)
One of the things I love most about this podcast is I get to hear intelligent, informed people discuss crazy stuff I've been thinking about alone in my head, and articulate their beautiful opinions on it. It was a joy and thrill to listen to this, especially the talk of subjective reality.
I didn't expect to ever meet a guest that could rival lex in his authenticity, openness, honesty, and the kind of love it takes to hug the whole world. I can't think of words that wouldn't sound incredibly cheesy to describe how amazing this conversation was in so many different ways.
I completely agree and I if you haven't watched it already, I would wholeheartedly recommend to you and to everyone who liked and finds Edward interesting and the topics he touches here, please watch these couple of episodes of Nuberphile on YT with him. That was my first introduction to him and I was instantly bought, unbelievably interesting stuff.
Man knows so many hard-hitting, eye-opening and awe-striking lines from the greatest minds in science, philosophy and psychology. Every time he quoted a saying and went on to elaborate it hit like wave after wave of wisdom and inspiration. Being an applied maths and physics student myself, I don't think I have a better person to look up to ;)
I think this is literally one of hte greatest conversations ever recorded. Edward Frenkel is absolutely brilliant. Damn, he even raised theme of paradoxes and Necker's Cube, which I tought others... Unbelievable. So many great points and arguments, even not arguments, but pure thoughts.
What a beautiful soul. Both a genius and mystic all at the same time and vulnerable and open. Thankyou Lex for introducing me to him it gives me hope about the possibilities of being human. I wish I could express it better.
Lex, please do more Math related interviews. As someone who hasn’t studied math since high school and have now realised it’s importance in philosophy (Wittgenstein), art/design, literature (David foster Wallace), and of course physics and the sciences, it always feels amazing to learn more and understand more about complex mathematical problems which hold secrets about the truth of the universe- beyond what words can describe. And the more i underhand math the more it makes sense in the context of every day life and seemingly unrelated (humanities) fields.
I lost my love of mathematics in high school when the instructor insisted that we students do all the Trig computations in our minds without paper and pencil. I could thrilled at doing Trig on paper and gave up. Now my aspie grandson laughs and tells me it is not possible to get credit UNLESS one shows their work on paper.
@@ultmiddle4991 ya that’s crazy. On paper was the way for me too as that’s how you show proof you actually did it the right way and just copy some answer. sad for you, but you should still give it another try, get back into it. Buy a textbook or watch some educational vids. Or just try and find Mathematical problems in your everyday life or in your work and try and solve it on your own. That’s always more organic than forcing yourself to leave for the sake of it. I’ve been trying to do that and taking online courses help too- they give you a clear objective and end goal.
It was hard for me to hear his ideas because I was distracted by listening to,and being blow away by how good his English is. I had never heard of him, and his expertise is not my thing, but I'm a fan of this guy now. I absolutely love how he is open to the mystery of things instead of claiming that he knows the truth. So refreshing, especially by someone so intelligent and well studied.
I saw Edward on that Numberphile video years ago, and I immediately got this impression that this guy is special, would have made for an amazing teacher and colleague. So awesome to see him on here, this interview was truly great.
Lex - the master of conversation. How brilliant he can join different disciplines, points of view, humours, personalities. Incredible. How elastic-minded he has to be to make 3-4 hours talk with the best current scientists. Impressive and this is a treasure in the mud of idiotic internet.
@@babouras84 Like how he correlates freewill with quantum mechanics. Even if the world is not deterministic, freewill will won’t exist. We have freedom of choice, not freewill.
@@CausallyExplained Could be that he was thinking freedom of choice, but he said freewill. In some Slavic languages you need extra words to describe the difference. So in a daily conversation (and he's speaking very fast), it happens that your choice of words doesn't always reflect the proper meaning. It hardly makes him delusional.
I have dyslexia.. I honestly read that as "Edward Frenkel is a real jew" 😂 it also must have been partly because he was speaking of the mathematics university in Moscow and his father when I read it.. I didn't know that in Russia if one's family name is of Jewish heritage that the person's nationality is Jewish - I never knew that was even a nationality.. (have I perhaps heard it wrong?) To be persecuted for this is truly TERRIBLE!☹️ I was under the impression that Russia was (historically) home to many many Jewish people. Alex's surname for example. Just thought that was strange, regarding nationality etc
I was not expecting this to be one of my all-time favorite interviews, but it is. Edward is amazingly briliant and thought provoking - Please have him on again sometime!
What an extraordinary mathematician and "liberated" human being Edward Frenkel is! Overcoming rejection and turning it into a great lesson or opportunity without blaming others and/or himself "liberated" his mind, in a Buddhist sense. He made me laugh and cry throughout the entire episode. Thank you so much Lex for this enlightening podcast. I enjoy and love every bid of it.
It is his overall intelligence and very clear thinking. And, of course, his automatic care of meaning that his thought process delivers. An example of mathematical precision in spoken language with a natural human touch. I enjoyed listening to this conversation so much!
At 1.50.00ish in when he slowed down and spoke softer - I just wished he'd spoke like that the whole time.. But I understand why, he was excited & passionate about what he was saying. So it's not a criticism, it was just a little hard to understand everything he was saying. Very interesting guy
@@roddy2body yeah I kept having to rewind a few seconds. Clearly he was excited, interrupted lex a few times. But I think he would be wonderful to listen to in Russian, if I knew Russian haha.
Been such a fan of his for almost a decade after first seeing him on Numberphile! Highly recommend his book Love & Math to everyone. Lex you are a legend for your guest selection.
I'm at roughly the 1 hour and 50 minute point and I have just started watching this discussion again. I wasn't going to comment bcuz I don't want to embarrass myself, but when I put this back on I heard you ask Mr Frenkel about Eric. What a joy this is for an uneducated nobody like me bcuz Eric is the reason why I decided to watch this. I got to know him for the first time on the JRE and now I'm being introduced to Ed in your class. I can see why these two deeply spiritual beings have such an admiration for each other. All three of you claim that you are men of science. I don't know anything about that side of life, yet you all have such a uniquely soulful way of talking about your life's work that even I am allowed to connect to it's beauty and wonder. Thank you all, sincerely Genevieve 🙏🏽🙏🏻🙏🏾
The type of clear thinking you only get from a true scientist. It's inspirational to see such a level of passion and involvement in everything that one does. Absolutely knocked it out of the park, one of the best podcasts I've ever listened to.
Edward Frenkel would definitely be a top 5 pick for a great dinner party guest. I can imagine the wonderful conversations about any number of far-reaching topics.
Lex accent is present, but Edwards accent is so heavy, that at some point my жена зашла и спросила "почему они не начнут уже просто говорить по русски" great episode, as allways)
I just listened and listened and could not stop. Those almost 4 hours passed very fast. Fascinated both by his genious as well as by his big love to things and his way to see the world, Edward really captivated me.
Lex Fridman and Edward Frenkel stand as titans of intellect, transcending the mundane and daring to ascend the heights of thought. Lex, the fearless inquisitor, pierces the veil of complacency, awakening the slumbering spirit within us. Edward, the mathematical poet, weaves a tapestry of eternal truths, defying the nihilism of ignorance. United, they become an unstoppable force, heralding a new era of intellectual prowess and enlightenment.❤
This is the visual of two lights connecting and bringing an emerged new light that touches people even across the world. every second of this dialogue was beautiful. Love and appreciation from Tehran
Lex, your podcasts give me comfort and hope for humanity. It's so wonderful to go on all these thought trips. I don't have many friends I can talk to about any of all this, and I run in highly educated circles, but everyone is closed off. Your attitude towards all your guests is what the world needs. I love you and this podcast more than any online content anywhere. Thank you.
Educated people tend to be proficient only in the subjects they study/teach, it's a generalisation but I do think we could all be a little more open minded. Mind you, I'd say those of us who listen to Lex's wide array of guest's are naturally more open minded, curious & hungry for knowledge of all kinds 😉 I'll add that in no way am I highly educated, I have very minimal academic education to be honest
Beautiful comment, Deirdre. I do think there is a huge difference in highly educated and high intelligence, but I would say that though 😂 Agree with you totally! The young Lex is outstanding.
@@roddy2body I agree, it's totally not education or even pure intelligence that defines an agile mind, but curiosity.But I am grateful there are experts as well because then they can explain it all to those of us who like to learn a little about everything! :)
So much to choose from this conversation that touched my heart, my mind and banged them both around a hundred times. If I were to choose one, I'd point to how Edward Frenkel thought his dreams were over at 16 as a consequence of anti-Semitic, unspoken polices of the ex-Soviet Union - how loss fueled his work and within a few years he would be a professor at Harvard. That arc he traveled is universal in many ways, and certainly made me think of my and my own father's lives. Thanks Lex and Prof. Frenkel for a brave and beautiful voyage into love and math.
Earlier I was suspicious/untrusting when to trust Lex Fridman, now I know he is for real. REAL meaning he is really an intelectual person, a life-long learner. Go Lex! You have such great people visiting your show. Keep going
Edward Frenkel is a genuinely good person and an extremely gifted mathematician. He exudes a refreshingly deep understanding of the hidden reality beyond our common intuition and is a pleasure to listen to his exquisite insights. Thank you, Lex, for yet another interesting dialogue with this special guest!
What a beautiful example of a truly wise scientist who is not afraid to share his personal spiritual growth and open attitude towards the mystery, reminding everyone to embody their childlike playfullness and innate curiosity. I hope that many young scientifically minded people will feel inspired by Edward to expand their perception.
This was the first podcast that I kept getting interupted while listening, but over 3 days, just kept coming back to hear you both speak. Edward's views on so many different topics really put a smile on my face. Thank you for speaking with him and sharing that with us!
I was terrible in the sciences and math in school - I am 52 today and still don’t understand most of the technical details. I watched this podcast in one sitting and was totally enthralled with the conversation - the mathematician is so well spoken and distills complex phenomenon in to simple and understandable verbiage. Amazing. Lex is absolutely the best at this format
Lex you’re a living legend bro. These podcasts and special guest do so much for the world and the thinker. We’re all trying to get closer to the truth even though the closer we get the more we don’t know. Life is a beautiful mysterious phenomenon
Beautiful!!! From 40:00-44:00 (ish) talking about paradox and confirmation bias…THANK YOU, Edward, for speaking truly about the nature of mystery, the possibility of missing truth because we only are willing to see what we already see. Beautiful! I have long desired to hear more modern scientists/mathmeticians get their minds around these philosophical understandings! Your depth of reading is lovely…thank you for being a very open, truly curious, knowledge addict! ;)
My journey is nothing like that of Edward but I so recognise where he is now. This deep connection is beautiful and inspires and informs me as to the truth of love and our universe. Love you man. Love you Lex. 🙏
Wow, just 10 minutes in, and already loving this conversation. Lex, you are a true gem, finding people who can shine their light onto reality and make it not only understandable, but who bring a love for the understanding that propagates... I am curious to see how and whether the question of causality will come up. One of the ways in which I imagine mathematics and physics differ is the extent to which physics seems to imply causal "directedness", whereas mathematics seems more agnostic, and willing to consider a "hand-in-handedness" of the two sides of an equation, allowing the recipient of a force or energy (or information) exchange to be just as involved in the process as the transmitter, not privileging one over the other...
oT256Cr has the most potential to do more than X10. ETH and BTC will most likely do a X5-X6, but that's fine for me. Gotta look for better entry points while I stake IRIS and PGEN, then wait for Polygen's next raise as I also look at their new partnership with Kenzo Ventures.
I love Edward. I've seen him on numberphile and the topics he discussed were instantly engaging. The one he mentioned about the sum of all natural numbers is the one that got me into math right before college. Graduated with a minor in math and have been continuing to learn on my own for the past 2 years. His passion is infectious. More people like him need to become elementary school teachers. Being able to teach math is different than being able to communicate the beauty behind it. I will be reading his book, love and math have both been resonating with me recently.
Lex, Edward Frenkel has presented a philosophical masterclass on multidisciplinary Sciences - so eloquently - intuitive, divine, mystical, inner child's wonder
Reading love & math as we speak after listening to this podcast and why did I like based on his voice Edward was much older...anyway... I am SO ENTHRALLED with this book. Thank you Lex and thank you Edward.
I am a high-school Math teacher (16-18 year olds) in Canada and I teach imaginary numbers in every age above 15 years old. It's not part of the curriculum but I make space for it anyway. I learnt it in university in the 90's. Maybe when my students become teachers themselves, it will be taught in all high-school curriculums both as a calculation technique and as an exploratory paradigm.
I think it's great that you leave the beaten path of the curriculum to teach something you are passionate about. I recently started a video series on complex numbers, in which I try to make them more intuitive. I would be very curious to find out what your reaction would be as a high school teacher. If you're interested, you can find the series here: ruclips.net/video/p13kiue-sCY/видео.html
Hi there. I like your video if I am working one on one with a student or in a tutor situation. In a larger class, I need to be able to grab their attention quickly and feed their curiosity/imagination -- especially if I am "going off-script". Because it is not part of the actual curriculum where I work, I cannot assign any major marks to its study. So I give bonus marks. The video that I show my students is this one: ruclips.net/video/T647CGsuOVU/видео.html&ab_channel=WelchLabs Ultimately, my goal is to have students with an early grasp of imaginary numbers skills, history and applications when they graduate so that they don't need to be introduced when they go off to university. The skill can be introduced during the study of the quadratic formula and the discriminant, the history has its own unique learning moments, and the practical applications are found in the quantum biology and Tibees does a good explanation too.
During year 10 go 12 of school I started a junior engineering program and I studied math from arithmetic to triogonometry to differential equations and usually The cource had a letter (I.e. A,B,C...etc.) but wheb studying computors and programming I hade to take a complimentary 50H cource of 'Descrete Math' involving complex nummers. I learnt abort complex nummers including 'E‐1' and my conception Washington that this was a very specific "exception" we use for very specific technical problems with computors. Tjena The math of quantom physics emerges and complex nummers are The essential part of reality, first this was deeply unsettelling... Haninge the proper education to 'Solveig for' this where probably essential in how fast I got integrate this new science and I never used comolex nummers outside of my education, so you are doping Great work. Math teachers havet my love and support, they are everyday herpes.
Here are the timestamps. Please check out our sponsors to support this podcast.
0:00 - Introduction & sponsor mentions:
- House of Macadamias: houseofmacadamias.com/lex and use code LEX to get 20% off your first order
- Shopify: shopify.com/lex to get free trial
- ExpressVPN: expressvpn.com/lexpod to get 3 months free
1:10 - Mathematics in the Soviet Union
11:20 - Nature of reality
22:39 - Scientific discoveries
36:00 - Observing reality
52:12 - Complex numbers
1:00:58 - Imagination
1:08:49 - Pythagoreanism
1:16:44 - AI and love
1:29:22 - Gödel's Incompleteness Theorems
1:49:48 - Beauty in mathematics
1:54:17 - Eric Weinstein
2:16:12 - Langlands Program
2:22:51 - Edward Witten
2:25:57 - String theory
2:31:25 - Theory of everything
2:40:18 - Mathematics in academia
2:45:45 - How to think
2:51:31 - Fermat's Last Theorem
3:06:22 - Eric Weinstein and Harvard
3:13:47 - Antisemitism
3:34:00 - Mortality
3:41:58 - Love
Thanks for all❤
Dr Gavin wood!
John Perkins 'Confessions of an Economic Hit Man.'
I'm just in on *the Nature of Reality and I almost came to tears, this is absolutely beautiful. Thank you both wonderful beings Alex and Edward.. I really need to get Love & Mathematics 🤍🖤
I have always been curious about the complexities regarding a creative imagination and dreams in particular... as a former fashion designer, I was always able to just close my eyes, follow my intuition and focus on evening dresses in my mind (like switching the channel on a television to escape to another dimension,) and eventually I find myself walking through an upscale fashion boutique with random mannequins shown on display, all wearing fabulous dresses that I can touch, lift up and explore the hidden details, then choose to make a mental note of a few favourite dresses. After awhile, I open my eyes and sketch them quickly and note the colorways, fabrics and any details. I could also find evening dresses when I was asleep... I would often dream that I was wondering through a fashion boutique, as a lone observer looking at various evening dresses on display. Aware that I was dreaming, I would choose to make mental notes of my favourites and then force myself to wake up to sketch a few and add notes, (Often I would find myself 'dreaming within a dream' and my mind would register the conscience state I was in and I would have to force myself to wake up from a dream state again.) Now as a designer of high-end contemporary furniture/objects of art, I am still able to just close my eyes and find myself walking through an art gallery or boutique furniture showroom and find myself choosing the furniture pieces I love the most and make a mental note of the details, materials used, colors and then choose to wake up to reality and make quick sketches and note the various colors and details of each piece. I do not understand where these random mysterious designs come from, if they are 'discovered or invented' and why they are always commercial designs suited to a very sophisticated customer. (Also strange to me is why some people are born with the ability to draw... designing and drawing are 2 separate skill sets, as many designers cannot draw. I compare it to exceptionally talented musicians that can write their own music and are also able to sing well... both skills don't usually occur together with one person.)
Lex, I am a 73 year mama and life learner. Listening to your podcasts has brought a new meaning to my life. Please stick around and do not give up ❤
This is the best thing I read on the internet today. Thanks for sharing.❤
Love this !!!! Lex's reach is so far , ! Lex's podcast are a gift to those who want to learn !
You summed up exactly how I feel about this person, much admired. Thank you.
Mine too! I have derived SO MUCH pleasure and knowledge and wisdom from this one podcast. It will go down in history
I also love learning new things. I hope I can still continue to learn when I'm 73. You're my inspiration now. 🙏
Wtf, how does this podcast consistently bring forth people that I’ve never heard of, yet absolutely adore within minutes.
You like academics perhaps
They are among the best people from all fields of life
Apparently, he teaches at Berkeley. Wish I could take his class💀
@@magician_aleks2726 You can watch his videos on Numberphile
@@magician_aleks2726 no
In a world of artificial conversations, clickbait preachings, and misleading information, Lex's podcast is a breath of authenticity and deep insights.
True.
@@MarkStoddard tragically true
Perfectly true
Totally agree!
A few of his guests were meh, but FUCK the subjects the touch on sometimes. SUCH a good listen, everyday.
Am I the only one who thinks this is one of the most emotional of Lex’s interviews? Towards the end, 3 hrs onwards, Edward’s discussion of his discrimination, reconciling with his trauma, his younger self and his talk on mortality and his father is one of the most mind bending, enthralling listening experiences. Who would have thought the story of a famed mathematician would pull at the heart’s strings? Thank you Edward and thank you Lex for such great questions and allowing Edward the floor for much of this interview 🙏
yes this one is extraordinary.
His vulnerability and humanity is incredibly touching.
Absolutely simpatico........what a moving dramatic revelatory experience of empathy; I am a produced playwright and I wept.
You are absolutely right! That is just beautiful!🥰It resonates with my soul so deep!
Yep, I felt the same! It was incredible and just kept getting better...the last 30 min were astoundingly profound.
What a rare combination - a genius mathematician, superior orator (in a second language) and a beautiful personality. I’m blown away by this individual! Lex, you’re ok too!
They're 2 KGB AGEnts😂
Agreed Joe!
@@Sai-ns2sk Vlad P makes more sense than Joe B...
@@savage22bolt32 not to me lol - I don't understand Russian.
@@Sai-ns2sk I don't understand demented gibberish...
Edward Frenkel was my professor at Cal. Without a doubt the best professor I’ve had. His lectures were so well explained and captivating. He is a gift to this world!
Couldn’t agree more. Go bears!
lucky you!!
I got my degree in geophysics from Cal. I LOVED being at Berkeley.
Indeed he is a gift to this world!!
Great teachers are a blessing, my chemistry teacher was one and I got 💯
Lex is frickin' killing it with the guests lately! The work ethic on this man is insane.
Disciplined!
he's a real life AI automaton :) researching his guests, prepping for the interview, and churning out episode after episode... machine 🙇
Agree.
why dont you marry him if you like him so much ?
@@MrCGangsta bully
He was my favorite math teacher at Berkeley. His explanations were always really clear, and he had a sense of humor. One time in Linear Algebra, some students were chatting in the back of the room, and he asked them "Are there some eigen spaces back there?" They immediately stopped.
😂
sounds kewl....
Aww he doesn't teach there anymore??
It's crazy how a teacher can make such a difference. I hated math in high school because it seemed useless. The teachers I had then could not explain to me what it was for. All I wanted to know was what X was and why we give a shot about finding it!?!? Later in college I had really great math teachers who were able to really explain the practicality of what we were doing. For some reason that unlocked something for me. Knowing the why/what of math was very important to me finding joy in learning it.
Hahaha 🤣😂🤣😂
Mr. Frenkel seems like an absolute fantastic person. The way he seems constantly on the edge of laughing fills me with joy.
i would love to go on a 2 mile walk with him
He’s giddy, as a child tasting ice cream for the first time ❤
This conversation is so moving that I've cried several times through it, and I barely cry for anything in life. Edward is such a gift to this world! Same for Lex.
😂
Get checked out
@@sharaudramey9336 it is special to hear a mathematician describing his grief for a special father
@@YQVN35 3:37:40, talking about how proud his dad was in Boston at the 2 lectures.
I think you cry more than you’re leading on. Quite often.
- 🧐
The chemistry between these two wise, humble, eloquent people is reassuring about the future of humanity. Well worth the entire time to view and listen!
I think Lex got a bit annoyed that Frenkel interrupted him so often...
@@roberttahlmann7316 I agree.. At the start at least
@@roberttahlmann7316 I think Dr Frenkel was just a little excited to speak his mind
Quite possibly the best conversation on this podcast yet, and that’s saying a lot. I’m already hoping for Edward Frenkel part 2
I took Calculus with Frenkel waaaaaaayyyyy back at Cal. To this day he's easily my favorite professor. He made lectures fun and his charisma was Feynman-esque. A wonderful person
Lucky you!
I have watched 90% of your podcasts in the quest for learning and understanding. This is rhe very, very best. A humble guest who is is one of the best in the world and Lex thank you for letting him rock. This coukd be the highest intellectual you looped with. Lex thank you for doing a disciplined listening without showing your intellect. I can't thank you enough. Peace Love Light Laughter, brother
I agree.
💯
He's gotten better at it, podcast by podcast. Being the wallpaper is a great art. Beautiful inviting wallpaper though!
Would you have any other suggestions to watch?? This is the first full length Lex podcast I’ve watched and I thoroughly enjoyed it as well. I’ve been looking for equally good talks but nothing compares to giving this a second listen haha. Any suggestions much appreciated, Lex or other.
This is completely not what the topic is about but his vocabulary is perfect. I am from Georgia and love vocabulary but his choice of words is far above the perfect words I would have chosen. Not to mention he is brilliant and humble. I have yet to hear from a more smart, humble person in my lifetime. I never knew this type of conversation was available. I never rewatch information but I may watch this 3-5 times. Thank you Lex.
Can't agree with you more, Clay. I said elsewhere these words about Edward’s grasp of the language and his descriptive powers: ‘It is his overall intelligence and very clear thinking. And, of course, his automatic care of meaning that his thought process delivers. An example of mathematical precision in spoken language with a natural human touch.
I enjoyed listening to this conversation so much!’
Just wanted to share the joy with you as you noticed his choice of words and his superior smartness… And English is his second language acquired in his adulthood, not when he was a child.
Now I need to order the book. ;-))
I don't mind admitting I'm about ten years older than Lex is but I wanna be like him when I grow up.
Based
Luv that! Really made me laugh - joyfully - thanks ( from someone at least 20 years older)
Always aim high❣️ and be okay with what, as something will, comes out of it. Your definitely helping others already, thanks👍💞
He might be the wisest man alive because he has listened and talked to different lives over and over again.
Same
"It is impossible to be a mathematician without being a poet in the soul." Amazing. And an amazing interview with this beautiful man. Thank you for it.
I cried at Edward's revealing of his deep trauma.....it was a purgative experience and I am grateful for your having this touching interview; while my own teenage trauma was at the hands of my parents, I can relate as despite this I went on to a fruitful career in law and now in the arts. Blessings to you and Edward.
Thanks for the positivity of your comment.
Trauma can be overcome.
No one mentions how insanely clear and Well produced/engineered the audio is on every episode. Your mic gain is absolutely chefs kiss and the gate levels you're using are icing on the cake!!!
As an Engineer, hats off to you bc it's so sauce to enjoy these just that much more.
Much love!!!!!! This episode is unreal
Getting compression just right and keeping up with around -16 to -14 LUFS
I’ve always wanted to see the process of Lex setting rolling up to a hotel room and settling up the audio gear
Haha that’s the last thing I’d notice, listening on a janky old iPhone with only half working speakers
Loved every second.
Can part 2 be 6 hours?!
@@Mr88Andrew88 it’s affecting you the most then, my friend. You would not believe the nuances and the impact of properly engineered audio. When done such as Lex’s pinnacle quality, it translates to all mediums for the best and most pleasing listening experience. That goes for teeny headphones or a broken iPhone, all the way to stadium loud speakers.
Engineering the sound to be actualized in clarity is the most integral and unnoticed aspect (to the laymen!) much love fam!
What a beautiful conversation. The way Edward Frenkel manages to put into words the feelings, thoughts and events that shape us and relate us to each other is so impressive! He's funny, he's charming, he's brutally honest, truthful and so.. human! Such insight, wisdom and vulnerability. This is as much a dialogue about what it means to be a human as it is about mathematics and science. A fantastic experience from start to finish! Thank you, Lex
@@Zoomo2697 you ever done psychedelics? Probably not, judging by your comment.
@@Mr88Andrew88 xd
Lex’s guests never cease to amaze me. And might I add his comment sections are equally wonderful, sincere, and genuine. The positivity is very refreshing :)
Expct some bots spamming in this video lol
I totally agree
He calms me. And the comments do to. Unlike most things on social media which brings me pure stress
It just goes to show how much we appreciate the sharing of knowledge and viewpoints from genuine, scientific fellow humans.
I didn’t know how deeply my heart needed this conversation.
One of the things I love most about this podcast is I get to hear intelligent, informed people discuss crazy stuff I've been thinking about alone in my head, and articulate their beautiful opinions on it. It was a joy and thrill to listen to this, especially the talk of subjective reality.
The amount of joy I get from listening to stuff like this
I didn't expect to ever meet a guest that could rival lex in his authenticity, openness, honesty, and the kind of love it takes to hug the whole world. I can't think of words that wouldn't sound incredibly cheesy to describe how amazing this conversation was in so many different ways.
I completely agree and I if you haven't watched it already, I would wholeheartedly recommend to you and to everyone who liked and finds Edward interesting and the topics he touches here, please watch these couple of episodes of Nuberphile on YT with him. That was my first introduction to him and I was instantly bought, unbelievably interesting stuff.
As a mathematician and just a human being, I cherished and enjoyed tremondously this talk. Edward is a magician!
Agreed, & I know because I was raised by people.
Yes
Man knows so many hard-hitting, eye-opening and awe-striking lines from the greatest minds in science, philosophy and psychology. Every time he quoted a saying and went on to elaborate it hit like wave after wave of wisdom and inspiration. Being an applied maths and physics student myself, I don't think I have a better person to look up to ;)
I think this is literally one of hte greatest conversations ever recorded. Edward Frenkel is absolutely brilliant. Damn, he even raised theme of paradoxes and Necker's Cube, which I tought others... Unbelievable. So many great points and arguments, even not arguments, but pure thoughts.
What a beautiful soul. Both a genius and mystic all at the same time and vulnerable and open. Thankyou Lex for introducing me to him it gives me hope about the possibilities of being human. I wish I could express it better.
And with this interview Edward Frankel has become one of my favorite people in modern mathematics and science and general
Lex, please do more Math related interviews. As someone who hasn’t studied math since high school and have now realised it’s importance in philosophy (Wittgenstein), art/design, literature (David foster Wallace), and of course physics and the sciences, it always feels amazing to learn more and understand more about complex mathematical problems which hold secrets about the truth of the universe- beyond what words can describe. And the more i underhand math the more it makes sense in the context of every day life and seemingly unrelated (humanities) fields.
I lost my love of mathematics in high school when the instructor insisted that we students do all the Trig computations in our minds without paper and pencil. I could thrilled at doing Trig on paper and gave up. Now my aspie grandson laughs and tells me it is not possible to get credit UNLESS one shows their work on paper.
@@ultmiddle4991 ya that’s crazy. On paper was the way for me too as that’s how you show proof you actually did it the right way and just copy some answer. sad for you, but you should still give it another try, get back into it. Buy a textbook or watch some educational vids. Or just try and find Mathematical problems in your everyday life or in your work and try and solve it on your own. That’s always more organic than forcing yourself to leave for the sake of it. I’ve been trying to do that and taking online courses help too- they give you a clear objective and end goal.
@@giuoco 🖖🫶🏼👍🔥
Witten!
It was hard for me to hear his ideas because I was distracted by listening to,and being blow away by how good his English is. I had never heard of him, and his expertise is not my thing, but I'm a fan of this guy now. I absolutely love how he is open to the mystery of things instead of claiming that he knows the truth. So refreshing, especially by someone so intelligent and well studied.
Btw, Lex the edits of images of topics that come up is very much noticed and appreciated!
I kept coming back to youtube for 3 days to finish this interview. So thrilling to watch. I could see the "Love and Math" in every word he spoke.
I saw Edward on that Numberphile video years ago, and I immediately got this impression that this guy is special, would have made for an amazing teacher and colleague. So awesome to see him on here, this interview was truly great.
Lex - the master of conversation. How brilliant he can join different disciplines, points of view, humours, personalities. Incredible. How elastic-minded he has to be to make 3-4 hours talk with the best current scientists. Impressive and this is a treasure in the mud of idiotic internet.
A wonderful man, a wonderful mind, a wonderful soul.
Edward Frenkel is a real gem.
Nah looks kinda delusional
@@CausallyExplained in what sense?
@@babouras84 Like how he correlates freewill with quantum mechanics. Even if the world is not deterministic, freewill will won’t exist. We have freedom of choice, not freewill.
@@CausallyExplained Could be that he was thinking freedom of choice, but he said freewill. In some Slavic languages you need extra words to describe the difference. So in a daily conversation (and he's speaking very fast), it happens that your choice of words doesn't always reflect the proper meaning. It hardly makes him delusional.
I have dyslexia.. I honestly read that as "Edward Frenkel is a real jew" 😂 it also must have been partly because he was speaking of the mathematics university in Moscow and his father when I read it..
I didn't know that in Russia if one's family name is of Jewish heritage that the person's nationality is Jewish - I never knew that was even a nationality.. (have I perhaps heard it wrong?)
To be persecuted for this is truly TERRIBLE!☹️ I was under the impression that Russia was (historically) home to many many Jewish people. Alex's surname for example.
Just thought that was strange, regarding nationality etc
I was not expecting this to be one of my all-time favorite interviews, but it is. Edward is amazingly briliant and thought provoking - Please have him on again sometime!
Edward is just pouring the light of knowledge and of his heart in this conversation. So grateful to witness this!
What an extraordinary mathematician and "liberated" human being Edward Frenkel is! Overcoming rejection and turning it into a great lesson or opportunity without blaming others and/or himself "liberated" his mind, in a Buddhist sense. He made me laugh and cry throughout the entire episode. Thank you so much Lex for this enlightening podcast. I enjoy and love every bid of it.
This amazing guy not only is a brilliant mathematician but has a wonderful grasp of the English language as well as a great accent
It is his overall intelligence and very clear thinking. And, of course, his automatic care of meaning that his thought process delivers. An example of mathematical precision in spoken language with a natural human touch.
I enjoyed listening to this conversation so much!
@@sergeirusakov4888wow Iove your comment, what a beautiful insight :)
At 1.50.00ish in when he slowed down and spoke softer - I just wished he'd spoke like that the whole time.. But I understand why, he was excited & passionate about what he was saying. So it's not a criticism, it was just a little hard to understand everything he was saying. Very interesting guy
@@roddy2body yeah I kept having to rewind a few seconds. Clearly he was excited, interrupted lex a few times. But I think he would be wonderful to listen to in Russian, if I knew Russian haha.
Been such a fan of his for almost a decade after first seeing him on Numberphile! Highly recommend his book Love & Math to everyone. Lex you are a legend for your guest selection.
Why is it that when I fall asleep with RUclips on, that I always wake up to this guy?
How he talked about his father had me crying, what a beautiful person through and through. Thank you Lex & Edward, this was phenomenal.
I loved the words of making every person valuable. Every person is a unique answer.
Любовь это уникальное событие.....Спасибо,Вам
"Love is a unique event....thank you" ❤
@@jarrodanderson2124 thank you 😊
What a great mind and human being.... It was a pleasure to listen to him.
I'm at roughly the 1 hour and 50 minute point and I have just started watching this discussion again. I wasn't going to comment bcuz I don't want to embarrass myself, but when I put this back on I heard you ask Mr Frenkel about Eric. What a joy this is for an uneducated nobody like me bcuz Eric is the reason why I decided to watch this. I got to know him for the first time on the JRE and now I'm being introduced to Ed in your class. I can see why these two deeply spiritual beings have such an admiration for each other. All three of you claim that you are men of science. I don't know anything about that side of life, yet you all have such a uniquely soulful way of talking about your life's work that even I am allowed to connect to it's beauty and wonder. Thank you all, sincerely Genevieve 🙏🏽🙏🏻🙏🏾
The type of clear thinking you only get from a true scientist. It's inspirational to see such a level of passion and involvement in everything that one does. Absolutely knocked it out of the park, one of the best podcasts I've ever listened to.
34:34 - first time a guest of the podcast looks directly at the camera and into our souls
Edward Frenkel would definitely be a top 5 pick for a great dinner party guest. I can imagine the wonderful conversations about any number of far-reaching topics.
I love this guest. So positive, so honest, so smart, so kind. Thank you!
This was incredible. The world feels warmer after you realise there are humans of this intellectual and emotional grandeuse. Thank you.
This is a very good one, he is light and deep in his learning and has joy, with his study of many things., thanks .
Lex accent is present, but Edwards accent is so heavy, that at some point my жена зашла и спросила "почему они не начнут уже просто говорить по русски"
great episode, as allways)
😂😂😂
Till today I didn't realize you can fall in love with a conversation, just like you do with a person, a place or a song.
such a charming and humble man
I just listened and listened and could not stop. Those almost 4 hours passed very fast. Fascinated both by his genious as well as by his big love to things and his way to see the world, Edward really captivated me.
Been watching this in pieces so it doesn't end... Edward Frenkel has such a charisma, it's really inspiring
Dude this guy’s quote game is off the charts
Lex Fridman and Edward Frenkel stand as titans of intellect, transcending the mundane and daring to ascend the heights of thought. Lex, the fearless inquisitor, pierces the veil of complacency, awakening the slumbering spirit within us. Edward, the mathematical poet, weaves a tapestry of eternal truths, defying the nihilism of ignorance. United, they become an unstoppable force, heralding a new era of intellectual prowess and enlightenment.❤
One of the best podcasts ever. Edward is magnificent
This is the visual of two lights connecting and bringing an emerged new light that touches people even across the world. every second of this dialogue was beautiful. Love and appreciation from Tehran
This episode is absolutely "Из Вечности"... Thank You both.
Lex, your podcasts give me comfort and hope for humanity. It's so wonderful to go on all these thought trips. I don't have many friends I can talk to about any of all this, and I run in highly educated circles, but everyone is closed off. Your attitude towards all your guests is what the world needs. I love you and this podcast more than any online content anywhere. Thank you.
Educated people tend to be proficient only in the subjects they study/teach, it's a generalisation but I do think we could all be a little more open minded. Mind you, I'd say those of us who listen to Lex's wide array of guest's are naturally more open minded, curious & hungry for knowledge of all kinds 😉
I'll add that in no way am I highly educated, I have very minimal academic education to be honest
Beautiful comment, Deirdre.
I do think there is a huge difference in highly educated and high intelligence, but I would say that though 😂
Agree with you totally! The young Lex is outstanding.
@@roddy2body I agree, it's totally not education or even pure intelligence that defines an agile mind, but curiosity.But I am grateful there are experts as well because then they can explain it all to those of us who like to learn a little about everything! :)
Edward's logic thought process and reasoning are inspirational. He fuses scientific knowledge with emotions like no other. Worth it every minute!
He’s a natural philosopher! Speaking of paradox, read Chesterton.
Makes me very happy that people like this are at the forefront of academic thinking
So much to choose from this conversation that touched my heart, my mind and banged them both around a hundred times. If I were to choose one, I'd point to how Edward Frenkel thought his dreams were over at 16 as a consequence of anti-Semitic, unspoken polices of the ex-Soviet Union - how loss fueled his work and within a few years he would be a professor at Harvard. That arc he traveled is universal in many ways, and certainly made me think of my and my own father's lives. Thanks Lex and Prof. Frenkel for a brave and beautiful voyage into love and math.
Earlier I was suspicious/untrusting when to trust Lex Fridman, now I know he is for real.
REAL meaning he is really an intelectual person, a life-long learner.
Go Lex! You have such great people visiting your show. Keep going
I love how you can take these very complicated topics and explain them with wit and humour.
Edward frenkel is so inspirational.he made me fall in love of maths.
This episode was incredibly comfy. Cozy, even. Like warm socks and hot apple cider.
And a nice, ordered set.
Edward Frenkel is a genuinely good person and an extremely gifted mathematician. He exudes a refreshingly deep understanding of the hidden reality beyond our common intuition and is a pleasure to listen to his exquisite insights. Thank you, Lex, for yet another interesting dialogue with this special guest!
What a beautiful example of a truly wise scientist who is not afraid to share his personal spiritual growth and open attitude towards the mystery, reminding everyone to embody their childlike playfullness and innate curiosity. I hope that many young scientifically minded people will feel inspired by Edward to expand their perception.
Great conversation. He’s very charismatic and makes math sound really fun. You have to bring him back again.
This conversation has its claws into me already
Waiting for part 2... the best interview out of every single one. Thank you.
It is awesome to hear “Paradox is Fundamental” echoing through the worldview!
This was the first podcast that I kept getting interupted while listening, but over 3 days, just kept coming back to hear you both speak. Edward's views on so many different topics really put a smile on my face. Thank you for speaking with him and sharing that with us!
I was terrible in the sciences and math in school - I am 52 today and still don’t understand most of the technical details. I watched this podcast in one sitting and was totally enthralled with the conversation - the mathematician is so well spoken and distills complex phenomenon in to simple and understandable verbiage. Amazing. Lex is absolutely the best at this format
This guy is like an alternate reality version of Lex.
Edward might be one of the best humans on earth ♥️ that was an amazing episode.
I have literally fallen in love with this man
This was a masterclass on life & how to approach science from Mr. Edward Frenkel. He is a true legend.
Thank you for sharing this with us. What a gift Frenkel is to the world!
Lex you’re a living legend bro. These podcasts and special guest do so much for the world and the thinker. We’re all trying to get closer to the truth even though the closer we get the more we don’t know. Life is a beautiful mysterious phenomenon
Another great performance by Rob Lowe.
Beautiful!!! From 40:00-44:00 (ish) talking about paradox and confirmation bias…THANK YOU, Edward, for speaking truly about the nature of mystery, the possibility of missing truth because we only are willing to see what we already see. Beautiful! I have long desired to hear more modern scientists/mathmeticians get their minds around these philosophical understandings! Your depth of reading is lovely…thank you for being a very open, truly curious, knowledge addict! ;)
My journey is nothing like that of Edward but I so recognise where he is now. This deep connection is beautiful and inspires and informs me as to the truth of love and our universe. Love you man. Love you Lex. 🙏
most inspiring interview i have seen - and edward is so interesting
Wow, just 10 minutes in, and already loving this conversation. Lex, you are a true gem, finding people who can shine their light onto reality and make it not only understandable, but who bring a love for the understanding that propagates... I am curious to see how and whether the question of causality will come up. One of the ways in which I imagine mathematics and physics differ is the extent to which physics seems to imply causal "directedness", whereas mathematics seems more agnostic, and willing to consider a "hand-in-handedness" of the two sides of an equation, allowing the recipient of a force or energy (or information) exchange to be just as involved in the process as the transmitter, not privileging one over the other...
oT256Cr has the most potential to do more than X10. ETH and BTC will most likely do a X5-X6, but that's fine for me. Gotta look for better entry points while I stake IRIS and PGEN, then wait for Polygen's next raise as I also look at their new partnership with Kenzo Ventures.
Scam bot
These bots really spamming everywhere
Scam
Sounds like someone trying to convince me that the letter 'e' exists...
I love Edward. I've seen him on numberphile and the topics he discussed were instantly engaging. The one he mentioned about the sum of all natural numbers is the one that got me into math right before college. Graduated with a minor in math and have been continuing to learn on my own for the past 2 years. His passion is infectious. More people like him need to become elementary school teachers. Being able to teach math is different than being able to communicate the beauty behind it. I will be reading his book, love and math have both been resonating with me recently.
Lex, Edward Frenkel has presented a philosophical masterclass on multidisciplinary Sciences - so eloquently - intuitive, divine, mystical, inner child's wonder
Reading love & math as we speak after listening to this podcast and why did I like based on his voice Edward was much older...anyway...
I am SO ENTHRALLED with this book. Thank you Lex and thank you Edward.
That guy is an example of a great scientific mind; in search of truth.
I am a high-school Math teacher (16-18 year olds) in Canada and I teach imaginary numbers in every age above 15 years old. It's not part of the curriculum but I make space for it anyway. I learnt it in university in the 90's. Maybe when my students become teachers themselves, it will be taught in all high-school curriculums both as a calculation technique and as an exploratory paradigm.
I think it's great that you leave the beaten path of the curriculum to teach something you are passionate about.
I recently started a video series on complex numbers, in which I try to make them more intuitive. I would be very curious to find out what your reaction would be as a high school teacher. If you're interested, you can find the series here: ruclips.net/video/p13kiue-sCY/видео.html
Hi there. I like your video if I am working one on one with a student or in a tutor situation. In a larger class, I need to be able to grab their attention quickly and feed their curiosity/imagination -- especially if I am "going off-script". Because it is not part of the actual curriculum where I work, I cannot assign any major marks to its study. So I give bonus marks. The video that I show my students is this one: ruclips.net/video/T647CGsuOVU/видео.html&ab_channel=WelchLabs
Ultimately, my goal is to have students with an early grasp of imaginary numbers skills, history and applications when they graduate so that they don't need to be introduced when they go off to university. The skill can be introduced during the study of the quadratic formula and the discriminant, the history has its own unique learning moments, and the practical applications are found in the quantum biology and Tibees does a good explanation too.
During year 10 go 12 of school I started a junior engineering program and I studied math from arithmetic to triogonometry to differential equations and usually The cource had a letter (I.e. A,B,C...etc.) but wheb studying computors and programming I hade to take a complimentary 50H cource of 'Descrete Math' involving complex nummers.
I learnt abort complex nummers including 'E‐1' and my conception Washington that this was a very specific "exception" we use for very specific technical problems with computors.
Tjena The math of quantom physics emerges and complex nummers are The essential part of reality, first this was deeply unsettelling...
Haninge the proper education to 'Solveig for' this where probably essential in how fast I got integrate this new science and I never used comolex nummers outside of my education, so you are doping Great work.
Math teachers havet my love and support, they are everyday herpes.
Wow!!! This man is on fire! If this man does a psychedelics session, he will advance humanity 5000 years.
Haha omg if someone like Ed frenkel did shrooms he would reinvent calculus
😂
I am listening this interview second time. Amazed.