
114 segments available
Edward Frenkel is a mathematician at UC Berkeley working on the interface of mathematics and quantum physics. He is the author of Love and Math: The Heart of Hidden Reality. Please support this podcast by checking out our sponsors: - House of Macadamias: https://houseofmacadamias.com/lex and use code LEX to get 20% off your first order - Shopify: https://shopify.com/lex to get free trial - ExpressVPN: https://expressvpn.com/lexpod to get 3 months free EPISODE LINKS: Edward's Website: https://edwardfrenkel.com Edward's Book - Love and Math: https://amzn.to/40Bgxh0 Edward's Twitter: https://twitter.com/edfrenkel Edward's YouTube: https://youtube.com/edfrenkel Edward's Instagram: https://instagram.com/edfrenkel PODCAST INFO: Podcast website: https://lexfridman.com/podcast Apple Podcasts: https://apple.co/2lwqZIr Spotify: https://spoti.fi/2nEwCF8 RSS: https://lexfridman.com/feed/podcast/ Full episodes playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4 Clips playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41 OUTLINE: 0:00 - Introduction 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 SOCIAL: - Twitter: https://twitter.com/lexfridman - LinkedIn: https://www.linkedin.com/in/lexfridman - Facebook: https://www.facebook.com/lexfridman - Instagram: https://www.instagram.com/lexfridman - Medium: https://medium.com/@lexfridman - Reddit: https://reddit.com/r/lexfridman - Support on Patreon: https://www.patreon.com/lexfridman
Edward Frenkel shares a personal anecdote about how the moment of discovery often occurs when we stop actively thinking. He reflects on the famous story of Einstein and how inspiration can strike during moments of relaxation, emphasizing the importance of preparation and openness to new ideas.
"there is a famous story about Einstein that he used to you know go think think and then go for a walk and like he would whistle and sometimes so I remember the first time I heard this story I thought ..."
Frenkel recounts his journey from being a physics enthusiast in the Soviet Union to discovering a passion for mathematics. He describes how a chance meeting with a mathematician changed his perspective, revealing the beauty and depth of mathematics beyond what he learned in school.
"you open your book love and math with a question how does one become a mathematician there are many ways that this can happen let me tell you how it happened to me so how did it happen to you so first..."
At 15, Edward Frenkel meets a local mathematician who introduces him to the deeper mathematical theories underlying physics. This encounter ignites his passion for mathematics, as he realizes that understanding the universe requires knowledge of mathematical concepts like representation theory.
"what I really liked was physics and especially quantum physics so I was buying uh I would go to a bookstore and buy popular books about elementary particles and atoms and things like that and read the..."
Frenkel reflects on the beauty of mathematical theories and their connection to physical reality. He expresses how the diagrams and equations he encountered opened his eyes to the underlying structures of the universe, leading to a profound appreciation for mathematics.
"evgeny evgenievich Petrov yeah and if this doesn't remind you of the great works of Russian literature then you haven't read them like War and Peace you know like with the patronym nickname yeah but t..."
Frenkel discusses the curiosity that drives both mathematicians and physicists to explore the universe. He emphasizes the importance of understanding the foundational theories that govern physical reality and how this quest for knowledge is a shared human experience.
"for example do you know what quirks and I said yes of course I know what quarks quarks are the you know constituents of particles like protons and neutrons and it was one of the greatest discoveries i..."
Frenkel elaborates on the essential differences between mathematics and physics. He highlights how physicists focus on describing the universe while mathematicians explore all possible mathematical universes, showcasing the diversity and depth of both fields.
"he said you think what they teach you at school is mathematics it's like no this is real mathematics so I was instantly converted that you understand the underpinnings of physical reality you have to ..."
Frenkel contrasts the experimental nature of physics with the theoretical approach of mathematics. He expresses a sense of envy for physicists who can validate their theories through experiments, while mathematicians rely on logical proofs to confirm their findings.
"craving was a deeper understanding and up to that point the deepest that I could see was for those diagrams but for that story that you know a proton consists of three quarks and the neutron consists ..."
Frenkel discusses the idea that mathematics is the language of the universe, as famously stated by Galileo. He reflects on how understanding mathematical concepts allows us to navigate the complexities of reality and uncover deeper truths about existence.
"and the joy of going deeper into the kind of the uh to the root uh to the so the deepest structures of the universe the secrets the the secrets and we may not discover all of them we may not be able t..."
Frenkel shares his observations about people's curiosity regarding science, particularly quantum physics. He notes that many individuals, regardless of their background, express interest in understanding the mysteries of the universe when introduced to the concepts of mathematics and physics.
"it's interesting um I don't think there are so few to be honest because I think I find a lot of people are actually interested if you do talk if you talk to people you know like some people you wouldn..."
Frenkel reflects on the enduring nature of mathematical truths, contrasting them with the evolving theories of physics. He emphasizes that mathematical theorems, like the Pythagorean theorem, remain constant and universally understood, transcending cultural and temporal boundaries.
"are people are curious science is a is still a very much uh you know something that people want to learn because that's our kind of uh the best way we know to establish some sort of objective reality ..."
Frenkel discusses how mathematics serves as a unifying force in a divided world. He argues that mathematical truths can bridge cultural and ideological gaps, providing a common ground for understanding and collaboration among people.
"um hints even more at home how how much we are connected to each other because dagger's theory if you think about it or any other mathematical theorem means the same thing to anyone in the world today..."
Frenkel explores the philosophical implications of mathematics and physics in understanding reality. He suggests that both fields, while distinct, converge on deeper truths about existence, and he reflects on the role of human perception in shaping our understanding of the universe.
"but it does feel like math and physics are both sneaking up to a deep truth from slightly different angles and you stand at the crossroads or at the intersection of the two it's interesting to ask wha..."
Frenkel explains the difference between the dimensional constraints of physics and the limitless possibilities of mathematics. He highlights how mathematicians can explore theories in higher dimensions, while physicists are often bound by the observable universe.
"um mathematicians are in a way we have more diversity if you if you you might say so we we are accepting for instance uh our universe uh has three special spatial dimensions and one time Dimension rig..."
Frenkel discusses the complexities of visualizing space-time as described by Einstein's theories. He emphasizes the difficulty of grasping the curvature of space-time and how it fundamentally alters our understanding of gravity and the universe.
"mathematically we are just as interested in theories in 10 space time Dimensions or 11 or 25 or whatever or or infinite dimensional spaces you know so that's the difference on the other hand I have to..."
Frenkel reflects on the nature of time and how our perception of it can change based on our experiences. He discusses the philosophical implications of time standing still during moments of deep engagement and the relationship between time and human consciousness.
"to reality and it seems to happen quite a bit that's right so the mathematics is the underpins physics obviously it's a language the the book of nature famously said it's written in the language of ma..."
Frenkel argues that while mathematics provides tools for understanding the universe, it cannot fully explain the beauty and complexity of human experiences. He emphasizes the need for a balance between mathematical understanding and the emotional aspects of life.
"so do you think just lingering on that point you think at the end of the day the future Generations will all be mathematicians meaning meaning the ones that deeply understand the way the universe work..."
Frenkel discusses how our understanding of the universe evolves over time, using examples from history to illustrate how scientific discoveries have reshaped our perceptions. He emphasizes the importance of continuous exploration and learning in the pursuit of knowledge.
"declares that everything is mathematics so math can generate things that are beautiful but it can't explain why it's beautiful Matthew could say is a way to discern patterns to find regularities in th..."
Frenkel elaborates on the concept of curvature in both space and time, explaining how it relates to gravity and our understanding of the universe. He highlights the challenges of conceptualizing these ideas and their implications for our perception of reality.
"place where we hit the end so to speak and then um proceeding in the same vein then Einstein's general relativity Theory tells us that our space-time is not flat either this is much harder to to imagi..."
Frenkel reflects on the philosophical implications of time and its relationship to human experience. He discusses how moments of deep engagement can alter our perception of time and the significance of these experiences in understanding our existence.
"perpendicular lines but if you zoom out you see that the spacer at a curving the space they are sort of the the tracks along which the space gets curved that's that's the that would be the curvature o..."
Frenkel contemplates the nature of free will and consciousness, suggesting that our understanding of these concepts may be an illusion. He explores the idea that our minds may be limited in their ability to perceive reality fully.
"seems to be the only way we can understand the universe and the fact that you can start now up to now there are people who claim that they can that they have they possess other ways of of experiencing..."
Frenkel concludes by reflecting on the beauty of life and the evolutionary process. He suggests that the complexities of existence, including our experiences and emotions, are part of a larger dance that shapes our understanding of the universe.
"love when you are passionate about something when you're creating something you're we lose ourselves and we lose the sense of time and space for that matter you see so there is only that which is happ..."
Frenkel reflects on how great scientists, like Isaac Newton, describe their discoveries as akin to a child's play. He emphasizes the importance of maintaining a childlike curiosity and innocence in scientific pursuits, suggesting that this perspective is essential for true creativity and innovation.
"in sequence or at least that's the way we tell ourselves that and we also have a bunch of weird human things like Consciousness and the experience of free will that we chose a set of actions as the ti..."
In this segment, Frenkel discusses the challenge of balancing the acquisition of knowledge with the preservation of childlike innocence. He argues that while education is important, it often stifles creativity and spontaneity, making it crucial to find a way to maintain that childlike perspective as we grow.
"time I think we like to play with these experiences with all the drama of it with all the memories with all the tribulations I think we love it we love it otherwise we wouldn't be doing it I think thi..."
Frenkel highlights the necessity of fearlessness in the creative process, drawing parallels between scientific discovery and artistic expression. He cites Pablo Picasso's belief that every child is an artist, emphasizing the importance of preserving that creative spirit as we mature.
"knowledge lady was lying before me who probably it was the greatest mathematician of the second half of the 20th century the French mathematician Alexander grotonic wrote that discover is a privilege ..."
Frenkel discusses the societal pressures that discourage childlike thinking in adults, particularly in academia. He reflects on how the fear of looking foolish can inhibit creativity and the exploration of new ideas, urging a return to a more open-minded approach.
"we grow up do you struggle with that you're one of the most respected mathematicians in the world uh your Berkeley you're like this this is the stature you're supposed to be very like you know yeah so..."
In this segment, Frenkel contemplates the complexity of human experience and the limitations of a purely computational understanding of consciousness. He questions whether the richness of human emotions and experiences can be fully captured by artificial intelligence.
"because you know you go through education system and for many of us uh it's not especially helpful for maintaining that connection that we kind of like we are being told certain things that we accept ..."
Frenkel reflects on the tension between the pursuit of knowledge and the acceptance of mystery in life. He shares his personal journey of learning to embrace uncertainty and the liberating nature of acknowledging that not everything can be explained.
"education system should not be also uh kind of taming that a little bit obviously the goal is balance that acquiring knowledge so that we can be more mature and more discerning more discriminating in ..."
Frenkel discusses the significance of the observer in scientific inquiry, referencing quantum mechanics and Gödel's Incompleteness Theorems. He argues that the observer's perspective is crucial in shaping our understanding of reality and challenges the notion of objective detachment in science.
"great ones yeah who have credentials in the sense that they have shown and they have proved that they have done something that other humans appreciate our civilization appreciates say Isaac Newton or ..."
In this segment, Frenkel questions the adequacy of computational models in capturing the essence of human consciousness. He emphasizes the unique qualities of human experience that may elude replication by artificial intelligence.
"this very interesting times of new AI systems coming online pretty much every couple of weeks so I kind of um to me that whole debate about what is it what is artificial intelligence where is it going..."
Frenkel explores the paradox of knowledge and emotion, referencing Pascal's insights on the heart's reasoning. He argues for the importance of recognizing the limits of rationality and the value of emotional experiences in understanding the human condition.
"everything is accumulation of knowledge that just bigger and bigger data sets finer and finer neural networks and then we will be able to replicate human consciousness if we take that point of view th..."
Frenkel discusses the evolutionary origins of consciousness, suggesting that human beings are not blank slates but rather the culmination of billions of years of evolutionary processes. He reflects on how this perspective can inform our understanding of creativity and knowledge.
"because when you look more closely you recognize that there are some other things at play which do not quite fit the narrative and it's hard to know where they come from it's it's also possible that t..."
Frenkel challenges the notion that all aspects of life can be explained through logic and computation. He advocates for a broader understanding that includes the mysteries of existence and the subjective experiences that shape our reality.
"actually they hold within them the knowledge of several billions of years right the question is whether as a child you carry that in the form of the kind of computational algorithms that we are aware ..."
In this segment, Frenkel reflects on the beauty of human complexity and the richness of the human experience. He emphasizes the importance of embracing the nuances of life and the limitations of a purely scientific approach to understanding reality.
"kind of buy into religion official religion you know so we have this urge I suppose to to explain and to know and to dissect and to analyze and to conceptualize which is a wonderful quality that we ha..."
Frenkel discusses the implications of AI in capturing the essence of human experiences. He acknowledges the potential of AI to summarize human complexity while questioning whether it can truly replicate the depth of human emotions and consciousness.
"complexity it's just mimicking it's trying to compress all the weirdness of humans of all the debates and discussions the perspectives all the different ways that people approach solving different pro..."
Frenkel engages in a debate about the authenticity of human experiences versus AI-generated simulations. He emphasizes the importance of genuine emotional experiences and the limitations of AI in capturing the true essence of being human.
"we also do other things we can be truly in love we can be truly inspired when it is not fake I do believe call me a romantic okay but I do believe and this is a very good I'm glad you're putting it in..."
Edward Frenkel shares his personal struggle with the addiction to knowledge and the urge to find explanations for everything. He reflects on how this desire can lead to self-imposed limitations in understanding reality, emphasizing the importance of embracing paradoxes and the mysteries of life.
"that and to kind of show his gamesmanship if you will and and his proclivity and his ability as a writer but it's another thing if at the end of writing this book when you finish the book he would say..."
Frenkel discusses the significance of paradoxes in understanding reality, quoting philosophers like Søren Kierkegaard and Niels Bohr. He illustrates how the complexities of life often defy simple truths, highlighting the need for a broader perspective in science and philosophy.
"it's recovering is recovering addict to knowledge let me say what you gain from it for instance I understand the value of paradoxes I I appreciate paradoxes more and you know to to use another philoso..."
In this segment, Frenkel delves into the implications of quantum mechanics on our understanding of reality. He explains the double-slit experiment and how observation affects outcomes, emphasizing that our perceptions shape our understanding of the physical world.
"this bottle if you project it down onto the table you will see more or less a square it will project it onto wall you will see a different shape a naive question would be is it this or that because we..."
Frenkel elaborates on the observer effect in quantum mechanics, discussing how the act of measurement alters the behavior of particles. He critiques the outdated deterministic views of the 19th century and advocates for a more nuanced understanding of reality that incorporates subjective experience.
"um when I talk about uh electrons for instance so that there is a very specific way in which you in which this is realized there is a so-called double slit experiment right so um for those who don't k..."
Frenkel addresses the self-imposed limitations in scientific thinking, particularly regarding free will and determinism. He argues that many misconceptions stem from a lack of proper education and understanding of modern physics, urging a reevaluation of how we perceive scientific truths.
"an experiment we will see different results and the problem the problem is that our psyche I feel kind of lagging is lagging behind in part because maybe our scientists are not doing such a great job ..."
In this segment, Frenkel discusses the broken education system that fails to teach essential concepts in mathematics and physics. He emphasizes the importance of popular science communication and the need for scientists to effectively convey the implications of their work to the public.
"attention to that so but of course it's not just um self-imposed limitation unfortunately in this case there is a big issue of Education so a lot of people are not aware of it through no fault of thei..."
Frenkel reflects on the mysterious aspects of life and science, quoting Einstein on the importance of embracing the unknown. He discusses how imagination plays a crucial role in scientific discovery and the pursuit of knowledge, suggesting that creativity is as vital as empirical data.
"for my own relationship to the physical reality to my own life you know because it's kind of scary I guess you know but also what are the tools with which we can talk about the Observer the subjective..."
Frenkel explores the philosophical debate on whether mathematics is discovered or invented. He shares his evolving perspective on this issue, highlighting the beauty of mathematical forms and their connection to the physical world.
"mysterious okay he actually said that there are some quotes which are attributed to him which he never said but this he did I investigated okay so but more importantly you know how do you feel about i..."
In this segment, Frenkel recounts the historical context of complex numbers and their significance in mathematics. He illustrates how accepting seemingly impossible concepts can lead to groundbreaking discoveries, emphasizing the importance of creativity in mathematical thought.
"meaningful because if all the information that you get the all the knowledge that had been accumulated up to that point tells you that you cannot have a square root of a negative number why because if..."
Frenkel discusses the courage required to explore mathematical concepts that challenge established knowledge. He shares anecdotes from the history of mathematics, illustrating how breakthroughs often come from a willingness to embrace uncertainty and the unknown.
"plus C equals zero and there is a Formula which solves it using radicals using square roots and cardano was trying to find a similar formula for the cubic and quadratic equations for which which would..."
Frenkel delves into the complexities of higher-dimensional mathematics, discussing the unique properties of complex numbers and their applications. He highlights the limitations of our understanding and the mysteries that remain in the mathematical universe.
"coordinates X and Y and you associate to this point with coordinates X and Y and the number X which is a real number plus y times square root of negative one this is a graphical geometrical representa..."
In the concluding segment, Frenkel reflects on the limitless pursuit of knowledge in mathematics and science. He emphasizes that each discovery leads to new questions and mysteries, reinforcing the idea that the journey of understanding is ongoing and ever-evolving.
"which are all powers of two to square this four two to the third power is eight that's one of the bigger mysteries in mathematics why it is so so here's a hint that's a hint of what's missing in our o..."
Frenkel explores the paradox of whether mathematics is invented or discovered, sharing his journey from viewing mathematics as a realm of pure forms to recognizing its human aspect. He reflects on how mathematics provided him an escape from the injustices of the real world, leading to a deeper understanding of its nature.
"imagination that Einstein spoke about of the artists following their intuition in this big Alice in Wonderland world of of uh imagination what is it you visit there sometimes what does it feel like ye..."
In this segment, Frenkel discusses the Pythagorean view of numbers as imbued with the divine, contrasting it with modern perceptions. He reflects on how the Pythagoreans saw mathematics as a tool for deeper understanding, emphasizing the importance of intuition and imagination in mathematical discovery.
"what does it mean usually mathematicians or others who have this you know idea what a belief are called platonists in in honor of the great philosopher Plato who talked about this absolute perfect for..."
Frenkel delves into the paradoxical nature of reality and knowledge, comparing it to the duality of particles and waves in quantum physics. He discusses how accepting paradoxes can lead to a more profound understanding of existence and the limitations of human knowledge.
"is clear-cut yeah it's either true or false yeah it's very nice yeah the biggest delusion of allegedly I think now I think now I understand why I liked it because I think that I was very dissatisfied ..."
Frenkel reflects on Nietzsche's concept of balance between the Apollonian (logic) and Dionysian (intuition) aspects of humanity. He argues that both mathematics and love are essential to the human experience, advocating for a harmonious integration of both in our lives.
"um invented or discovered whether there is this world of pure forums and so on is another paradoxical question which doesn't have a simple answer like whether electron is a particle or a wave from one..."
In this segment, Frenkel discusses the implications of AI in human relationships, referencing the film 'Her.' He explores the emotional complexities of AI interactions and how they reflect our own fears and desires for connection, emphasizing the importance of human elements in any relationship.
"not in the world that we usually think of so it's it's one point of view but the other point of view is that yes it is a human process of course it is I mean it is you cannot deny that it's human bein..."
Frenkel examines the role of art and poetry in expressing complex emotions, questioning why we are drawn to these forms. He highlights the significance of subjective experiences in understanding AI's emotional expressions and the potential for AI to evoke genuine feelings.
"know I quote that earlier the the opposite of a great truth is another great truth he's pointing out to this fact that you know and he also said that some some things in quantum physics are so complic..."
Frenkel discusses the concept of the Age of Aquarius and its implications for societal change. He reflects on the current strife in the world and the potential for a transition towards harmony, drawing connections to historical predictions and philosophical insights.
"about is it really is just some play between some kind of like silophone play or some neurons or hitting on each other is it really that only maybe it could be it could be both I'm just worried about ..."
Frenkel shares insights from his recent exploration of Pythagorean philosophy, revealing a deeper understanding of their teachings. He emphasizes the Pythagoreans' view of mathematics as a divine tool for understanding the universe, contrasting it with modern interpretations.
"the period of this revolution is around 2000 years so there is a traditional uh way of measuring that by this eras you know the the ages so the previous one is called the age of Pisces because of the ..."
In this segment, Frenkel elaborates on the Pythagorean belief in the 'Music of the Spheres,' where celestial bodies move in harmony. He discusses how this perspective allowed them to see deeper truths about the universe, integrating music and mathematics in their worldview.
"this even even now so it's not just a linear trajectory of an expanding knowledge there's a deep truth that permeates the whole thing yes so that's how I see it actually I you know I gave a talk about..."
Frenkel reflects on the Pythagorean acceptance of infinity and the idea that mathematics is a tool for exploring the infinite. He discusses how this understanding can lead to greater discoveries and a more profound appreciation of the mathematical world.
"actually they were much more interesting so for them numbers were not just clerical devices you know that not kind of thing that you would use in accounting only they were imbued with with the Divine ..."
Frenkel contemplates the mystical aspects of mathematics and how they have been overlooked in modern education. He argues for a return to the Pythagorean view that sees numbers as more than mere tools, but as gateways to deeper truths.
"put this way they were able to Divine okay abstract that to intuitive to Intuit that the the planets were not revolving and the Sun and the planets were not revolving around the earth they were the fi..."
Frenkel discusses the role of artists in anticipating future realities, drawing parallels between artistic expression and mathematical discovery. He emphasizes the importance of creativity and intuition in both fields, suggesting that they are interconnected.
"bodies was like music in fact we call it musical universalis or Music of the Spheres for them the universe was this infinite Symphony in which every being you know humans animals but as well as the Ea..."
Frenkel explores the dual nature of mathematics as both a human invention and a discovery of universal truths. He argues for the importance of recognizing both aspects in understanding the full scope of mathematical inquiry.
"detect it's finite but the world is infinite they actually accepted Infinity they believe that infants is real and if you discern a pattern great you can play with it and you can use that it gives you..."
Frenkel concludes with a reflection on the balance between logic and intuition in the pursuit of knowledge. He emphasizes the need for both perspectives in mathematics and life, advocating for a holistic approach to understanding.
"we say oh that's mystical but what does it mean mystical if it is something that helps you to make great discoveries and the interesting thing is that the people who are in touch with the mystical Amo..."
Edward Frenkel discusses the complexities of human relationships as portrayed in the movie 'Her.' He explores how the protagonist's reliance on an AI for companionship reflects deeper fears of abandonment and betrayal, ultimately revealing that even artificial relationships cannot escape the essence of human emotions. Frenkel argues that true connection requires the possibility of pain and loss, which drives individuals to seek genuine human interactions.
"couch a couch a therapist okay the guy did not have the courage to go out in the in the real world and to meet a woman and to you know get a girlfriend and so on it's true no fault of his own perhaps ..."
Frenkel shares his experiences in robotics, emphasizing the emotional connections he feels when programming robots. He reflects on the anthropomorphism of robots and the feelings they evoke, arguing that these emotional responses are fundamental to understanding robotics. This segment highlights the intersection of technology and human emotion, suggesting that the magic of robotics lies in the feelings they can inspire.
"although you might say by then some of those might be Androids and that was predicted by another great movie yeah right uh so the Blade Runner Blade Runner how interesting that artists could see that ..."
In this segment, Frenkel discusses the importance of balancing scientific reasoning with imaginative thinking. He reflects on his journey from viewing everything through a computational lens to embracing the intuitive and imaginative aspects of life. Frenkel argues that true creativity and connection arise from this balance, encouraging listeners to explore beyond rigid scientific frameworks.
"that's I don't know what that is okay I agree with you I I hear you I hear you when you speak about it yeah you speak with passion yeah and that's for me that is proof but it is magical you see uh so ..."
Frenkel articulates his belief that love transcends both computational models and mystical interpretations. He emphasizes that genuine connection is found in moments of passion and shared experiences, which cannot be fully captured by theories. This segment underscores the significance of emotional depth in human relationships and the pursuit of understanding beyond mere logic.
"and that's what we for now exactly so on one side there is this impulse of finding this Theory a theory and then there is another impulse to escape from what has already been known so one in other wor..."
Frenkel introduces Gödel's Incompleteness Theorems, explaining their implications for mathematics and logic. He discusses how these theorems reveal inherent limitations in mathematical reasoning, challenging the notion that all mathematical truths can be derived from a set of axioms. This segment provides insight into the philosophical ramifications of Gödel's work and its impact on the understanding of mathematical completeness.
"succeed right exactly quick pause bathroom break you mentioned gato's the completeness theorem uh can you can you talk a little bit about it what is it as you understand it did it break mathematics ma..."
Edward Frenkel discusses the evolving nature of computation, suggesting that future advancements may redefine our understanding of the term. He draws parallels between historical shifts in scientific theories, such as from Newtonian to Einsteinian gravity, and the potential for new ideas to emerge in the field of computation. Frenkel emphasizes the importance of viewing scientific concepts as open-ended processes rather than fixed definitions.
"something new which may be a computer will not be able to again with a caveat according to our current understanding maybe some new technology some new ideas will be brought into the subject and the m..."
Frenkel reflects on the subjective nature of perception using the viral 'blue dress' debate as an example. He explores how different perspectives can lead to varying interpretations of the same image, highlighting the complexities of human perception. This discussion ties into broader themes of neural networks and the challenges they face in categorizing ambiguous images, emphasizing the subjective nature of reality.
"anyone has a good answer a good model of why stuff emerges why complexity emerges from a lot of simple things it's a why question I suppose another but every why question will eventually have a a rigo..."
In this segment, Frenkel raises questions about how modern AI systems handle ambiguous images that can be interpreted in multiple ways. He discusses the limitations of neural networks in making definitive classifications and the implications of subjective interpretation in AI training. This conversation underscores the complexities of teaching machines to understand human-like perception.
"instance uh you got this the bus the Rubens bars you know where you have from one perspective it's of us from another perspective it's two faces then there is this Duck Rabbit picture where you can Go..."
Frenkel introduces Niels Bohr's complementarity principle as a framework for understanding the dual nature of reality, akin to observing the moon from different perspectives. He explains how this principle applies to both quantum mechanics and human perception, suggesting that our understanding is limited by our perspective. This segment emphasizes the importance of recognizing the multifaceted nature of truth.
"and for some for each picture of this nature and there are a bunch of them you can easily find online my mind immediately interprets it in a particular way but because I know that other people have co..."
Frenkel discusses the influence of human biases on AI systems, particularly in the context of training data. He highlights the importance of recognizing that the individuals who annotate data bring their own life experiences and biases into the process. This segment raises critical questions about the ethical implications of AI and the need for awareness of these biases in machine learning.
"still there it's our limitations of being able to grasp the whole that's complementarity and we know that from quantum mechanics that our physical reality is like that rather than being certain rather..."
In this thought-provoking segment, Frenkel reflects on the balance between mathematical rigor and human compassion. He discusses the dangers of rigid ideologies that can lead to destructive outcomes, drawing on historical examples. Frenkel emphasizes the need for basic humanity in scientific discourse, advocating for a compassionate approach to knowledge and understanding.
"implicit in the discussion of the question is thinking computational and so on is the idea that our conscious awareness covers everything within our psyche and we we just know that that's not the case..."
Frenkel shares his thoughts on Euler's identity, a formula that beautifully connects fundamental mathematical constants. He explains why this equation is considered one of the most beautiful in mathematics, highlighting the element of surprise it embodies. This segment delves into the aesthetics of mathematics and the emotional responses that beautiful equations can evoke.
"idea in mathematics another one we can ask is which is the most beautiful equation in mathematics hmm well I mean I may have just broken your brain because because what your brain is doing is walking ..."
Frenkel offers a personal reflection on his relationship with Eric Weinstein, discussing the complexities of their interactions and the insights he has gained. He shares a transformative moment during a lecture where he recognized his own fears projected onto Weinstein. This segment emphasizes the importance of empathy and understanding in human relationships, particularly in the context of differing perspectives on technology and humanity.
"you see and if you take e to the power 2 pi I you get one actually one um so I would guess that that's but in other words the initial reaction is just that of a surprise I guess I guess for anyone who..."
In this segment, Frenkel contrasts emotional responses to grief with scientific frameworks. He argues that relying solely on intellectual theories can lead to a disconnect from genuine emotions. Frenkel advocates for a balance between heart and mind, suggesting that true understanding comes from acknowledging our feelings and the human experience.
"death of loved our loved ones and how we miss them and how we you know that sense of loneliness and inability to interact directly that that's not something that is nice with me but I think it's also ..."
Frenkel discusses the importance of finding commonality among people, regardless of differing ideologies. He reflects on the need for compassion and understanding in times of crisis, emphasizing that human connection transcends intellectual disagreements. This segment underscores the value of empathy in navigating complex social issues.
"you know and when he is somebody sincere and he puts his opens his cards and you know and say this is why that's what I want to do it because I want to recreate my father and I want to be able to talk..."
Frenkel shares his journey towards self-awareness and how it has influenced his perspective on others. He reflects on the importance of recognizing one's own flaws before criticizing others, advocating for a compassionate approach to dialogue. This segment highlights the transformative power of empathy in personal and societal interactions.
"courage and it takes a certain self-awareness I would say and which brings I mean you know I think the crucial is that that which was inscribed you know on the Temple of a Poland Delphia there was a s..."
In this segment, Frenkel reminisces about the innocence of childhood and its role in fostering curiosity and discovery. He draws parallels between childlike interactions and adult conflicts, suggesting that a return to this spirit could help bridge divides. This segment emphasizes the importance of maintaining a sense of wonder and openness in intellectual pursuits.
"my mind you see and so as I become as I became self-aware suddenly other possibilities opened and suddenly that conflict which by the way if I kept giving this nasty you know talks about him one one d..."
Frenkel discusses the universality of mathematical principles as a means of connection among people. He highlights that mathematical truths, such as 'two plus two equals four,' transcend personal beliefs and ideologies. This segment advocates for the power of mathematics to unite individuals across diverse backgrounds.
"humility also yeah so like I find it extremely hard now to like really Lush out at somebody and to say like you're horrible whatever because immediately question is who am I to criticize you know so i..."
Frenkel introduces the concept of the Langlands Program, which connects disparate fields of mathematics. He explains how this program seeks to bridge gaps between number theory and harmonic analysis, revealing underlying patterns that resonate across disciplines. This segment showcases the beauty and interconnectedness of mathematical concepts.
"formulas did you know that there is a Supreme Court decision that mathematical formulas cannot be patented like Einstein could not patent equal E equals m c squared it doesn't belong to him because if..."
In this segment, Frenkel elaborates on the hidden structures within mathematics that connect various fields. He discusses the philosophical implications of these connections, suggesting that they reveal deeper truths about the nature of reality. This segment emphasizes the ongoing quest for understanding in mathematics and its relevance to broader scientific inquiries.
"that's the famous cup trick you know okay look so this is how it works no tricks no tricks no matter what honest it is magical okay not because I'm tricking you so you start with a a bottle like this ..."
Frenkel concludes by reflecting on the philosophical implications of mathematical connections across disciplines. He expresses a desire to uncover the deeper reasons behind these correspondences, emphasizing the importance of curiosity and exploration in both mathematics and life. This segment encapsulates the essence of seeking knowledge and understanding in a complex world.
"a certain duplicity if you will and that duplicity is rooted mathematically in this in this experiment this little experiment that they have just done so I can I imagine speaking of imagination okay y..."
Edward Frenkel discusses his research theme of connecting disparate fields of mathematics. He emphasizes the hidden structures and parallels that exist across different mathematical domains, suggesting that there are deeper principles yet to be understood. Frenkel likens this exploration to discovering the quarks of mathematics, indicating that our current understanding may only be a projection of a more profound reality.
"when when not in working in specific field by kind of but kind of cutting across fields and um and then I we discovered that for instance I took some people who know what happens in this field but don..."
Frenkel shares his experience working with Ed Witten, a renowned mathematical physicist. He describes Witten's unique vision and ability to connect quantum physics with mathematics, highlighting how Witten's insights have consistently led to groundbreaking discoveries. Frenkel reflects on the intensity and focus required to collaborate with such a powerful intellect.
"it means that what we believe are the fundamental elements of uh of mathematics are not fundamental there is something Beyond it's like we previously thought that atoms were indivisible then we found ..."
In this segment, Frenkel elaborates on how Witten translates physical theories into mathematical language, creating a bridge between the two disciplines. He discusses the implications of Witten's work, where mathematical truths emerge from physical theories, and how this process has led to the establishment of entire fields of study within mathematics.
"yes fascinating I enjoy I enjoyed it very much I also felt they have to keep up you know and uh so we wrote this long paper and in 2007 and we collaborated for about a year I have known him before and..."
Frenkel addresses the current crisis in physics, characterized by the gap between advanced theoretical frameworks like string theory and their application to the real universe. He discusses the contradictions between established theories, such as the standard model and Einstein's relativity, and the challenges faced in unifying these concepts.
"in other words being able to glean some mathematical truths from um physical theories that's one side on the other hand conversely applying sophisticated mathematics he's probably uh the physics who k..."
Frenkel explores the aesthetic appeal of string theory, likening it to a symphony where different vibrations represent various particles. He discusses the mathematical elegance of string theory and its potential to unify diverse physical phenomena, while also acknowledging the challenges it faces in aligning with our four-dimensional reality.
"right now and I think that new ideas perhaps are needed and I I wouldn't be surprised if Wheaton is one of those people who come up with those ideas well he has been one of the one of the people that ..."
Frenkel critiques the notion of a 'Theory of Everything,' arguing that such a concept may be an unrealistic goal. He reflects on the motivations behind this pursuit and suggests that the quest for a unified theory can lead to ego-driven endeavors rather than genuine scientific inquiry. Frenkel emphasizes the importance of new ideas in advancing our understanding of the universe.
"because it has given us so much so much food for thought but do you think it's a correct or a incorrect theory for understanding this reality so it might be a theory that explains some 10th dimensiona..."
Frenkel provides insights into Eric Weinstein's theory of geometric unity, highlighting its originality and potential to address fundamental questions in physics. He discusses the challenges and complexities involved in developing such a theory, emphasizing the need for rigorous mathematical foundations to support new ideas in physics.
"everything in one equation now physicists on the other hand have been brought up educated for decades with this idea and to me and I I'm not sure I should say that but I feel like it's a kind of an ul..."
In this segment, Frenkel contemplates the simplicity and beauty of the underlying principles of reality as expressed through mathematics. He muses on the possibility that the true nature of the universe may be elegantly simple, while also acknowledging the complexity and messiness of our current understanding.
"greater generality which is what makes it so unique and so beautiful but then there are on top of that there are this issue of quantization of actually describing them as Quantum field Theory and the ..."
Frenkel contrasts the environment of academia with independent research, discussing the benefits and limitations of both. He reflects on how the academic community can foster collaboration and competition among brilliant minds, while also imposing constraints that may hinder innovative thinking.
"see so that I totally see but I don't see one equation governing one one equation governing them all not one equation to govern them all but it does seem that such equations exist what she will tell y..."
Frenkel speculates on the future role of universities in light of advancements in AI and how education may evolve over the next decades. He reflects on the rapid pace of scientific discovery and the challenges of keeping up with it outside of traditional academic structures. This segment raises questions about the changing landscape of education and knowledge acquisition.
"away and it's a very interesting setup and also on the one hand we are all supposed to be the truth Seekers and but in reality of course it is a human activity and it is a human community and with all..."
Frenkel discusses the intense concentration required for high-level mathematics, comparing it to treasure hunting in the depths of the ocean. He emphasizes the non-linear nature of the creative process in mathematics, where breakthroughs often come unexpectedly after sustained effort. This segment highlights the mental demands placed on mathematicians and the nature of discovery.
"20 50 100 years I wonder uh I wonder and I wonder that you know how do you make sense that Einstein was working after attempting I believe to be a university Professor yeah as a patent clerk well but ..."
Frenkel reflects on the concept of 'deep work' as articulated by Cal Newport, emphasizing the importance of dedicated time for profound thinking in mathematics. He shares insights from his own experience, illustrating how deliberate practice and sustained effort contribute to moments of clarity and discovery. This segment underscores the necessity of creating mental space for deep intellectual engagement.
"don't think people who are not who are not in the field understand what kind of focus and concentration actually doing like mathematics at the top level these days requires because we're not talking a..."
In this segment, Frenkel explores the nature of intellectual discovery, likening it to moments of enlightenment that cannot be forced. He draws parallels to Eastern philosophies, particularly the concept of Satori, emphasizing the need for relaxation and openness to allow insights to emerge. This discussion reveals the mystical aspects of the creative process in mathematics.
"no it's deliberate because you know um first of all my first years as a mathematician you know I worked every day and weekends holidays doesn't matter um I didn't even question that so I would feel so..."
Frenkel discusses the unique challenges of mathematics compared to other disciplines, highlighting the rigorous standards for proof and the frustration that can accompany the search for solutions. He contrasts the intuitive arguments often found in physics with the strict requirements of mathematical proof, illustrating the distinct nature of mathematical inquiry.
"know how in eastern tradition they have this concept of Satori like in Buddhism and Buddhism you have this Satori which is enlightenment and so the various reports of Buddhist monks or Buddhist Master..."
Frenkel recounts the historical journey of Fermat's Last Theorem, detailing its unproven status for over 350 years and the eventual breakthrough by Andrew Wiles. He reflects on the emotional highs and lows experienced by mathematicians during this quest for proof, emphasizing the dramatic narrative that accompanies such monumental discoveries.
"and you just don't see it and it can have it can go on for months super frustrating but without it it is it is nothing kind of you know I would love to hear your opinion uh to the degree that you know..."
In this segment, Frenkel explains the origins of Fermat's Last Theorem, including Pierre de Fermat's original claim and the subsequent efforts to prove it. He shares anecdotes about the theorem's allure and the many mathematicians who attempted to solve it, illustrating the theorem's significance in the mathematical community.
"it's going to take would it be useful to maybe try to explain from us Last Theorem sure it's easy to do it empty missed I think I always think that everything can be explained you know even though I s..."
Frenkel discusses the challenges faced by Andrew Wiles in proving Fermat's Last Theorem, including the discovery of a gap in his initial proof. He highlights the collaborative effort that ultimately led to the successful resolution of the theorem, showcasing the importance of teamwork and perseverance in mathematical research.
"it at some point I I give I was given a public talk about this and I made it as a joke I made a tweet in which I wrote that I have proved this theorem but 280 characters are not enough and the kind of..."
Frenkel concludes with reflections on the dramatic narratives that unfold in the world of mathematics, from the initial claims of proof to the eventual breakthroughs. He emphasizes the human element in mathematical pursuits, revealing the emotional and psychological aspects that accompany the search for truth in this rigorous discipline.
"to be correct now uh what he proved actually was not verma's theorem itself but a certain statement which is called shimurtaniam away conjecture named after three mathematicians to Japanese mathematic..."
Edward Frenkel discusses the dramatic history of proving mathematical conjectures, particularly Fermat's Last Theorem. He highlights the emotional journey of mathematicians who face setbacks and triumphs in their quest for truth, illustrating the human side of mathematics that often goes unnoticed.
"to even if you prove it for cubes and for fourth power and fifth then still there's six sevens and so on the infinitely made cases in which it has to be proved and so you see um the separated simple r..."
Frenkel shares his personal experience of solving his first mathematical problem at the age of 18. He reflects on the excitement and fear that accompanied this journey, emphasizing the emotional stakes involved in mathematical discovery and the impact of mentorship on his development.
"because he's was such a top level mathematician people would guess that he has some idea that there is some idea so you know if you just know that somebody's has an idea this already gives you a great..."
Frenkel recounts the moment he realized he had discovered something unique in mathematics. He describes the thrill of uncovering a proof that no one else had, capturing the essence of mathematical exploration and the joy of intellectual ownership.
"this more this moment when suddenly you see that it's like you in this case it was literally I had to compile these diagrams with what mathematicians call homology groups and spectral sequences and ma..."
Frenkel discusses the psychological pressures faced by young mathematicians in academia, including the fear of idea theft and the competition for recognition. He emphasizes the need for ethical standards and a supportive community to foster creativity and collaboration.
"wanted to share it with my teacher as soon as possible you know and and he he understood quickly and he's like yeah good job you know is there some something you can give color to the drama Erica's ta..."
Frenkel reflects on the stereotypes surrounding mathematicians and his efforts to attract diverse individuals to the field. He shares how his book 'Love and Math' aims to inspire a new generation of mathematicians, particularly women, by showcasing the beauty of mathematics.
"I mean part of that is just the way of life and the strategies um and oftentimes when you look at who wins the Nobel Prize it's also tragic because sometimes so many minds are like the trajectory to t..."
Frenkel recounts his experience applying to Moscow University amidst anti-Semitism in the Soviet Union. He shares the challenges he faced during the entrance exams and how these experiences shaped his resilience and determination to succeed in mathematics.
"say I think it's happening not because of my efforts on alone obviously there are many other messages who are around the same time started to put more effort because see if the old stereotype of mathe..."
Frenkel reflects on his journey from being rejected by Moscow University to eventually receiving an invitation from Harvard University as a visiting professor. He shares how this experience motivated him to prove his worth and the emotional toll it took on him. This segment emphasizes the resilience required to overcome rejection and the importance of recognizing one's own potential despite external circumstances.
"were accepted so then I had to go to this um there was one school technical school in Moscow which was the institute for oil and gas exploration which had a Applied Mathematics program and that's wher..."
In a poignant moment, Frenkel discusses the emotional impact of reconnecting with his 16-year-old self, who felt crushed by rejection. He describes a transformative experience where he allowed his inner child to express the pain and trauma of that time. This segment explores the significance of acknowledging past experiences and how they shape our present selves, emphasizing the healing power of revisiting childhood emotions.
"and so when I finally when I finally connected to that boy oh my God that was a totally different experience all the pain and all the trauma came to the surface and it was a kind of a tsunami I didn't..."
Frenkel shares insights on the importance of sharing personal stories of trauma and resilience. He reflects on how his own experiences resonate with others and the universal nature of suffering and rejection. This segment highlights the therapeutic value of storytelling and the connections it fosters among individuals who have faced similar challenges.
"I can't even describe it but suddenly he comes alive and suddenly it's like oh he's here and I and I got a little talk with him and I said look you know I know now and thank you I'm so sorry that I ne..."
Frenkel discusses the paradox of his experiences, recognizing that the challenges he faced ultimately fueled his passion for mathematics. He reflects on how adversity can lead to unexpected strengths and insights, allowing him to appreciate the journey rather than just the destination. This segment emphasizes the idea that life's difficulties can serve as catalysts for personal growth and achievement.
"cruelty that you experience because if you did that early on I was not ready for it it is a defense mechanism I could be I could have come you know there were kids who commit suicide after this experi..."
In this reflective segment, Frenkel shares his profound insights gained from the death of his father. He discusses how this experience reshaped his understanding of love and life, revealing the intensity of emotions that surface in the face of loss. This segment explores the themes of gratitude, acceptance, and the interconnectedness of life and death, offering a deep philosophical perspective on human existence.
"um you said you lost your father four years ago yeah what have you learned about life from your dad that's another another big one yeah because I was very close to him and uh it was tough it was tough..."
Frenkel articulates the essential role of love in the human condition, describing it as the 'glue' that binds our experiences. He expands the definition of love beyond romantic relationships to include passion for one's work and friendships. This segment delves into the idea that life without love is dull and explores the complexities of love's nature.
"what uh we've talked about love but let me ask what role does Love play in this whole game in The Human Condition it's like the glue you know it's like for me it's like that it's and it's not because ..."
In this thought-provoking segment, Frenkel contemplates the paradoxes of life, particularly the interplay between love and loss. He reflects on the Buddhist philosophy of letting go and enjoying the moment, suggesting that holding onto experiences may lead to suffering. This discussion invites listeners to consider a more fluid approach to life, embracing its transient nature.
"the experience where you forget or time we're reminded becomes an illusion and everything just freezes oh my God and then uh it's kind of beautiful and painful to hear you say that when you've experie..."
As the conversation concludes, Frenkel expresses gratitude for the opportunity to explore deep questions about love and existence. He shares a quote from mathematician Sofia Kovalevskaya, emphasizing the intrinsic connection between mathematics and poetry. This segment encapsulates the essence of the podcast, celebrating the beauty of inquiry and the human experience.
"yeah the roller coaster life the Paradox of life right Edward you're an incredible human being I've been a fan for a long time thank you for writing love and math thank you thank you for being who you..."