I had a great time talking with
@lexfridman
on his podcast. We discussed a wide range of topics related to math, physics and AI - with paradoxical nature of reality being predominant theme.
And Lex also inspired me to venture deeper into things like meaning of life, love & death.
Here's my conversation with Edward Frenkel (
@edfrenkel
), a mathematician at UC Berkeley, working on the interface of mathematics and quantum physics. Ed is a brilliant mind and a truly special human being. This was challenging, moving, and fun!
Disturbing news from Turkey where two students of Boğaziçi University, Enis Berke Gök & Caner Perit Özen, have been imprisoned for over a month for participating in protests against the gov't appointed rector. They should be released immediately and allowed to study.
THREAD 1/5
I visited Boğaziçi in 2015. I stayed at the Kennedy Lodge on campus and gave a public lecture, one of the most memorable I've ever given. I was deeply moved by the response of the students.
It pains me that today I speak not about math but about two students held in prison.
5/5
In the Fall of 2015, a crew from the Japanese TV channel NHK recorded my 4 lectures on the Langlands Program for general audience at
@Mathmoves
in Berkeley. They were then broadcast on TV in Japan as a mini-series. The first is now available on YouTube:
This week I gave one of 4 “challenge talks” at the annual String Theory conference. Here's the video:
I started with Richard Feynman’s notes on quantum integrable models & went on to explain the modern view linking them to dualities in math & physics. 1/5
Yuri Manin has died. He was a brilliant mathematician who has influenced numerous fields of math and physics, founder of a school, deep thinker & philosopher, and a kind, gentle, generous human being.
Inspired by his works since I was a teenager... 1/3
Boğaziçi University was established in 1863 and is a jewel of Turkish higher education. And Turkey plays a vital role in the world today. But how can one have a vibrant society and economy if freedom of expression is not permitted even in its elite academic institutions?
3/5
I am reminded of the Freedom of Speech movement here at
@UCBerkeley
in the 1960s, when students were also arrested for demanding freedom of expression.
Here's Mario Savio speaking at the Sproul Plaza in 1964. He was arrested too. But the flame of freedom keeps burning.
4/5
According to their int'w w/
@cumhuriyetgzt
, the students have been denied medicine and textbooks.
Arrests were made during widespread peaceful protests on campus that have been going on for over 300 days. Call for Solidarity summarizes the situation:
2/5
@ivanastradner
It is ambiguous. Without the brackets, it is not clear in what order to do division and multiplication in the numerator. If division first (36 divided by 3) followed by multiplication by (8-6), then the numerator is 24, and so the overall result is 4. If multiplication first (3
“Horrific Russian rocket strikes on Kyiv. Last time our capital experienced anything like this was in 1941 when it was attacked by Nazi Germany,” Ukraine’s Minister of Foreign Affairs tweeted. “Ukraine defeated that evil and will defeat this one.”
Yesterday I gave 4-hour master class at Caltech on quantum integrable systems. It was a tribute to Richard Feynman whose office was next door. In fact, on his last blackboard it was written “TO LEARN: Bethe Ansatz Problems” which was the subject I was talking about!
#loveandmath
I highly recommend this video of Peter Woit on
@TOEwithCurt
podcast. It contains
(1) Concise & insightful summary of the Standard Model and unification proposals;
(2) Subtleties of the Wick rotation in QFT that are rarely discussed;
(3) Peter's alternative approach... (cont.)
New Episode with Mathematician Peter Woit
Link:
In this episode, Peter Woit critiques the long-standing theories of unification in physics, arguing that the pursuit of extra dimensions and supersymmetry has failed. Peter introduces a new approach
Wonderful to see this groundbreaking work by
@EricRWeinstein
&
@PiaMalaney
getting the attention of economists. Eric gave a talk about it
@UChicago
this week, which I attended & enjoyed. Using bundles w/connection (gauge theory) to define indices like CPI is a very promising idea
The proposal to extend the Cost-Of-Living framework to changing ordinal preferences using differential geometry is now up at
@uchicago
here, as our inflation numbers soar. Thanks to my mathematical colleague
@edfrenkel
for going over the draft Tues night:
A very nice piece in
@newscientist
about a decades-long quest to prove the geometric Langlands correspondence (which I've been deeply involved in) that has culminated with a series of papers posted online a few weeks ago:
The article quotes me in a few
New paper with Etingof and Kazhdan laying the foundations for the analytic Langlands correspondence which we introduced 4 years ago. We also obtain new results on quantum integrable systems:
Dedicated to the great Italian mathematician Corrado De Concini.
Here's a playlist of about 30 clips of my recent conversation with
@lexfridman
on his podcast, organized by topics (they are all from the Lex Clips YouTube channel -- check it out!):
Super-happy that my paper with D. Kazhdan & P. Etingof on the analytic Langlands correspondence has been published in Duke Mathematical Journal (one of the world's top math journals):
One of my 5 best works (out of about 100)
The third episode of the Japanese TV series on the Mysteries of Mathematics is now available on YouTube. I talk about the fascinating Shimura-Taniyama-Weil conjecture. Filmed at
@Mathmoves
of
@UCBerkeley
and broadcast in Japan on the NHK TV channel in 2015
We covered a lot of territory w/ Curt Jaimungal on his
@TOEwithCurt
podcast: the human element in our research, how we grow and evolve as scientists, what Alan Turing wrote about "thinking machines" and the failure of the original promise of string theory
Sidney Coleman's 1994 lecture "Quantum Mechanics in Your Face" is a gem (h/t
@notevenwrong
)
I finally see how to talk about Everett interpretation without invoking "many worlds" and it's just pure joy to watch/read it.
Video:
Notes:
Here one can look for guidance to the sages of the past, such as Richard Feynman. They liked mathematical models but never lost sight of the big prize: understanding the physics of THIS Universe. And I think that's still a good guiding principle for today's physicists. 5/5
Lev Landau — a great physicist, Nobel Prize winner, died 50 years ago today.
He was my hero when I was growing up. I read all the books about him that I could find, and even had his photo on my desk.
Here he is, with his teacher Niels Bohr, in Moscow in 1961.
I have enjoyed every minute of this 3-hour interview of Peter Woit by Curt Jaimungal on his
@TOEwithCurt
podcast:
Through his book "Not Even Wrong" and his highly popular blog
@NotEvenWrong
, Peter has done a great service to the community in the past 20
Mathematicians use novel tools to design an algorithm producing solutions of an equation called "Cursed Curve" in whole numbers, cracking a 40-year old problem.
Cool piece by
@KSHartnett
in
@QuantaMagazine
, which even includes the equation itself.
Watching this conversation of
@Tegmark
&
@LexFridman
and greatly enjoying it. Appreciate Max's depth and clarity -- and above all, his optimism. So important to have faith that life has meaning, that we can -- and will -- build a better world together.
Fumiharu Kato, a mathematician from Tokyo Institute of Technology, gave a 90-minute public lecture on Mochizuki's IUT in Tokyo in October. According to the organizers, it was watched online in realtime by more than 100,000 people (via Niconico website). Wow!
(h/t Ivan Fesenko)
On this episode of
@TOEwithCurt
podcast, I give an overview of the Langlands Program in down-to-earth terms, accessible to non-specialists:
I also talk about the general idea of Unification in Mathematics, the differences between Math & Physics, the
Observer-dependence of quantum mechanics is well-known: different experimental setups reveal different facets of reality. In my new article just published by
@IAI_TV
:
I argue that there's a similar "observer problem" in mathematics: to do math we have to
Congratulations to Karen Uhlenbeck, winner of 2019
@Abel_Prize
! Her work on moduli spaces of instantons ("Uhlenbeck compactification") revolutionized several fields of math & physics. For more, read this excellent
@QuantaMagazine
piece by
@EricaKlarreich
:
Our new paper with D. Hernandez is out on
@arxiv
. It describes an extended family of relations between representations of quantum affine algebras:
This is my math paper No. 100, so I guess it's something to celebrate:
The second episode of the Japanese TV series on the Mysteries of Mathematics is now available on YouTube. It's focused on symmetry groups and Galois theory. Based on my lectures at
@Mathmoves
of
@UCBerkeley
, filmed and broadcast in Japan by NHK in 2015:
Science started as a project to unite us, to bring us closer to nature:
And yet, today we are being told by scientists: "You are a bag of particles" (Brian Greene) or "a bunch of neurons" (Robert Sapolsky) - suggesting that we are separate from each other,
I'm proud of my Russian heritage, but today I'm ashamed of being Russian. Russia's aggression against Ukraine is a despicable power grab which heralds a catastrophe for Russian people and all Slavic people. This cannot stand and the response must be swift.
Great to see
@DrBrianKeating
here at
@UCBerkeley
on this lovely Spring day. I really enjoyed our conversation on his INTO THE IMPOSSIBLE podcast back in December (check it out: )
And it’s even more fun to talk in person!
I am not talking about models of nature (i.e. "physical reality"). There's a big difference between math and physics: Only a tiny portion of mathematics is realized in nature (for example, the Universe we observe has 3 spatial dimensions, but in math we study spaces of all
@edfrenkel
@lexfridman
We discover progressively better (and more accurate) models of nature. We use our best models to discover new nuances of reality - and then use the new nuances to create better models. It’s a positive feedback cycle of discovery, but the models do describe reality as we see it.
We mourn
@mit
Institute Professor Emeritus Isadore Singer, who died Feb. 11. His seminal Atiyah-Singer Index Theorem and other achievements earned him the Bôcher Prize, Natl Medal of Science,
@amermathsoc
Steele Prize, and Abel Prize.
@mathmoves
@mitscience
Congratulations to Masaki Kashiwara on winning the
@KyotoPrize
!
His foundational work in the theory of D-modules and microlocal analysis underpins several branches of modern mathematics.
Barry Mazur is not only one of the greatest living mathematicians; he is also a sage. There's a new documentary film about him,
"Barry Mazur and the Infinite Cheese of Knowledge."
A trailer just dropped on YouTube, and it looks awesome!
h/t Michael Harris
His discovery was “one of the great jewels of the unity of mathematics.”
"He was larger than life in many ways, but at the same time he was very humble.”
A very nice tribute to Vaughan Jones by
@dcastelvecchi
in
@Nature
:
I have deleted my earlier tweet which I wrote being unaware that S.Mochizuki is Editor-in-Chief of the journal to which he submitted his papers. This is unfortunate. It creates the appearance of a conflict of interest & hence undermines one's confidence in the refereeing process.
My friend Jaron Lanier is one of the deepest thinkers in Silicon Valley. Loving his new piece on AI in
@NewYorker
: "The most pragmatic position is to think of AI as a tool, not a creature... what we are building today is as an innovative form of social collaboration.
Seeing AI as
My position on "Is math invented or discovered?" has evolved: whereas in Love & Math I was squarely in the "discovered" camp, I see it now as a paradoxical question, like the question "Is electron a particle or a wave?" See my conversation w/
@lexfridman
:
Nice to see
#GoogleDoodle
marking Carl Friedrich Gauss's birthday.
One of the greatest mathematicians of all time, he wrote:
"It is not knowledge but the act of learning, not possession but the act of getting there, that grants the greatest enjoyment."
I'm excited about my online conversation this Saturday, 12/16 @ 11 am PST, with the founders of
@NondualScience
conference about the nature of reality and the fallacy of the naive ideas of determinism and computationalism. To join us, use this link:
I had the pleasure to interact with many members of the string community. I'm truly impressed with their brilliance, especially the young minds.
However, for the health of the subject going forward, I believe it is necessary to reckon with the past and accept responsibility. 4/5
Mathematicians have benefited tremendously from string theory in the last 40 years. But string theorists' promise to produce physics of THIS Universe from string theory (which starts out with a 10-dim'l spacetime) has not panned out. The subject is now at the crossroads. 3/5
The new version of our joint paper w/ P. Etingof & D. Kazhdan is now available on
@arxiv
:
We have added a lot of new material, including an analogue of the functoriality principle in the novel analytic Langlands correspondence that my co-authors and I have
Excellent piece by
@kennethsilber
in
@SpliceToday2022
about the current debate on determinism:
It includes a neat summary of my recent
@NondualScience
online event:
"Frenkel uses an intriguing analogy to counter claims, such as those of physicist Brian
"Virtual reality is sold as an illusion but is real for what it is. Good magicians will tell you 'this is all an illusion, I’m faking you out.' As compared to con artists. In the same way, VR is the real thing and AI is the fake thing."
Jaron Lanier
@WIRED
Photographer
@chrismichel
is Artist-in-Residence at
@theNASEM
who has been working on a series of photographs of scientists:
Do you recognize this guy?
Excellent piece by
@KSHartnett
in
@QuantaMagazine
about a fruitful unification framework for 3 areas of math proposed by André Weil:
The article quotes me saying that this shows the essential role intuition plays in mathematical research:
" 'These ideas
Interview of the mathematician and educator
@ClaraGrima
in Spanish newspaper
@el_pais
. Alas, it's behind a paywall. But as the quote below indicates, it's about making mathematics more accessible, so it's not just a small elite that knows math and has power over us as a result.
La profesora Grima: "Como dice Edward Frenkel [profesor de Matemáticas de la Universidad de Berkeley, en EE UU], hay una pequeña élite que tiene el poder. Y lo tiene porque sabe matemáticas y tú no".
Just answered a question someone asked me on Quora for the first time:
Is there a real, conceptual difference between rational and irrational numbers or are the differences an artifact of our numbering system? by Edward Frenkel
Video of my
@NondualScience
conversation:
I talk about the alarming trend in popular science today that pushes people to believe that we are separate from each other and from nature. We are told, "you are a bag of particles" or "a bunch of neurons" or "a
Love the message here:
"Being human will only be more important as AI becomes more powerful."
But disagree with this:
"Is there going to be a great human-versus-robots war? Yes. My goal is to make sure the humans win."
Let's make love (and math), not war!
Excellent summary of my recent article about the "observer problems" in math by Tony Philips on the
@amermathsoc
website:
In my article, I argued that the choice of axioms brings an "observer" into the picture. One such choice is whether to include the
This tweet just came up in my Notifications. The talk I gave at
@UniBogazici
almost 7 years ago, at a gorgeous university library which was packed -- people sitting on the floor and the stairs -- is one of the most memorable talks I've ever given.❤️
#loveandmath
#sweetmemories
In addition to his groundbreaking works, he published dozens of books & essays on a variety of topics. He had a unique writing style & passion that made you fall in love with math, gave you hope that truth & beauty will triumph after all. E.g.
RIP, teacher
Breakthroughs in economics often happen b/c new mathematical tools are used. This work is about using diff. geometry to measure inflation in a novel way, and its impact could be huge.
I've been following it since 2012 and wrote about it in
@Slate
in 2013:
New work proposes an extension of Bell's inequalities questioning the very existence of objective reality.
To paraphrase, "Plato is my friend, Aristotle is my friend, but my greatest friend is Wigner"🤓
Fascinating account by
@anilananth
in
@QuantaMagazine