I can not find the source but I remembered reading that John von Neumann was present when Gödel first presented his Incompleteness theorem and was the only person in the crowd that understood what it actually meant. Von Neumann had a great admiration of Gödel. He campaign to have Gödel be accepted full time at Princeton saying "How can any of us be called professor when Gödel is not?".
@paryanindoeur also sorry for late response. There is also a letter Gödel wrote to Von Neumann while he was on his health was declining on PvsNP. They didn't really "work" together in scholarly work but they often bounce ideas I am sure. I been trying to post the link but RUclips keeps taking it down. A simple Google search worked for me
Today, while watching the Limits of knowledge, I discovered Kurt Gödel. The man should be known by all western civilization. I think he has been swept under the rug of scientism.
_"I think he has been swept under the rug of scientism"_ Exactly! It's amazing how many physicists, for example, ignore the Incompleteness Theorems and their extrapolations, seemingly to maintain Scientism -- science as a worldview -- and thus support reductive materialism and a priesthood-like hierarchy & orthodoxy... corruptions of science in the name of Science.
The problem was {still “izz”} that if pure mathematicians were to ‘really’ take Gödel’s Incompleteness Theorems seriously, they’d have to shutdown ‘all’ the math departments on every university campus; …thus, Truth, in this instance, leads to a ‘dead end’, but Gödel’s theorems “in German” do ‘ηοt’ translate into ‘Incompleteness’, rather they are called “Unentscheidbare” Sätze, or, {lit.} ‘Undecidable’ Theorems - thus, not yet “final”, rather open-ended, i.e. …there’s hope.
Thanks for your clarity. I'm an 83 y.o. "recovering math phobic." both fascinated and intimidated by Hofstadter's famous book. If I finish it and go further with Godel, you'll have done me an astonishing kindness.
Gödel left in his papers a fourteen-point outline of his philosophical beliefs, that are dated around 1960. They show his deep belief in the rational structure of the world. Here are his 14 points: The world is rational. Human reason can, in principle, be developed more highly (through certain techniques). There are systematic methods for the solution of all problems (also art, etc.). There are other worlds and rational beings of a different and higher kind. The world in which we live is not the only one in which we shall live or have lived. There is incomparably more knowable a priori than is currently known. The development of human thought since the Renaissance is thoroughly intelligible (durchaus einsichtige). Reason in mankind will be developed in every direction. Formal rights comprise a real science. Materialism is false. The higher beings are connected to the others by analogy, not by composition. Concepts have an objective existence. There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science. Religions are, for the most part, bad- but religion is not.
@@lobstered_blue-lobster There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science. Religions are, for the most part, bad- but religion is not.
@@EshaanBanerjee Hao Wang's A Logical Journey: From Godel To Philosophy Chapter 9 Page 316. Hao Wang comments "Unfortunately we know very little of Gödel's reasons for holding [these beliefs]. Undoubtedly the centrepiece is his belief that the world is rational. This key belief is an empirical generalization from his interpretation of human experience, but what is known of his arguments is hardly convincing." Wang is referring to four lengthy letters Godel wrote his ailing mother about his religious beliefs (these make up chapter 3 of said book).
Why didn't Godel just learn to prepare his own meals? He could have sourced his own food, asked his wife where she shopped and made his own food. The fact he didn't do that tells me that it was a bit more than being scared of being of being poisoned as Godel must have known he could die by starvation too. Plenty of people have been scared of being poisoned but they don't all starve themselves to death if one particular trusted person cannot make their food. Godel seems to have trapped himself in his own logic prison when it came to eating food.
The story of him eating food only by his wife is heartbreaking but the fact that he couldn't prepare his own food and relied on a woman to prepare his food shows how dangerous religion and faith can be for health.
I could think of ways to convince any person having any trace of sanity to eat. For example, I would share the meal with him proving to him that it is not poisoned.
@@crisgon9552 Multiplicity of those who share the meals and random choice of them would negate the validity of that objection. Gödel himself could have contributed to that, had he been of any degree of sanity at the time. My point is that I doubt the claim that he refused to eat for fear of being poisoned while his mental faculties were still with him.
@nahidhkurdi6740 you are correct there are ways to mitigate his anxiety of being poison but at the end you can't make a horse drink water when you lead it to the river. It's a shame how he died but his legacy is secured
In those days, a Privatdozent never got paid “from the university”. One with this qualification was allowed to post courses and interested students would sign-up, gather together and agree upon a set time to meet. It was at the prerogative of the students who attended {and anyone, like other faculty members & approved private citizens} to personally pay a ‘recommended’ sum of money or ‘’give what they could.” BTW, for future reference (because I see this all the time by those who either do not know German or have never studies in Germany) the terms: Extraordinarius Professor does ‘not’ mean an ‘extraordinary’ {as in super brilliant, or Genius professor), rather, almost just the opposite, it means ‘’Adjunct or Assistant” professor. A Dozent is more of an ‘Instructor or adjunct’. An ‘Ordinarius Professor’ is a Full Professor, …and, btw, even in Germany today, to become a full professor {Ordinarius} one must *earn* the degree for this position, and that [so-called] ‘Professor’ degree is the ‘Habilitationschrift’ {Habilitation Thesis}, which only can be done ‘after’ a doctoral degree. (( I wrote two doctoral dissertations at Hamburg University (1975-1980; then 1980-1983), the second one ‘in German.’ }}
he easily could of had a damaged heart, rheumatic fever and infection in general often spreads to the heart and causes valve damage and other kinds of damage. He easily could of had heart damage and indeed wasn't a hypochondriac on that point. Who ACTUALLY knows though, but there isn't zero reason to suspect heart damage. As someone personally who has had heart damage from a "normal fever" type illness. It can happen, and it could of easily happened to him.
Great video and you do a great job of trying to get the pronunciation of foreign names right. Note that "Privatdozent" is pronounced like "preewatdotcent", i.e., the "z" is not spoken like an "s" but rather like a "ts" (or "tc") sound.
That was beautiful, but odd and untrue quote from him on the end. His own theorems prove that we can never know all of mathematics even in principal. If we want to have consistent system of mathematical axioms and theorems, it must be incomplete. Nevertheless, Godel is my #3 greatest mind of all time, after Cantor and Archimedes.
The Institute for Advanced Study is in no way connected to Princeton University, at least during Einstein & Gödel’s time, and there was even some quite cold relations between the two institutions.
There is an inaccuracy in your presentation. For Godel's incompleteness theorem only applies to axiomatic systems that contain natural number theory, or Peano's axioms. Hilbert had already shown that Euclidean geometry was complete.
GB: Mathematical axioms themselves are "neither provable nor disprovable". - The discovery of Spanish wax is the process, isn't it... The sky is blue and the grass is green... like. H: Már maguk a matematikai axiómák is "se nem bizonyíthatóak, se nem cáfolhatóak". - Spanyol viasz felfedezése a folyamat ugye... Kék az ég és zöld a fű ... szerű.
I can not find the source but I remembered reading that John von Neumann was present when Gödel first presented his Incompleteness theorem and was the only person in the crowd that understood what it actually meant. Von Neumann had a great admiration of Gödel. He campaign to have Gödel be accepted full time at Princeton saying "How can any of us be called professor when Gödel is not?".
It's somewhat curious therefore that Godel and Von Neumann never worked together (as far as I know) or ever wrote any papers together at Princeton.
I recall reading that, too -- only von Neumann even spoke to Gödel that day
Here is an article about Von Neumann talking to Gödel on Game Theory. They worked on different things and Gödel didn't publish much work.
@@crisgon9552 Got a link?
@paryanindoeur also sorry for late response. There is also a letter Gödel wrote to Von Neumann while he was on his health was declining on PvsNP. They didn't really "work" together in scholarly work but they often bounce ideas I am sure.
I been trying to post the link but RUclips keeps taking it down. A simple Google search worked for me
Today, while watching the Limits of knowledge, I discovered Kurt Gödel.
The man should be known by all western civilization.
I think he has been swept under the rug of scientism.
_"I think he has been swept under the rug of scientism"_ Exactly! It's amazing how many physicists, for example, ignore the Incompleteness Theorems and their extrapolations, seemingly to maintain Scientism -- science as a worldview -- and thus support reductive materialism and a priesthood-like hierarchy & orthodoxy... corruptions of science in the name of Science.
The problem was {still “izz”} that if pure mathematicians were to ‘really’ take Gödel’s Incompleteness Theorems seriously, they’d have to shutdown ‘all’ the math departments on every university campus; …thus, Truth, in this instance, leads to a ‘dead end’, but Gödel’s theorems “in German” do ‘ηοt’ translate into ‘Incompleteness’, rather they are called “Unentscheidbare” Sätze, or, {lit.} ‘Undecidable’ Theorems - thus, not yet “final”, rather open-ended, i.e. …there’s hope.
You’re kidding me. He was a German speaking mathematician, how scientistic do you want it to get
Thanks for your clarity. I'm an 83 y.o. "recovering math phobic." both fascinated and intimidated by Hofstadter's famous book. If I finish it and go further with Godel, you'll have done me an astonishing kindness.
Great work as always. A sad ending for Gödel... Starving to death is definitely towards the bottom of the list of ways I want to go.
No offense but he should've just cooked his own food, i wonder what made him have a fear of being poisoned because not ALL food are poisoned.
Gödel left in his papers a fourteen-point outline of his philosophical beliefs, that are dated around 1960. They show his deep belief in the rational structure of the world. Here are his 14 points:
The world is rational.
Human reason can, in principle, be developed more highly (through certain techniques).
There are systematic methods for the solution of all problems (also art, etc.).
There are other worlds and rational beings of a different and higher kind.
The world in which we live is not the only one in which we shall live or have lived.
There is incomparably more knowable a priori than is currently known.
The development of human thought since the Renaissance is thoroughly intelligible (durchaus einsichtige).
Reason in mankind will be developed in every direction.
Formal rights comprise a real science.
Materialism is false.
The higher beings are connected to the others by analogy, not by composition.
Concepts have an objective existence.
There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science.
Religions are, for the most part, bad- but religion is not.
I didn't get the last two ones...could you please clarify those?
@@lobstered_blue-lobster There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science.
Religions are, for the most part, bad- but religion is not.
Source ??
@@EshaanBanerjee Hao Wang's A Logical Journey: From Godel To Philosophy Chapter 9 Page 316. Hao Wang comments "Unfortunately we know very little of Gödel's reasons for holding [these beliefs]. Undoubtedly the centrepiece is his belief that the world is rational. This key belief is an empirical generalization from his interpretation of human experience, but what is known of his arguments is hardly convincing." Wang is referring to four lengthy letters Godel wrote his ailing mother about his religious beliefs (these make up chapter 3 of said book).
I can’t help feeling the RUclips author missed a golden opportunity to title this video “An Incomplete History of Kurt Gödel”
Oh yes I totally needed one of these
He has a cool cameo in Oppenheimer (2023).
Vienna calling. Thanks for the video. I've shared your video around a bit, if you don't mind.
I don't mind at all! Share away :D
Beautiful work, moderndaymath!
I'm always like "Kurt was a master philosopher..."
This is a super video. Thanks for making it.
Great job as always, thank you!
Ay another one got released! Looking forward to bingeing all the episodes I missed lol
Why didn't Godel just learn to prepare his own meals? He could have sourced his own food, asked his wife where she shopped and made his own food. The fact he didn't do that tells me that it was a bit more than being scared of being of being poisoned as Godel must have known he could die by starvation too. Plenty of people have been scared of being poisoned but they don't all starve themselves to death if one particular trusted person cannot make their food.
Godel seems to have trapped himself in his own logic prison when it came to eating food.
I mean true, if he recover his obsessive fear or his mental health he would still be alive.
The story of him eating food only by his wife is heartbreaking but the fact that he couldn't prepare his own food and relied on a woman to prepare his food shows how dangerous religion and faith can be for health.
The cause of his starvation was OCD , not religion , he was doubting that someone will put poison in his food .
I could think of ways to convince any person having any trace of sanity to eat. For example, I would share the meal with him proving to him that it is not poisoned.
What if you have the antidote or acquired immunity to the poison? Gödel was probably too smart for his own safety
@@crisgon9552
Multiplicity of those who share the meals and random choice of them would negate the validity of that objection. Gödel himself could have contributed to that, had he been of any degree of sanity at the time. My point is that I doubt the claim that he refused to eat for fear of being poisoned while his mental faculties were still with him.
@nahidhkurdi6740 you are correct there are ways to mitigate his anxiety of being poison but at the end you can't make a horse drink water when you lead it to the river. It's a shame how he died but his legacy is secured
Mental illness is not defined by ur current state of mind when u get them u know it , hopefully u don't get it
@@nahidhkurdi6740 he didn't eat because he had OCD about being poisoned , educate yourself about OCD , it's a doubt disorder .
In those days, a Privatdozent never got paid “from the university”. One with this qualification was allowed to post courses and interested students would sign-up, gather together and agree upon a set time to meet. It was at the prerogative of the students who attended {and anyone, like other faculty members & approved private citizens} to personally pay a ‘recommended’ sum of money or ‘’give what they could.”
BTW, for future reference (because I see this all the time by those who either do not know German or have never studies in Germany) the terms: Extraordinarius Professor does ‘not’ mean an ‘extraordinary’ {as in super brilliant, or Genius professor), rather, almost just the opposite, it means ‘’Adjunct or Assistant” professor. A Dozent is more of an ‘Instructor or adjunct’. An ‘Ordinarius Professor’ is a Full Professor, …and, btw, even in Germany today, to become a full professor {Ordinarius} one must *earn* the degree for this position, and that [so-called] ‘Professor’ degree is the ‘Habilitationschrift’ {Habilitation Thesis}, which only can be done ‘after’ a doctoral degree.
(( I wrote two doctoral dissertations at Hamburg University (1975-1980; then 1980-1983), the second one ‘in German.’ }}
It is so pity Germany today academically is not even the shadow of its older self...
Couldn't someone convince him that not eating will result in him dying and that is the same as getting poisoned?
self referential. Died in order not to die
he easily could of had a damaged heart, rheumatic fever and infection in general often spreads to the heart and causes valve damage and other kinds of damage. He easily could of had heart damage and indeed wasn't a hypochondriac on that point. Who ACTUALLY knows though, but there isn't zero reason to suspect heart damage.
As someone personally who has had heart damage from a "normal fever" type illness. It can happen, and it could of easily happened to him.
Girdel knew water turn into drop this becoming vapor is the answer to his computation
completely enjoyed. graze
Great series.
Sorry, Einstein was ‘ηενεr’ a member of Princeton’s Faculty.
"essentially web-md him self" 😂
Great video and you do a great job of trying to get the pronunciation of foreign names right. Note that "Privatdozent" is pronounced like "preewatdotcent", i.e., the "z" is not spoken like an "s" but rather like a "ts" (or "tc") sound.
That was beautiful, but odd and untrue quote from him on the end. His own theorems prove that we can never know all of mathematics even in principal. If we want to have consistent system of mathematical axioms and theorems, it must be incomplete. Nevertheless, Godel is my #3 greatest mind of all time, after Cantor and Archimedes.
10:34 Wait, what? What? How does that follow???
The Institute for Advanced Study is in no way connected to Princeton University, at least during Einstein & Gödel’s time, and there was even some quite cold relations between the two institutions.
Jesus, imagine getting nerfed in your office by your PhD student wtf bro
I know it says a very brief history... but you missed the line where his wife fought off the nazi thugs with an umbrella!
4 years before godel was born makes no sense the older brother was also a godel.
There is an inaccuracy in your presentation. For Godel's incompleteness theorem only applies to axiomatic systems that contain natural number theory, or Peano's axioms. Hilbert had already shown that Euclidean geometry was complete.
GB: Mathematical axioms themselves are "neither provable nor disprovable". - The discovery of Spanish wax is the process, isn't it... The sky is blue and the grass is green... like. H: Már maguk a matematikai axiómák is "se nem bizonyíthatóak, se nem cáfolhatóak". - Spanyol viasz felfedezése a folyamat ugye... Kék az ég és zöld a fű ... szerű.
Educate yourself. Gentzen's consistency proof
Daniil Kharms, the Russian writer, starved himself to death, in a psychiatric hospital....
Do you think he had autism or Asperger’s?
austrio-hungarian? Really?
Gertle and Einshtein eh?
Unusual death