### Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)

Kurt Godel: The World's Most Incredible Mind.

Either mathematics is too big for the human mind or the human mind is more than a machine ~ Godel

Kurt Godel (1931) proved two important things about any axiomatic system rich enough to include all of number theory.

1) You'll never be able to prove every true result..... you'll never be able to prove every result that is true in your system.

2) Godel also proved that one of the results that you can never prove is the result that says that the system is consistent. More precisely: You cannot prove the consistency of any mathematical system rich enough to include the known theory of numbers.

Hence, any consistent mathematical system that is rich enough to include number theory is inherently incomplete.

Second, one of the propositions whose truth or falsity cannot be proved within the system is precisely the proposition that states that the system is consistent.

What Godel's proof means, then, is that we can't prove that arithmetic—let alone any more-complicated system—is consistent.

For 2000 years, mathematics has been the model—the subject—that convinces us that certainty is possible. Yet Now there's no certainty anywhere—not even in mathematics.

More...

Goedel's Ontological Proof.

For those interested in a discussion of Goedel's reasoning for God, then I suggest starting with this heavily annotated work, which I recently stumbled upon.

It's not that God is subject to the Freedom Proof or the Doubt Proof.

According to Gödel, He's not. But we have to be, or else we are not free. So

our truth game with God turns into something like Feynman had described.

Feynman's Gods, every time physicists think they have the rules of the game

figured out, throw in a new wrinkle. They let people like Feynman make

progress, but if the Feynmans of the world learn too much, physics will stop

being the joy and challenge that it is. The Gods don't let that happen.

Gödel's God has to be very careful about how he lets our universe unfold.

If the world becomes totally controllable and comprehensible, we'll be God.

God does not object to that. In fact, according to Gödel, that is our destiny.

But it is also the end of us as free human beings. And human freedom is an

essential part of the beauty of God's universe.

~ page 251

### Kurt Gödel - from the Limits of understanding

A brief bio of Kurt Gödel from :-

The Limits of Understanding - World Science Festival

### 24/42: Secret History - Kurt Gödel and the Secrets of Genius (and Abstraction)

The saga continues. It's been a while since I released a video. I hope to have more soon. To keep this project moving, feel free to donate at

### Gödel's Incompleteness Theorem - Numberphile

Marcus du Sautoy discusses Gödel's Incompleteness Theorem

More links & stuff in full description below ↓↓↓

Extra Footage Part One:

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Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.

Professor du Sautoy's book as mentioned...

In the US it is called The Great Unknown -

In the UK it is called What We Cannot Know -

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### Kurt Gödel & the Limits of Mathematics

Kurt Gödel and his famous Incompleteness Theorems are discussed by Mark Colyvan, Professor of Philosophy and Director of the Sydney Centre for the Foundations of Science. This is from Key Thinkers (Sydney Ideas).

### Kurt Gödel Centenary - Part I

Institute for Advanced Study

November 17, 2006

Karl Sigmund (University of Vienna) Solomon Feferman (Stanford University)

More videos on

### Kurt Gödel's Philosophical Viewpoint

In his book, “A Logical Journey: from Gödel to Philosophy,” Hao Wang describes how he found a list of 14 philosophical points written by Gödel around the year 1960. Gödel had titled the list, “My Philosophical Viewpoint.” To understand Gödel's strange and magnificent worldview, we will go through each of these 14 points and analyze their greater significance.

Here are links to sources from the video:

### Math's Existential Crisis (Gödel's Incompleteness Theorems)

Math isn’t perfect, and math can prove it. In this video, we dive into Gödel’s incompleteness theorems, and what they mean for math.

Created by: Cory Chang

Produced by: Vivian Liu

Script Editors: Justin Chen, Brandon Chen, Elaine Chang, Zachary Greenberg

Special thanks to Ryan O’Donnell, associate professor at Carnegie Mellon University (

Twitter:

—

Extra Resources:

Ryan O’Donnell’s slide deck:

Wikipedia Entry:

Axiomatic Systems:

Peano Axioms:

Principle of Explosion:

Picture credits:

### Gödel's Incompleteness Theorem - Professor Tony Mann

A short mind-bending trip through the wonderful world of Mathematical Paradoxes: An examination of some recent work on paradoxes by the Austrian-American Mathematician Kurt Gödel. You can watch the full lecture by Professor Tony Mann here:

### CSC180: Godel's Incompleteness Theorem in 5 minutes

An informal intro to Godel's Incompleteness Theorem (omitting discussion of axioms)

Better version:

(Part 1)

(Part 2)

### Gödel's Incompleteness Theorems - In Our Time

In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so, Gödel changed the way we understand what mathematics is, and the implications of his work in physics and philosophy take us to the very edge of what we can know. Melvyn Bragg discusses Gödel’s Incompleteness Theorems with Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.

This is from a BBC program called In Our Time. For more information, go to

### The Time Gödel Told A Joke...Maybe

Gerald Sacks answers one of the great mysteries of the universe: Did Kurt Gödel have a sense of humor? This is from a lecture Gerald Sacks gave on Gödel as part of the Williams Lecture Series for the Advancement of Logic and Philosophy given at the University of Pennsylvania.

### 22/42 The Secrets of Kurt Gödel 1080 HD (The Secret History with Gary Geck, part 22 of 42)

for more info.

This is part 22 of 42. As you may have noticed, I am releasing them totally out of order, but that won't matter. In this part we begin our study of Kurt Gödel. We will focus on Gödel from parts 22-28.

### El Teorema de Gödel por fin Explicado Fácilmente

Gödel´s theorem easy. El teorema de Gödel explicado de forma fácil.

Esta historia, es una metáfora del Teorema de Gödel.

Comparte el nucleo de ideas de este teorema.

1. Las cajas representan las proposiciones de lógica de primer orden de la aritmética de Peano.

2. El escaner representa la función recursiva que permite saber si una secuencia de proposiciones constituyen la demostración de la proposición de la caja.

3. Godel permite que los objetos , los numerales, definidos por la proposiciones de la teoría, se refieran a otras proposiciones de esa teoria (con la famosa numeración de Godel). Es lo que digo: Inventó un método para que las cajas hablasen de otras cajas.

4. Crea una sentencia con una variable libre y luego introduce en esa variable el numeral de esa misma sentencia. Así crea una sentencia indirectamente autoreferencial que afirma que no existe una secuencia de numerales que corresponda a una demostración de ella misma. Esto corresponde a la caja que dice: la caja del interior introduce una copia suya en su interior, y ya no pasa la barrera, el interior vacío de la caja es la analogía de una variable libre en una proposición.

No digo, al final, que demuestre la incompletud de la aritmética de Peano, pero que esta arítmetica no puede ser completa y consistente a la vez. Y esta conclusión ya es un duro golpe para el Programa de Hilbert.

### La historia de las matemáticas - 4. Hacia el Infinito y más allá

“Son los grandes problemas por resolver los que mantienen con vida a las matemáticas”, declara el presentador al inicio de este capítulo, que comienza con Hilbert desde la Sorbona para dedicarse después a recorrer algunos de sus célebres 23 problemas. Primer problema, hipótesis del continuo (Georg Cantor, el infinito, distintos tipos de infinito: biyección entre racionales y naturales, imposible con los números reales), Conjetura de Poincaré (Intento infructuoso de entrevistar a Grigori Perelman), Segundo problema (Kurt Gödel y el teorema de incompletitud, Círculo de Viena), la batuta matemática se traslada a EE. UU. (Universidad de Princeton) por la ocupación nazi (Hermann Weyl, John Von Neumann), Octavo problema, Hipótesis de Riemann, “la joya de la Corona” (Paul Cohen), Décimo problema (Julia Robinson, Yuri Matiyasevich, teoría de Galois, André Weil) y finalmente enlaza a Weil con el grupo Bourbaki y en particular con Alexander Grothendieck. Si Du Sautoy empezó con una cita, acaba con otra de Hilbert en una emisión de radio en 1930, que suscribe completamente (y probablemente lo hacemos todos): “Debemos saber, y sabremos”.

### The Rotating Godel Universe

A lecture by our friend, Dr. Moninder Singh Modgil, given to QGR staff on November 15, 2017.

The Logician Kurt Godel, known for his “Incompleteness Theorems”, was a friend of Albert Einstein's while they were both at the Institute of Advanced Studies at Princeton.

In 1949, on the occasion of Einstein’s 70th birthday, Godel, in a seminar, presented a model of a rotating universe--the model which bears his name. This was the first solution of Einstein’s field

equation in which it was demonstrated that time travel was possible. Obukhov has researched a metric which combines expansion with rotation. The rotation is high in the early stages of the universe, and slows down as the universe expands. Observational evidence for

rotation of the universe is discussed.

About Dr. Moninder:

Dr. Moninder Singh Modgil specializes in the “Godel Universe,” which is a rotating universe solution of Einstein’s field equations. He received his PhD in General Relativistic Physics from the Indian Institute of Technology, Kanpur, India. He did his B.Tech. (Hons.) at the Indian Institute of Technology in Kharagpur, India, in Aeronautical Engineering and has worked on the aerodynamic design of the Tejas fighter jet. He has also worked on a collaborative atmospheric project between the Indian Space Research Organization (ISRO) and the National Oceanic and Atmospheric Administration (NOAA) in Boulder, Colorado.

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### Kurt Gödel's Incompleteness Theorem and the Origin of the Universe (part 1)

Perry Marshall, Author of Industrial Ethernet and Communications Engineer Bill Jenkins give a technical Treatment of Information Theory as it relates to DNA and Evolution.

### Godel's Lasting Legacy

Austrian logician Kurt Gödel’s incompleteness theorems showed us the limitations of mathematics within mathematics. While math is still useful for proving scientific theorems, Gödel transformed the perception of pure mathematics in a way that still makes modern mathematicians uncomfortable. Here, leading thinkers—a mathematician, a philosopher, and a physicist—wrestle, almost literally, with the implications of Gödel’s legacy.

Watch the full program here:

Original program date: June 4, 2010

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### Computer Scientists "Prove" The Existence of God

### Les théorèmes d'incomplétude de Gödel — Science étonnante #37

En mathématiques, il existera toujours des choses vraies, mais indémontrables. Merci Kurt Gödel...

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