Joel David Hamkins: Philosophy of Mathematics and Truth

08/17/23 • 87 min

1 Listener

Joel David Hamkins is a renowned mathematician and philosopher whose work covers logic, computability, game theory, the philosophy of infinity, and more. He’s also the top rated user by reputation on the MathOverflow network.

Find episode details, video and more at: https://www.matthewgeleta.com/

Topics:

the concept of truth in maths and elsewhere

the nature of proof in mathematics

the acclaimed completeness and incompleteness theorems

the relationship between mathematical thinking and the human mind ...

and other topics

Joel's links:

Substack: https://www.infinitelymore.xyz/

Book of infinity: https://www.infinitelymore.xyz/s/the-book-of-infinity

Panorama of logic: https://www.infinitelymore.xyz/s/panorama-of-logic

Other books: https://www.infinitelymore.xyz/p/books

SUPPORT & CONNECT:

Follow and leave a 5-star review

LinkedIn: https://www.linkedin.com/in/matthewgeleta/

Twitter: https://twitter.com/MatthewGeleta

Donate: https://bit.ly/donate-to-paradigm

PODCAST INFO:

Spotify: https://spoti.fi/3IVDF2W

Apple Podcasts: https://apple.co/3oEZYmJ

Google Podcasts: https://bit.ly/paradigm-on-google

YouTube: https://bit.ly/paradigm-on-youtube

RSS: https://api.substack.com/feed/podcast/1656558/s/65176.rss

Timestamps:

0:00 Intro

1:17: Truth

8:38 Intuition vs objective truth

13:15 Proof

20:39 Completeness

30:18 Incompleteness

37:20 Is completeness a 'problem'?

43:07 Hierarchies of logical systems

48:44 Axioms and where they come from

1:03:50 Motivations for studying pure mathematics

1:19:57 Joel's books

1:22:58 Who should represent humanity to an AI superintelligence?

Find episode details, video and more at: https://www.matthewgeleta.com/

Topics:

the concept of truth in maths and elsewhere

the nature of proof in mathematics

the acclaimed completeness and incompleteness theorems

the relationship between mathematical thinking and the human mind ...

and other topics

Joel's links:

Substack: https://www.infinitelymore.xyz/

Book of infinity: https://www.infinitelymore.xyz/s/the-book-of-infinity

Panorama of logic: https://www.infinitelymore.xyz/s/panorama-of-logic

Other books: https://www.infinitelymore.xyz/p/books

SUPPORT & CONNECT:

Follow and leave a 5-star review

LinkedIn: https://www.linkedin.com/in/matthewgeleta/

Twitter: https://twitter.com/MatthewGeleta

Donate: https://bit.ly/donate-to-paradigm

PODCAST INFO:

Spotify: https://spoti.fi/3IVDF2W

Apple Podcasts: https://apple.co/3oEZYmJ

Google Podcasts: https://bit.ly/paradigm-on-google

YouTube: https://bit.ly/paradigm-on-youtube

RSS: https://api.substack.com/feed/podcast/1656558/s/65176.rss

Timestamps:

0:00 Intro

1:17: Truth

8:38 Intuition vs objective truth

13:15 Proof

20:39 Completeness

30:18 Incompleteness

37:20 Is completeness a 'problem'?

43:07 Hierarchies of logical systems

48:44 Axioms and where they come from

1:03:50 Motivations for studying pure mathematics

1:19:57 Joel's books

1:22:58 Who should represent humanity to an AI superintelligence?

Previous Episode

Junaid Mubeen: Artificial Intelligence & Education

Junaid Mubeen holds a PhD in maths from Oxford and a Masters in Education from Harvard. He has spent over a decade working on innovative learning technologies, including as Head of Product and Director of Education at Whizz Education, and as Chief Operating Officer at Write the World.

Find episode details, video and more at: https://www.matthewgeleta.com/

We discuss

AI in chess and other games

AI performance on standardised tests

Problems with the education system and the role AI might play in alleviating these troubles

Risks in the use of AI in tutors and teachers

... and other topics

Junaid’s links:

Book: Mathematical Intelligence (UK version, US version)

Website: www.fjmubeen.com

Substack:

PODCAST INFO:

Spotify: https://spoti.fi/3IVDF2W

Apple Podcasts: https://apple.co/3oEZYmJ

YouTube: https://bit.ly/paradigm-on-youtube

RSS: https://api.substack.com/feed/podcast/1656558/s/65176.rss

SUPPORT & CONNECT:

Follow and leave a 5-star review

LinkedIn: https://www.linkedin.com/in/matthewgeleta/

Twitter: https://twitter.com/MatthewGeleta

Donate: https://bit.ly/donate-to-paradigm

Timestamps:

0:00 Intro

1:24 Gary Kasparov & artificial intelligence in chess

5:32 GPT4 performance on standardised tests

11:21 Ken Robinson & risks of AI in traditional education

17:03 Khan Academy and advancements in EdTech

38:19 Government regulation of educational AIs

44:20 Will AIs replace teachers and tutors? 55:55 Big picture view of AI in education

1:02:49 Identifying high-potential young mathematicians

1:11:04 Junaid's work with Simon Singh

1:16:06 Advice for young ambitious people

1:19:44 Book recommendations

1:23:14 Who should represent humanity to a superintelligent AI?

1:25:05 Thanks and wrap-up

Next Episode

Chris Ferrie: Quantum Computing

Chris Ferrie is a physicist and mathematician, whose work focuses on quantum mechanics and quantum computing. He's the author of several highly successful science books, as well as cofounder of the quantum computing company, Eigensystems.

Find episode details, video and more at: https://www.matthewgeleta.com/

Topics:

The foundations of quantum computing

The state of quantum computing technology today

What impact quantum computers might have on the world

Quantum hype

... and other topics.

Chris’s links:

Website: https://www.csferrie.com/

Books: https://www.csferrie.com/books

SUPPORT & CONNECT:

Follow and leave a 5-star review