Vicky Neale is a great communicator of Mathematics. She was given an MPLS Teaching Award in 2016 and she also won an award for being the Most Acclaimed Lecturer in MPLS in the student-led Oxford University Student Union Teaching Awards 2015.

Follow her on Twitter: @VickyMaths1729

For some clear proofs of a selection of mathematical theorems, check out her YouTube channel: https://www.youtube.com/channel/UCBGhXXBCAzbzQV65JZoGhjw and her blog https://theoremoftheweek.wordpress.com/

Conversation Outline:

00:00 Guest Introduction

01:05 Vicky’s mathematical background

04:13 Motivations for writing a book on reasons to study mathematics

07:11 Are good reasons for studying Mathematics timeless? Would this book have more or less the same contents, had it been written many years ago?

10:10 Is the job of pure mathematicians safe from AI developments?

12:13 What are the benefits (for the non-mathematician) of knowing about mathematical notions such as integrals, derivatives, matrices and so on?

15:39 Are some people more mathematically talented than others?

18:45 Does the discussion of talent change when we are talking about research-level Mathematics? Douglas Hofstadter’s experience.

22:45 Aesthetics of Mathematics

25:00 Is Number Theory more beautiful than other mathematical subfields?

25:52 A mathematician’s view of the metaphysics of numbers

27:58 Fermat’s Last Theorem, Andrew Wiles and finding meaning in Mathematics

29:26 FLT and the Twin Prime Conjecture

32:27 Should graduate students tackle famous open problems?

33:41 Closing the Gap: significant progress towards solving the Twin Prime Conjecture

35:10 Polymath: an example of collaborative Mathematics

39:40 Do we have reasons to believe that the Twin Prime Conjecture is actually true?

Enjoy!

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/]]>

Vicky Neale is a great communicator of Mathematics. She was given an MPLS Teaching Award in 2016 and she also won an award for being the Most Acclaimed Lecturer in MPLS in the student-led Oxford University Student Union Teaching Awards 2015.

Follow her on Twitter: @VickyMaths1729

For some clear proofs of a selection of mathematical theorems, check out her YouTube channel: https://www.youtube.com/channel/UCBGhXXBCAzbzQV65JZoGhjw and her blog https://theoremoftheweek.wordpress.com/

Conversation Outline:

00:00 Guest Introduction

01:05 Vicky’s mathematical background

04:13 Motivations for writing a book on reasons to study mathematics

07:11 Are good reasons for studying Mathematics timeless? Would this book have more or less the same contents, had it been written many years ago?

10:10 Is the job of pure mathematicians safe from AI developments?

12:13 What are the benefits (for the non-mathematician) of knowing about mathematical notions such as integrals, derivatives, matrices and so on?

15:39 Are some people more mathematically talented than others?

18:45 Does the discussion of talent change when we are talking about research-level Mathematics? Douglas Hofstadter’s experience.

22:45 Aesthetics of Mathematics

25:00 Is Number Theory more beautiful than other mathematical subfields?

25:52 A mathematician’s view of the metaphysics of numbers

27:58 Fermat’s Last Theorem, Andrew Wiles and finding meaning in Mathematics

29:26 FLT and the Twin Prime Conjecture

32:27 Should graduate students tackle famous open problems?

33:41 Closing the Gap: significant progress towards solving the Twin Prime Conjecture

35:10 Polymath: an example of collaborative Mathematics

39:40 Do we have reasons to believe that the Twin Prime Conjecture is actually true?

Enjoy!

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/]]>

Note: I am sorry for the occasional internet connection problems. I hope the relevant parts can still be understood!

Conversation Outline:

00:00 What are the Incompleteness Theorems?

01:59 Why are Gödel’s results relevant for discussions concerning the mind?

03:28 Connections between Turing Machines and Formal Systems

04:20 When we talk about whether the mind can be mechanized or not, what do we mean?

06:56 Should Cognitive Scientists (or Philosophers of Mind) be interested in this discussion?

09:45 The First Generation of Arguments against The Prospects of Mechanizing the Mind

19:52 Three Versions of The Mechanistic Thesis

21:55 What makes Penrose’s New Argument harder to evaluate in theory EA+T?

22:56 Penrose’s Formulation of The Argument (Quote from his Book)

27:49 What are the explicit assumptions behind Penrose’s New Argument?

32:14 What are the indeterminate statements that Penrose uses in the argument?

36:10 Do you think we’ll ever have an adequate formal theory of type-free truth which settles Gödel’s First Disjunct (the one targeted by Penrose)?

37:18 Do you think your opponent would accept bringing the key notions of relative provability, absolute provability and truth in the setting of effectively formalized theories?

42:25 Why do you think Penrose does not abandon his New Argument, despite resistance from mathematical logicians?

44:35 Unlike Lucas or Penrose, some authors such as Hofstadter use Gödel’s results to illuminate the workings of the mind. Do you think the Incompleteness Theorems have anything worthwhile to say here?

Enjoy!

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/]]>

Note: I am sorry for the occasional internet connection problems. I hope the relevant parts can still be understood!

Conversation Outline:

00:00 What are the Incompleteness Theorems?

01:59 Why are Gödel’s results relevant for discussions concerning the mind?

03:28 Connections between Turing Machines and Formal Systems

04:20 When we talk about whether the mind can be mechanized or not, what do we mean?

06:56 Should Cognitive Scientists (or Philosophers of Mind) be interested in this discussion?

09:45 The First Generation of Arguments against The Prospects of Mechanizing the Mind

19:52 Three Versions of The Mechanistic Thesis

21:55 What makes Penrose’s New Argument harder to evaluate in theory EA+T?

22:56 Penrose’s Formulation of The Argument (Quote from his Book)

27:49 What are the explicit assumptions behind Penrose’s New Argument?

32:14 What are the indeterminate statements that Penrose uses in the argument?

36:10 Do you think we’ll ever have an adequate formal theory of type-free truth which settles Gödel’s First Disjunct (the one targeted by Penrose)?

37:18 Do you think your opponent would accept bringing the key notions of relative provability, absolute provability and truth in the setting of effectively formalized theories?

42:25 Why do you think Penrose does not abandon his New Argument, despite resistance from mathematical logicians?

44:35 Unlike Lucas or Penrose, some authors such as Hofstadter use Gödel’s results to illuminate the workings of the mind. Do you think the Incompleteness Theorems have anything worthwhile to say here?

Enjoy!

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/]]>

Conversation Outline:

00:00 Introduction

01:43 University teaching during the pandemic

04:15 “What is Logic?” YouTube series

06:00 So, what is Logic?

09:18 Should all University undergraduates have some logical training?

13:50 Some History of Logic

16:35 What was missing from Aristotle’s Logic?

20:32 How was Logic being taught back then?

24:16 Research in Medieval Logic

27:10 Women in the History of Logic

32:03 Onomastics

37:34 Does studying Logic improve one’s life?

45:35 Book recommendations

Enjoy!]]>

Conversation Outline:

00:00 Introduction

01:43 University teaching during the pandemic

04:15 “What is Logic?” YouTube series

06:00 So, what is Logic?

09:18 Should all University undergraduates have some logical training?

13:50 Some History of Logic

16:35 What was missing from Aristotle’s Logic?

20:32 How was Logic being taught back then?

24:16 Research in Medieval Logic

27:10 Women in the History of Logic

32:03 Onomastics

37:34 Does studying Logic improve one’s life?

45:35 Book recommendations

Enjoy!]]>

Conversation outline:

00:00 Introduction: What is Philosophy?

03:11 Can Philosophy help you have a better life?

06:47 What’s the story behind your book “Tetralogue”? A discussion on relativism about truth

12:44 Relativism about matters of taste

20:21 Moral relativism

29:47 Tips for finding out the truth about various issues

35:34 Vagueness and Classical Logic

48:20 Sharp cut-offs

52:40 Epistemicism says that you cannot know these cut-offs: why is that?

56:59 Baldness is not really a function of the number of hairs. Does your account apply to situations which are “non-discrete” situations?

01:01:47 How can a colour predicate (e.g. “_ is red”) latch on to an objective property out there in the world when people may have different perceptions?

01:05:37 If the properties expressed by predicates are person independent, wouldn’t this change the ramifications and implications of the epistemic view?

Enjoy!

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/]]>

Conversation outline:

00:00 Introduction: What is Philosophy?

03:11 Can Philosophy help you have a better life?

06:47 What’s the story behind your book “Tetralogue”? A discussion on relativism about truth

12:44 Relativism about matters of taste

20:21 Moral relativism

29:47 Tips for finding out the truth about various issues

35:34 Vagueness and Classical Logic

48:20 Sharp cut-offs

52:40 Epistemicism says that you cannot know these cut-offs: why is that?

56:59 Baldness is not really a function of the number of hairs. Does your account apply to situations which are “non-discrete” situations?

01:01:47 How can a colour predicate (e.g. “_ is red”) latch on to an objective property out there in the world when people may have different perceptions?

01:05:37 If the properties expressed by predicates are person independent, wouldn’t this change the ramifications and implications of the epistemic view?

Enjoy!

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/]]>

00:00 Intro

00:16 The story of CLRS plus remarks on the 4th edition

11:39 Relationships between Competitive Programming, Software Engineering and academic Computer Science

13:16 What makes an algorithm beautiful?

16:33 Thoughts on P=NP

19:32 Algorithmic efficiency and Artificial General Intelligence

24:12 Will progress in fields such as Deep Learning make the study of classical algorithms obsolete?

27:37 Algorithms Unlocked

33:07 What should the average lay person know about algorithms?

37:46 Advice for students, both graduates and undergraduates

Enjoy!

Twitter

00:00 Intro

00:16 The story of CLRS plus remarks on the 4th edition

11:39 Relationships between Competitive Programming, Software Engineering and academic Computer Science

13:16 What makes an algorithm beautiful?

16:33 Thoughts on P=NP

19:32 Algorithmic efficiency and Artificial General Intelligence

24:12 Will progress in fields such as Deep Learning make the study of classical algorithms obsolete?

27:37 Algorithms Unlocked

33:07 What should the average lay person know about algorithms?

37:46 Advice for students, both graduates and undergraduates

Enjoy!

Twitter

Conversation outline:

00:00 Introduction

01:04 What draws you to Philosophy?

04:36 The importance of focusing of subproblems of the big questions: insights into space, time and thinking machines

09:19 The Turing Test and the chinese room argument

15:37 What other philosophical areas would benefit from looking at Complexity Theory?

21:35 What is Computational Complexity after all?

30:03 NP, complexity classes and the P=NP problem

45:27 Complexity Theory in light of time and memory limitations

52:24 Why do we believe in Quantum Theory?

55:36 What is Quantum Computing?

01:05:45 How are qubits physically implemented?

01:11:14 Quantum Supremacy

01:13:26 Would the construction of a quantum computer which could run Shor’s algorithm confirm the many-worlds interpretation? Remarks on David Deutsch’s quantum views.

Enjoy!

Twitter:

https://twitter.com/tedynenu

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/

]]>Conversation outline:

00:00 Introduction

01:04 What draws you to Philosophy?

04:36 The importance of focusing of subproblems of the big questions: insights into space, time and thinking machines

09:19 The Turing Test and the chinese room argument

15:37 What other philosophical areas would benefit from looking at Complexity Theory?

21:35 What is Computational Complexity after all?

30:03 NP, complexity classes and the P=NP problem

45:27 Complexity Theory in light of time and memory limitations

52:24 Why do we believe in Quantum Theory?

55:36 What is Quantum Computing?

01:05:45 How are qubits physically implemented?

01:11:14 Quantum Supremacy

01:13:26 Would the construction of a quantum computer which could run Shor’s algorithm confirm the many-worlds interpretation? Remarks on David Deutsch’s quantum views.

Enjoy!

Twitter:

https://twitter.com/tedynenu

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/

]]>Conversation Outline:

00:00 Introduction

00:18 What is special about language?

03:31 How did we (as a species) get linguistic abilities?

05:24 What do people who work in Semantics do?

09:19 How can babies pick up language?

15:07 What is the meaning of words? Aren’t they just dictionary entries?

19:03 On idiolects

27:00 The meanings of sentences

33:43 What are possible worlds? Are they the same as the many-worlds of quantum theory?

39:52 Differences between ‘school’ grammar, syntax and formal logic

49:07 What is the meaning of ‘if’?

01:04:54 Does the research of Semanticists impact the field of Computational Linguistics?

01:07:39 The relationship between thought and language

Twitter:

https://twitter.com/tedynenu

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/]]>

Conversation Outline:

00:00 Introduction

00:18 What is special about language?

03:31 How did we (as a species) get linguistic abilities?

05:24 What do people who work in Semantics do?

09:19 How can babies pick up language?

15:07 What is the meaning of words? Aren’t they just dictionary entries?

19:03 On idiolects

27:00 The meanings of sentences

33:43 What are possible worlds? Are they the same as the many-worlds of quantum theory?

39:52 Differences between ‘school’ grammar, syntax and formal logic

49:07 What is the meaning of ‘if’?

01:04:54 Does the research of Semanticists impact the field of Computational Linguistics?

01:07:39 The relationship between thought and language

Twitter:

https://twitter.com/tedynenu

Apple Podcasts:

https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135

Spotify:

https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10

Google Podcasts:

https://podcasts.google.com/?q=philosophical%20trials

Instagram:

https://www.instagram.com/tedynenu/]]>

00:00 Memrise introduction

00:39 Grandmaster of Memory and memory feats

01:40 How long have you been into the art of memory?

02:48 Did your memory skills benefit your life outside competition?

04:16 Is there anything you have trouble remembering?

05:32 The scope of memory techniques and remembering your autobiography

08:30 How do you actually memorise a pack of cards in 45 seconds?

12:07 The functional role of memory and forgetting

17:22 Myths about memory

19:23 Relationship between memory and attention

23:39 False memories

27:41 Can memory give insights into consciousness?

33:07 Tell us about the work that takes place at Memrise

Enjoy!]]>

00:00 Memrise introduction

00:39 Grandmaster of Memory and memory feats

01:40 How long have you been into the art of memory?

02:48 Did your memory skills benefit your life outside competition?

04:16 Is there anything you have trouble remembering?

05:32 The scope of memory techniques and remembering your autobiography

08:30 How do you actually memorise a pack of cards in 45 seconds?

12:07 The functional role of memory and forgetting

17:22 Myths about memory

19:23 Relationship between memory and attention

23:39 False memories

27:41 Can memory give insights into consciousness?

33:07 Tell us about the work that takes place at Memrise

Enjoy!]]>

Conversation outline:

00:00 The problem of mental representation

10:38 Can a computer think? Is the Turing Test satisfactory?

14:15 Can a robot think?

18:32 What is the Computational Theory of Mind?

20:20 The Language of Thought Hypothesis

26:33 Do neural networks implement our language of thought?

31:32 Can deep neural networks achieve a complexity which brings about awareness or AGI?

33:03 What is general intelligence?

34:29 Are there necessary conditions for intelligence?

38:00 What is the mechanical view of the human mind?

42:35 Consciousness

46:32 Can we have free will on the mechanical picture?

50:58 Can God account for the explanatory gap between science and consciousness?

54:40 Comments on aspects of religion

https://www.twitter.com/tedynenu]]>

Conversation outline:

00:00 The problem of mental representation

10:38 Can a computer think? Is the Turing Test satisfactory?

14:15 Can a robot think?

18:32 What is the Computational Theory of Mind?

20:20 The Language of Thought Hypothesis

26:33 Do neural networks implement our language of thought?

31:32 Can deep neural networks achieve a complexity which brings about awareness or AGI?

33:03 What is general intelligence?

34:29 Are there necessary conditions for intelligence?

38:00 What is the mechanical view of the human mind?

42:35 Consciousness

46:32 Can we have free will on the mechanical picture?

50:58 Can God account for the explanatory gap between science and consciousness?

54:40 Comments on aspects of religion

https://www.twitter.com/tedynenu]]>

Outline of the conversation:

00:10 What motivated you to write 'Think'?

02:00 What is the role of Philosophy?

04:10 Progress in Philosophy

07:18 Remarks on the notion of Truth

09:27 Deflationism about Truth

14:15 The Correspondence Theory of Truth and problems with Facts

17:40 Is there anything wrong with abstract objects?

19:44 The Liar's Paradox

28:37 The relationship between religion and morality

33:55 Free Will

47:18 Which philosophers influenced you the most?

48:50 What contributions did Hume make to modern thought?

Twitter: https://twitter.com/tedynenu]]>

Outline of the conversation:

00:10 What motivated you to write 'Think'?

02:00 What is the role of Philosophy?

04:10 Progress in Philosophy

07:18 Remarks on the notion of Truth

09:27 Deflationism about Truth

14:15 The Correspondence Theory of Truth and problems with Facts

17:40 Is there anything wrong with abstract objects?

19:44 The Liar's Paradox

28:37 The relationship between religion and morality

33:55 Free Will

47:18 Which philosophers influenced you the most?

48:50 What contributions did Hume make to modern thought?

Twitter: https://twitter.com/tedynenu]]>

Outline of the conversation:

00:00 Podcast Introduction

00:50 MathOverflow and books in progress

04:08 Mathphobia

05:58 What is mathematics and what sets it apart?

08:06 Is mathematics invented or discovered (more at 54:28)

09:24 How is it the case that Mathematics can be applied so successfully to the physical world?

12:37 Infinity in Mathematics

16:58 Cantor's Theorem: the real numbers cannot be enumerated

24:22 Russell's Paradox and the Cumulative Hierarchy of Sets

29:20 Hilbert's Program and Godel's Results

35:05 The First Incompleteness Theorem, formal and informal proofs and the connection between mathematical truths and mathematical proofs

40:50 Computer Assisted Proofs and mathematical insight

44:11 Do automated proofs kill the artistic side of Mathematics?

48:50 Infinite Time Turing Machines can settle Goldbach's Conjecture or the Riemann Hypothesis

54:28 Nonstandard models of arithmetic: different conceptions of the natural numbers

1:00:02 The Continuum Hypothesis and related undecidable questions, the Set-Theoretic Multiverse and the quest for new axioms

1:10:31 Minds and computers: Sir Roger Penrose's argument concerning consciousness

Twitter: https://twitter.com/tedynenu]]>

Outline of the conversation:

00:00 Podcast Introduction

00:50 MathOverflow and books in progress

04:08 Mathphobia

05:58 What is mathematics and what sets it apart?

08:06 Is mathematics invented or discovered (more at 54:28)

09:24 How is it the case that Mathematics can be applied so successfully to the physical world?

12:37 Infinity in Mathematics

16:58 Cantor's Theorem: the real numbers cannot be enumerated

24:22 Russell's Paradox and the Cumulative Hierarchy of Sets

29:20 Hilbert's Program and Godel's Results

35:05 The First Incompleteness Theorem, formal and informal proofs and the connection between mathematical truths and mathematical proofs

40:50 Computer Assisted Proofs and mathematical insight

44:11 Do automated proofs kill the artistic side of Mathematics?

48:50 Infinite Time Turing Machines can settle Goldbach's Conjecture or the Riemann Hypothesis

54:28 Nonstandard models of arithmetic: different conceptions of the natural numbers

1:00:02 The Continuum Hypothesis and related undecidable questions, the Set-Theoretic Multiverse and the quest for new axioms

1:10:31 Minds and computers: Sir Roger Penrose's argument concerning consciousness

Twitter: https://twitter.com/tedynenu]]>