My name is Tedy Nenu and I am the host of the 'Philosophical Trials' podcast. This is a place where philosophers, mathematicians, linguists and other bright individuals share with us fascinating aspects of their work. Whether you are interested in the nature of mathematical reality or how language works, there will be an episode here that caters to your interests.
Vicky Neale on 'Why Study Mathematics?' and the Twin Prime Conjecture | Episode 11
Dr Vicky Neale is the Whitehead Lecturer at the Mathematical Institute and Balliol College at the University of Oxford. She is also a Supernumerary Fellow at Balliol and the author of two great books aimed at general audiences, namely ‘Closing the Gap’ and ‘Why Study Mathematics?’.
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/
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?
Peter Koellner on Penrose's New Argument concerning Minds and Machines | Episode 10
Professor Peter Koellner is a leading Logician and Philosopher based at Harvard University. He has made very important contributions to areas surrounding Mathematical Logic and today he was kind enough to join me for a discussion on Penrose's arguments...
Sara L. Uckelman on Medieval Logic, Onomastics and Teaching | Episode 9
Dr Sara L. Uckelman is an Assistant Professor of Philosophy at the University of Durham. She earned her PhD in Logic at the University of Amsterdam and her research interests cover many interesting areas including Medieval Logic, Onomastics, Philosophy...
Timothy Williamson on Relativism and Vagueness | Episode 8
Professor Timothy Williamson is one of the most important philosophers alive. He is the Wykeham Professor of Logic at the University of Oxford, a position that he has been holding since 2000. His groundbreaking work in the areas of philosophical logic, philosophy of language, epistemology and metaphysics has shaped many of the contemporary debates. Today I’m joined by him to discuss Relativism about Truth and the Epistemic account of Vagueness. Enjoy!
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?
Thomas Cormen on The CLRS Textbook, P=NP and Computer Algorithms | Episode 7
Thomas Cormen is a world-renowned Computer Scientist, famous for co-writing the indispensable 'Introduction to Algorithms' textbook. He is currently a professor at Dartmouth College and former Chairman of the Dartmouth College Department of Computer...
Scott Aaronson on Computational Complexity, Philosophy & Quantum Computing | Episode 6
Scott Aaronson is a world-renowned expert in the fields of Quantum Computing and Computational Complexity Theory. He is a David J. Bruton Centennial Professor of Computer Science at The University of Texas at Austin. Every Computer Science enthusiast knows who Prof. Aaronson is because of his extremely clear and engaging way of communicating difficult theoretical ideas. His book Quantum Computing since Democritus is a wonderful resource of dipping into the topics that we are discussing today.
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.