A group blog on math, physics and philosophy

- Pyknoticity versus Cohesiveness (Mar 28, 2020)
- Pyknotic stuctures
- Michael Harris on Virtues of Priority (Mar 19, 2020)
- Michael Harris’s new paper.
- Type Theory and Propositions (Feb 26, 2020)
- Propositions in HoTT
- Magidor on Category Mistakes and Context (Feb 14, 2020)
- context-dependent sentences
- Types in Natural Language (Feb 11, 2020)
- Types in natural language
- Modal Homotopy Type Theory - The Book (Feb 6, 2020)
- New book - Modal Homotopy Type Theory
- A Couple of Talks in Vienna (Dec 4, 2019)
- Two talks in Vienna
- The Narratives Category Theorists Tell Themselves (Sep 3, 2019)
- Narratives of a category theorist
- Summer Meanderings About Enriched Logic (Jul 23, 2019)
- Continuous logic as an enriched logic
- Type Theory, Category Theory and Philosophy (Jul 5, 2019)
- Type theory, Category theory and Philosophy conference
- Twisted Cohomotopy Implies M-Theory Anomaly Cancellation (Apr 24, 2019)
- M-theory and cohomotopy theory.
- Modal Types Revisited (Nov 18, 2018)
- Modal dependent type theory
- The Philosophy and Physics of Noether's Theorems (Aug 10, 2018)
- Noether anniversary conference
- Physics and 2-Groups (Feb 15, 2018)
- Higher gauge theory
- Arithmetic Gauge Theory (Dec 21, 2017)
- Arithmetic gauge theory
- Categorification and the Cosmic Cube (Oct 26, 2017)
- categorifying cohomology, homological algebra and homotopy
- M-theory from the Superpoint (Feb 13, 2017)
- M-theoretic entities as extensions of the superpoint
- HoTT and Philosophy (Sep 13, 2016)
- HoTT and philosophy
- The HoTT Effect (May 19, 2016)
- HoTT conference season
- Type Theory and Philosophy at Kent (Apr 21, 2016)
- workshop on type theory
- When Not To Use 'The' (Oct 21, 2015)
- Conditions for use ‘the’
- Carnap and the Invariance of Logical Truth (Jun 12, 2015)
- Awodey on invariance and logic
- SoTFoM III and The Hyperuniverse Programme (May 26, 2015)
- sotfom iii conference
- The Structure of A (Apr 12, 2015)
- How to define the structure of
- Mathematics Without Apologies (Mar 5, 2015)
- Book release of ‘Mathematics Without Apologies’
- Competing Foundations? (Dec 22, 2014)
- foundations conference
- Maths, Just in Short Words (Oct 30, 2014)
- Mathematical proofs in short words.
- 'Competing Foundations?' Conference (Oct 17, 2014)
- FINAL CFP and EXTENDED DEADLINE: SoTFoM II `Competing Foundations?’, 12-13 January 2015, London. The focus of this conference is on different approaches to the foundations of mathematics. The interaction between set-theoretic and category-theoretic foundations has had significant philosophical impact, and…
- Ronnie Brown in Paris (Sep 6, 2014)
- Ronnie Brown’s recent talk
- Homotopy Type Theory: Unified Foundations of Mathematics and Computation (Apr 29, 2014)
- Funding for homotopy type theory
- Call for Papers: Symposium on the Foundations of Mathematics (Feb 12, 2014)
- conference call for papers
- The Covariance of Coloured Balls (Nov 19, 2013)
- covariance through coloured balls
- The HoTT Approach to Physics (Oct 30, 2013)
- Urs’s book published
- Jet Categories at the nForum (Oct 21, 2013)
- nLab activity
- Witten Looking Anew at the Jones Polynomial (Oct 3, 2013)
- Witten at the Clay Meeting
- Good Mathematics (Sep 12, 2013)
- Conference announcement on values in mathematics
- Minhyong Kim in The Reasoner (Jul 28, 2013)
- Interview with Minhyong Kim
- In the News (May 22, 2013)
- article on category theory
- Modal Types (Apr 23, 2013)
- Applying modalities to types
- Categories for the Working Metaphysician (Mar 27, 2013)
- conference on category theory and philosophy
- Have You Left Off Beating Your Wife? (Feb 20, 2013)
- Continuing the series of what type theory can do for philosophy, let us take a look at the infamous question of the title. To forestall criticism, let me say straight away that I’m not proposing in these posts that…
- The Title of This Post is False (Feb 6, 2013)
- type theory and the liar paradox
- The King of France (Jan 30, 2013)
- Bringing dependent type theory to philosophy
- What Can Category Theory Do For Philosophy? (Dec 6, 2012)
- A possible philosophical meeting on category theory
- Back in Business (Nov 9, 2012)
- Sorry about that interruption in service. We seem to be back in business, but I fear we may have lost some of the more recent comments….
- The Ax-Grothendieck Theorem According to Category Theory (Sep 10, 2012)
- Can category theory account for Ax-Grothendieck
- Urs Schreiber in The Reasoner (Aug 30, 2012)
- Discussing Urs Schreiber’s interview in The Reasoner.
- Directed Homotopy at Liverpool (Aug 30, 2012)
- PhD position at Liverpool in higher category theory
- Categorical Unification (Aug 8, 2012)
- Postdocs in Categorical Unification
- Cohomology in Everyday Life (Jun 14, 2012)
- intuitive examples of cohomology
- Mathematical Cultures (Apr 19, 2012)
- Conference on mathematical cultures
- Circles Disturbed (Mar 19, 2012)
- Edited book on math and narrative appears
- Logic as Invariant-Theory (Jan 13, 2012)
- Erlanger program for logic
- Back from NIPS 2011 (Dec 19, 2011)
- Report on maching learning workshops
- Coalgebra Paper (Oct 31, 2011)
- the appearance of my paper on coalgebra
- Zalamea on Sheaf Logic (Oct 3, 2011)
- Zalamea seminar announcement
- Who's Your Friend? (Sep 12, 2011)
- derive category up to equivalence or isomorphism?
- Voevodsky on FOM (Sep 12, 2011)
- Does Voevodsky understand Godel’s results?
- The Set-Theoretic Multiverse (Aug 23, 2011)
- Why there are many universes of sets.
- Doctrinal and Tannakian Reconstruction (Jul 11, 2011)
- Seeking what is common between Gabriel-Ulmer style dualities and Tannaka duality
- A Bit More About Entropy (Jun 17, 2011)
- Entropy and geometry
- Making Things Simpler by Duality (May 12, 2011)
- How should we understand the simplification introduced by duality?
- Report on Peter Freyd's Lecture (Apr 16, 2011)
- Freyd on philosophy of mathematics.
- Category Theoretic Modal Logic (Apr 4, 2011)
- Category theoretic ideas on modal logic
- An Anti-Philosophy of Mathematics (Mar 25, 2011)
- Announcing a Peter Freyd lecture
- Category Theory and Metaphysics (Mar 9, 2011)
- How does category theory help metaphysics?
- Symposium: Sets Within Geometry (Mar 7, 2011)
- There is to be a Symposium – Sets Within Geometry – held in Nancy, France on 26-29 July, 2011. Confirmed speakers are: FW Lawvere (Buffalo), Yuri I. Manin (Bonn and IHES), Anders Kock (Aarhus), Christian Houzel (Paris), Colin McLarty…
- Tarski's Two Approaches to Modal Logic (Feb 25, 2011)
- What links Tarski’s two approaches to modal logic?
- Coalgebraic Tangles (Jan 25, 2011)
- I’m sinking in a sea of administrative duties at the moment, so for a bit of sanity I thought I’d jot down the glimmer of a thought I had. We spoke back here about the term model for a…
- Seminar on Higher-Dimensional Algebra (Jan 23, 2011)
- Some announcements
- Impact! (Jan 3, 2011)
- the impact of research
- Purity of Method (Dec 14, 2010)
- Purity of Method and Desargues’s theorem
- Over 4500 Entries in the nLab, and Its 2nd Birthday! (Nov 26, 2010)
- Describing nLab on its second birthday
- Transforms (Nov 4, 2010)
- What makes a transform tick?
- What Is This Category Enriched In? (Sep 14, 2010)
- Searching for enrichment in a stochastic category
- Grinding to a Halt? (Jul 8, 2010)
- future of the blog
- Inevitability in Mathematics (Jun 28, 2010)
- When is it unavoidable that a construct be found?
- Vladimir Arnold, 12 June 1937 - 3 June 2010 (Jun 8, 2010)
- Vladimir Arnold died last week
- nLab Digest (May 27, 2010)
- The latest and best at the wiki nLab
- Quinn on Higher-Dimensional Algebra (May 10, 2010)
- Frank Quinn’s critique of the tenth chapter of my book.
- Back in Business (May 7, 2010)
- The cafe is back again.
- Paris in the Spring (Apr 15, 2010)
- Mathematical ideas and how they combine
- Philosophy in the EMS Newsletter (Mar 16, 2010)
- articles on realism in the EMS newletter
- The Two Cultures Again (Mar 7, 2010)
- Trying to make sense of the two cultures of mathematics
- (Infinity, 1)-logic (Feb 25, 2010)
- In search of the internal logic of a $(\infty, 1)$-topos
- The Sacred and the Profane (Jan 18, 2010)
- Contrasting two attitudes towards mathematics.
- Looking for Compatible Structure (Jan 8, 2010)
- Can Fraisse limits support algebraic structure?
- Galois Theory in Two Variables (Dec 18, 2009)
- I have just returned from attending three days of the Final Workshop of the Newton Institute Non-Abelian Fundamental Groups in Arithmetic Geometry Programme. I was kindly invited by Café visitor Minhyong Kim, whose lecture we discussed a while ago. While…
- When Naturality Fails (Dec 8, 2009)
- Why should we make of important mathematical constructions which aren’t natural?
- What's So Special About the Rationals? (Nov 26, 2009)
- Trying to link the rationals’ structures together.
- Mathematical Emotion (Nov 19, 2009)
- Does mathematical writing express emotion?
- A Rose by Any Other Name (Nov 16, 2009)
- Getting Ola Bratteli’s name right
- Fraïssé Limits (Nov 6, 2009)
- How should we understand a Fraïssé Limit category theoretically?
- The Arrow of Time in Cat (Nov 3, 2009)
- Does the same broken symmetry that affects Set affect Cat?
- Math Overflow (Oct 19, 2009)
- The new math question and answer site
- A Dual for Set? (Oct 14, 2009)
- Question about structural set theory
- Shell What? (Oct 5, 2009)
- My ol blog pages
- Steve Lack Wins Medal (Oct 2, 2009)
- Steve Lack wins Australian Mathematics Society medal.
- The Mathematical Vocation (Sep 28, 2009)
- Collingwood on the value of the pure mathematician.
- Proof by Coinduction (Sep 18, 2009)
- How similar is coinduction to induction?
- Coalgebraic Modal Logic (Sep 7, 2009)
- Putting together ideas of modal logic and coalgebra with ways of modelling first-order theories.
- Where Have All the Solitons Gone? (Sep 2, 2009)
- A request for examples of applied soliton theory.
- Feynman the Babylonian (Aug 27, 2009)
- Feynman’s concerns about an axiomatic approach
- Chasing around the Triangle (Aug 17, 2009)
- Steve Awodey compares foundational frameworks: sets, types and categories.
- Being Tentative on
*n*Lab (Jul 17, 2009) - Is nLab the best place to discuss tentative ideas?
- Generalized Homotopy Theory (Jul 6, 2009)
- On doing the parallel generalization on homotopy as has been done on cohomology.
- Cohomology and Homotopy (Jun 26, 2009)
- On the duality between cohomology and homotopy
- Kan Lifts (Jun 20, 2009)
- Where is the dual of thenotion of Kan extensions?
- Accessible Even to a Philosopher (Jun 16, 2009)
- Frenkel’s new expository paper
- The Elusive Proteus (Jun 5, 2009)
- Continuing the thought that mathematics and physics share in having difficult to articulate general principles.
- Mathematical Principles (Jun 3, 2009)
- Cassirer describes certain physical principles. Are there corresponding ones in mathematics?
- Metric Coinduction (May 28, 2009)
- When does coinduction differ from induction?
- Where is the Philosophy of Physics? (May 19, 2009)
- Should we devote more time to the philosophy of physics?
- The Relevance of Predicativity (May 15, 2009)
- Whether the predicative/impredicative split is noticeable in mainstream mathematics.
- In Search of Terminal Coalgebras (May 8, 2009)
- Trying to understand a talk on terminal coalgebras
*n*Lab - More General Discussion (May 6, 2009)- Discussing nLab
- Gerundives (May 5, 2009)
- Naming ‘things to be categorified’
- Taming the Boundless (Apr 30, 2009)
- How in the modern period the boundless is divided between the infinite and the indefinite, and the former approached mathematically.
- Afternoon Fishing (Apr 23, 2009)
- A question on a picture of Spec(Q).
- A River and a Trickle (Apr 3, 2009)
- On the brief appearance of Lakatos in a Handbook of philosophy of mathematics
- Convex Spaces (Apr 1, 2009)
- Fritz on convex spaces as algebras for the finite Giry monad
- First-Order Logical Duality (Mar 27, 2009)
- Announcing a recent PhD thesis which looks to extend Stone duality to a duality between syntax and semantic for first-order theories.
- The Borromean Link Configuration (Mar 23, 2009)
- Looking for a general formulation of situations where 3 entities are pairwise unconnected, yet connected as a triple.
- Geometric Help Wanted (Mar 13, 2009)
- What does a result of Felix Klein mean?
- Synergism (Mar 10, 2009)
- Are we maximising the collaborative power of our blog?
- The Stabilizer of a Subcategory (Mar 2, 2009)
- Extending John Baez’s definition of the stabilizer of an object in a category to general subcategories
- Two Streams in the Philosophy of Mathematics (Mar 2, 2009)
- Announcing a philosophy of mathematics conference
- Lakatos as Dialectical Realist (Feb 26, 2009)
- Considering Lakatos’s idea of mathematicians aiming at the real through dialogue
- Can -oids save Group Theory 101? (Feb 17, 2009)
- Intriguing questions from Lieven le Bruyn.
- Dialectical Realism in Utrecht (Feb 16, 2009)
- My talk on Lautman in Utrecht
- Last Person Standing (Feb 2, 2009)
- On the effects of nobody being left who understands the totality of the huge proof of a result.
- Abstract Stone Duality (Jan 26, 2009)
- Paul Taylor’s programme to provide a computable foundation for topology
- The Space of Robustness (Jan 14, 2009)
- A discussion of a blog post by Tim Gowers on the structure of mathematics.
- Truth as Value and Duty (Jan 12, 2009)
- Manin on mathematical wisdom
- Categories, Logic and Physics in London (Jan 8, 2009)
- Reporting on the 4th CLP workshop
- Organizing the Pages at
*n*Lab (Dec 31, 2008) - How to organise pages at nLab
- Bridge Building (Dec 23, 2008)
- Might the cohomology of dynamical systems provide a meeting ground for researchers on the ‘combinatorics’ side of mathematics, and those on the ‘theory-building’ side?
- The Microcosm Principle (Dec 19, 2008)
- The microcosm principle finds aspects of the small reflected in the large.
- What to Make of Mathematical Difficulties (Dec 16, 2008)
- How to make the most of obstructions to a theory
- The Status of Coalgebra (Dec 9, 2008)
- Is coalgebra just as important as algebra?
- Tom Leinster in The Reasoner (Nov 30, 2008)
- Tom Leinster interviewed for The Reasoner
- Coalgebraically Thinking (Nov 27, 2008)
- How coalgebra differs from algebra.
- Beyond the Blog (Nov 25, 2008)
- How to make best use of blog material.
- Mathematical Robustness (Nov 20, 2008)
- Does the ‘robust’ appearance of mathematical entities indicate reality?
- Fourth Categories, Logic and Physics Workshop (Nov 18, 2008)
- Categories, Logic and Physics workshop announcement.
- Entropy, Diversity and Cardinality (Part 2) (Nov 7, 2008)
- Continuation of a discussion of entropy and cardinality and its relevance to ecology
- The Internal Language of a 2-Topos (Nov 6, 2008)
- Extracting the internal language from a 2-topos
- Maximum Entropy Distributions (Nov 2, 2008)
- Why are familiar distributions so often maximum shannon entropy distributions for their class?
- Reviewing Ruelle's Book (Oct 23, 2008)
- Announcing my review of Ruelle’s ‘The Mathematician’s Brain’.
- John McKay Visits Kent (Oct 21, 2008)
- What I took from John McKay’s talk on finite simple groups.
- Entropy, Diversity and Cardinality (Part 1) (Oct 16, 2008)
- Entropy in relation to biodiversity and categories
- New Directions in the Philosophy of Mathematics (Oct 8, 2008)
- To celebrate the founding of MIMS, the mathematics department of the recently unified Manchester University, it was proposed that various workshops named ‘New Directions in…’ be run. They kindly agreed to allow Alexandre Borovik and me to organise one…
- The Blog of Fun (Oct 5, 2008)
- The ‘field with one element’ has been honoured by a great accolade. As announced here, it has been awarded a blog all to itself. Not bad for an entity with dubious existence credentials….
- Mathematical Reality (Oct 1, 2008)
- Some thoughts on mathematical reality as pieces of mathematics inevitably encountered in different ways.
- Mathematical Miniatures (Sep 26, 2008)
- Short essays by Beno Eckmann
- The Volume of a Differentiable Stack (Sep 15, 2008)
- Weinstein’s generalisation of the Baez-Dolan groupoid cardinality concept to stacks.
- Who are Various? (Sep 10, 2008)
- Workshop announcement and an enquiry about a reference made by Saunders Mac Lane
- Reliability (Sep 9, 2008)
- A response to an article on the unreliability of the mathematical literature.
- Imperfections, Ambiguities and Physics (Aug 30, 2008)
- Can Lautman’s concept of the dialectical relationship between perfection and imperfection be realised in physics?
- Melliès on Functorial Boxes (Aug 22, 2008)
- Paul-André Melliès has a tutorial on incorporating functors
*between*categories into string diagrams… and applications to logic. - Freed on Chern-Simons (Aug 21, 2008)
- Daniel Freed has come out with an expository paper on Chern-Simons theory.
- Lautman on Reciprocity (Aug 14, 2008)
- Albert Lautman has a paper on the use of analysis in number theory — with a special emphasis on “reciprocity”.
- Category Theory and Model Theory (Jul 29, 2008)
- Category theory and model theory
- Real versus Complex Numbers (Jul 24, 2008)
- Comparing the reals and the complex numbers
- Girard on the Limitations of Categories (Jul 23, 2008)
- Girard on categories
- Hierarchy and Emergence (Jul 18, 2008)
- Emergence in hierarchies
- Sphere Eversion (Jul 7, 2008)
- Everting the sphere
- A Small Observation (Jul 3, 2008)
- A duality in 2-vector spaces
- Lerman on Orbifolds (Jun 30, 2008)
- Lerman on orbifolds
- Michael Polanyi and Personal Knowledge (Jun 28, 2008)
- Polanyi on personal knowledge
- Tim Porter on Formal Homotopy Quantum Field Theories and 2-Groups (Jun 24, 2008)
- Tim Porter on HQFT
- The Mathematical Sublime (Jun 17, 2008)
- The sublime
- Klein 2-Geometry XI (Jun 12, 2008)
- categorified geometry
- Dumbing Down (Jun 4, 2008)
- Mathematics exams for 16 year olds are getting easier, it is claimed. It’s fairly easy to check for yourself. Take a look at the Arithmetic, Algebra and Geometry papers from 1959 and compare with a contemporary specimen GCSE paper. Even…
- Manin on Foundations (May 28, 2008)
- Manin on mathematical foundations
- Ambiguity Theory (May 19, 2008)
- Galois theory as the study of ambiguity
- Pernicious Symbolization (May 8, 2008)
- Ryle against Carnap
- Quaternionic Analysis (May 6, 2008)
- Quaternionic analysis
- Questions on 2-covers (Apr 30, 2008)
- 2-covers
- Returning to Lautman (Apr 29, 2008)
- I mentioned in an earlier post that Albert Lautman had a considerable influence on my decision to turn to philosophy. I recently found out that his writings have been gathered together and republished as Les mathématiques, les idées et le…
- Klein 2-Geometry X (Apr 15, 2008)
- Acting on groups
- Categorical Sheaves (Apr 9, 2008)
- Toën and vezzosi on categorical sheaves
- Petitition to Save USQ Mathematics (Apr 9, 2008)
- Terry Tao on saving USQ Maths
- 2-Structure Types (Apr 2, 2008)
- 2-structure types
- Categorified Quantum Groups (Mar 27, 2008)
- categorifying quantum groups
- The World of L (Mar 17, 2008)
- Breaking news in number theory
- A Strange Link (Mar 11, 2008)
- Tim Porter on global actions
- Worrying About 2-Logic (Mar 6, 2008)
- More on 2-logic — some possible problems.
- A Deep Sense of Miserable Ignorance (Mar 3, 2008)
- Peirce on pedagogy
- Peirce on Mathematics (Feb 28, 2008)
- Charles Peirce on mathematics.
- A Question or Two (Feb 25, 2008)
- Is there a categorified spectrum?
- 2-Galois and 2-Logic (Feb 13, 2008)
- Categorifying logic
- Lautman Conference (Feb 12, 2008)
- Lautman conference
- Albert Lautman (Feb 4, 2008)
- The philosophy of Albert Lautman
- Virtually Real or Really Virtual (Feb 2, 2008)
- If NASA can have a presence in Second Life with their CoLab project, maybe we at the Café should be thinking about the next step….
- 101 things to do with a 2-classifier (Jan 17, 2008)
- What to do with a 2-classifier.
- 2-Toposes (Jan 12, 2008)
- What happens when you categorify topos theory. You get 2-topos theory… but what’s that like?
- Two Cultures in the Philosophy of Mathematics? (Jan 2, 2008)
- Should we have a conference bringing together the two kinds of philosophers of mathematics?
- Challenges for the Future (Dec 28, 2007)
- Benjamin Mann’s 23 challenges.
- Progic VI (Dec 21, 2007)
- Graphical models
- Is Mathematics Special? (Dec 17, 2007)
- A conference to be held in Vienna in May 2008 tackles the question “Is Mathematics Special?”
- A Dialogue on Infinity (Dec 15, 2007)
- The application Alexandre Borovik and I submitted to the John Templeton Foundation as part of their funding of the core theme of infinity was successful. We intend to discuss and disseminate ideas via a blog – A Dialogue on Infinity….
- Progic V (Dec 6, 2007)
- I’ve come across something promissing for the Progic project. Apparently there is a way to complete the analogy: propositional logic : predicate logic :: Bayesian networks: ? The answer, it is claimed, is ‘probabilistic relational models’. Now before we…
- MA in Reasoning (Nov 23, 2007)
- I would like to announce that we in the Centre for Reasoning here in Canterbury are launching a new MA course for September 2008. As you can see, this offers the chance to select from four core modules: Logical reasoning,…
- Category Theory and Biology (Nov 15, 2007)
- Does category theory have anything to say to biology?
- Klein 2-Geometry IX (Oct 18, 2007)
- More thoughts on 2-geometry
- Progic IV (Oct 9, 2007)
- More on unity probability theory and logic
- New Blog (Sep 28, 2007)
- Jeff Morton has a new blog!
- Progic III (Sep 28, 2007)
- More about reconciling logic and probability theory
- Progic II (Sep 25, 2007)
- More on merging probability theory and logic.
- Progic (Sep 18, 2007)
- My colleague here in Canterbury Jon Williamson is part of an international research group, progicnet, whose aim is to find a good integration of probability theory and first-order logic. For one reason or another, some technical projects get counted…
- Tim Gowers Joins the Blogosophere (Sep 11, 2007)
- Gowers’ new blog
- Category Theory in Machine Learning (Sep 5, 2007)
- Does category theory have a future in machine learning?
- The Reasoner (Aug 26, 2007)
- Contributing to The Reasoner.
- Justificatory Narratives (Aug 22, 2007)
- What’s special about special functions.
- Future Gazing (Aug 17, 2007)
- What to expect in the next year
- Math Teach Wiki (Aug 15, 2007)
- Back from Tuscany, I find two e-mails requests awaiting me. First, and I’m now very late on this story, Alexandre Borovik asked me to draw attention to the plight of a Mathematical Summer School held in Turkey. Second, Tim Porter…
- Algebra 1
*versus*Algebra 2 (Jul 28, 2007) - Rota on two algebras
- Delphic Inspiration (Jul 25, 2007)
- Mathematics and Narrative meeting
- Mathematical Imperatives (Jul 16, 2007)
- Mathematical ‘must’
- George Mackey (Jul 14, 2007)
- Who will collect the letters of George Mackey?
- Breaking Out of the Box (Jul 13, 2007)
- Try n-categories in spheres!
- Return of the Euler Characteristic of a Category (Jul 9, 2007)
- Leinster’s second paper on the Euler characteristic.
- Kernels in Machine Learning III (Jul 6, 2007)
- More about kernels, including heat kernels, in machine learning.
- Kernels in Machine Learning II (Jun 28, 2007)
- More about kernels in machine learning.
- Kernels in Machine Learning I (Jun 25, 2007)
- The use of kernels in machine learning
- Faith and Reason (Jun 21, 2007)
- Polanyi on faith and reason
- Degeneracy (Jun 19, 2007)
- Papers on degenerate n-categories
- Opetopes as Trees (Jun 16, 2007)
- A new paper on opetopes.
- Two ArXiv Papers (Jun 12, 2007)
- Two papers on bicategories.
- More Mathematical Blogging (Jun 12, 2007)
- A new mathematics blog.
- The Curious Incident of the Dog in the Night-time (Jun 8, 2007)
- The cyclic category.
- Categorifying Quantum Mechanics (Jun 7, 2007)
- Two approaches to categorifying quantum mechanics — compare them!
- Whose 2-Vector Spaces? (Jun 6, 2007)
- 2-vector spaces for elliptic cohomology.
- June Events (Jun 5, 2007)
- June conferences
- The Woodstock of the Mind (Jun 1, 2007)
- The Hay Festival
- Going Hi-Tech (May 25, 2007)
- Slides on n-categories
- The Two Cultures of Mathematics Revisited (May 22, 2007)
- Revisiting the idea of two cultures in mathematics.
*Linear Algebra Done Right*(May 18, 2007)- Doing linear algebra right! — the trouble with determinants.
- Two Physics Papers Involving Categorification (May 16, 2007)
- Physics papers dealing with categorification
- Klein 2-Geometry VIIIS (May 7, 2007)
- A few additional Klein 2-geometry thoughts.
- Probability in Amsterdam (May 1, 2007)
- Foundations of the Formal Sciences conference in Amsterdam.
- Learning from Our Ancestors (Apr 25, 2007)
- What can we learn from earlier mathematicians?
- Who's on the Right Track? (Apr 23, 2007)
- Connes on the wrong track for quantum gravity.
- The Field With One Element (Apr 17, 2007)
- For some grand theory building and an answer to the question ‘What is the field with one element?’, see Nikolai Durov’s New Approach to Arakelov Geometry.
- The Two Cultures of Mathematics (Apr 17, 2007)
- ‘Theory-builders’ and ‘problem-solvers’.
- Structure and Pseudorandomness (Apr 12, 2007)
- Terence Tao has written three delightful posts detailing his views on the relationship between structure and pseudorandomness in mathematics.
- Category Theory as Esperanto (Apr 11, 2007)
- If category theory is the Esperanto of mathematics, how many mathematicians speak it fluently?
- Whatever Happened to the Categories? (Apr 6, 2007)
- Are we doing our job as broadcasters well? Max Tegmark has a new paper out on the physical universe as an abstract mathematical structure. Not a whiff of categories, let alone nn-categories. Tegmark has read some of philosophy of…
- Automated Theorem Proving (Apr 5, 2007)
- In Brussels, we heard from Koen Vervloesem about attempts towards better automated theorem provers. Readers of my book will know that I devoted its second chapter to automated theorem provers, to provide a relief against which to consider ‘real…
- Rota on Combinatorics (Apr 2, 2007)
- From an interview with Gian-Carlo Rota and David Sharp: Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven’t. You get the feeling that…
- Bernard Williams on Scientism (Apr 1, 2007)
- In Brussels, Brendan Larvor took us through a range of options for those of us who want our philosophy of mathematics to take serious notice of the history of mathematics. A distinction he relied upon was one Bernard Williams introduced…
- Philosophising in Brussels (Mar 24, 2007)
- I’m off to Brussels tomorrow to speak at a conference called Perspectives on Mathematical Practices 2007. You can see the notes for my talk.
- Generalising Hopf Algebras (Mar 20, 2007)
- Gizem Karaali’s paper ‘On Hopf algebras and their generalizations’, in which she describes Hopf algebras and five attempts to generalise them.
- Manin on Mathematics (Mar 15, 2007)
- On the ArXiv today, Yuri Manin has one of those wide-ranging overviews of the life of mathematics: Mathematical knowledge: internal, social and cultural aspects. One comment - When Poincaré said that there are no solved problems, there are only problems…
- Computer Science and Physics (Mar 5, 2007)
- Samson Abramsky’s paper:
*What are the fundamental structures of concurrency? We still don’t know!* - Dynamics of Mathematical Reason (Mar 2, 2007)
- I’m having a spot of bother getting a paper published. It’s about the philosopher Michael Friedman’s treatment of mathematics in his
*Dynamics of Reason*. I’d be grateful for any comments from the Café clientele. - The Health Book (Feb 23, 2007)
- The book —
*Why Do People Get Ill?*— is finally out there in the shops. - Noncommutative Geometry Blog (Feb 21, 2007)
- A new blog on noncommutative geometry.
- Cake Talk (Feb 21, 2007)
- A talk on Bayesianism, information geometry, and nonparametric statistics.
- Congratulations! (Feb 17, 2007)
- It’s John’s wedding day today!
- Category Theoretic Probability Theory II (Feb 13, 2007)
- More on what category theory has to say about probability theory.
- Why Do I Bother? (Feb 10, 2007)
- Terence Tao’s paper ‘What is good mathematics?’, and what the philosophy of mathematics might say about this.
- Category Theoretic Probability Theory (Feb 7, 2007)
- Having noticed (e.g., here and here) that what I do in my day job (statistical learning theory) has much to do with my hobby (things discussed here), I ought to be thinking about probability theory in category theoretic terms….
- In the Footsteps of Rudolf Carnap II (Feb 5, 2007)
- The next day I set off East to Jena, following the path taken by Carnap, and by my host, David Green, a British mathematician who works on the cohomology of finite groups. While in Wuppertal, David had become interested…
- In the Footsteps of Rudolf Carnap I (Feb 5, 2007)
- Last week I gave a couple of talks in Germany. Thursday saw me in the town of Wuppertal, famous for its Schwebebahn, a railway built above the river Wupper, which snakes its way through the middle of the town. As…
- No Need to Apologise (Jan 29, 2007)
- Café regular John Armstrong has a blog. It goes by the name of The Unapologetic Mathematician. A subtle allusion to Hardy’s A Mathematician’s Apology, playing cleverly on the two meanings of apology?…
- Another Interview (Jan 28, 2007)
- It’s worth taking a look at an interview Mikio Sato gave to Emmanuel Andronikof in 1990, published in February’s Notices of the American Mathematical Society. Sato is famous for algebraic analysis, D-modules, and the like, about which I know next…
- Peering Through the Veil (Jan 27, 2007)
- Twice in recent days I have confronted the possibility of experiencing a kind of alienation due to interviews. First, my co-author Darian Leader and I were interviewed by the New Scientist about our book Why Do People Get Ill?. A…
- Two Café Owners Interviewed (Jan 23, 2007)
- As neither John nor Urs has announced it, readers might like to find out about their motivations for starting and running this blog in an interview they gave to Bruce Bartlett, available in written form and also as an MP3…
- More on Duality (Jan 19, 2007)
- Continuing our earlier discussion about duality, it’s worth noting a distinction that Lawvere and Rosebrugh introduce in chapter 7 of their Sets for Mathematics between ‘formal’ and ‘concrete’ duality. Formal duality concerns mere arrow reversal in the relevant diagrams,…
- Duality between Probability and Optimization (Jan 18, 2007)
- One of the reasons I have an interest in what we find out about mechanics in different rigs is that many machine learning algorithms are expressible in thermodynamic form, as the tutorial, Energy-Based Models: Structured Learning Beyond Likelihoods, by…
- Ubiquitous Duality (Jan 11, 2007)
- I’m in one of those phases where everywhere I look I see the same thing. It’s Fourier duality and its cousins, a family which crops up here with amazing regularity. Back in August, John wrote: So, amazingly enough, Fourier duality…
- Universality in Particularity (Jan 8, 2007)
- To keep me from brooding on the pleasure I’m missing out on by not being with my Café co-hosts in Toronto, let me try out a blog post. In just about every academic endeavour to which I’ve applied myself, I…
- Research Proposals (Jan 3, 2007)
- There’s nothing quite like a research proposal to give you a sense of some of the big stories out there. Try Geometry and Quantum Theory for what’s happening in Holland of relevance to the Café. From a couple of years…
- Common Applications (Dec 21, 2006)
- Why does the same piece of mathematics find many applications?
- Back from NIPS 2006 (Dec 13, 2006)
- Background knowledge in machine learning
- Bicat is Not Triequivalent to Gray (Dec 13, 2006)
- Steve Lack’s new paper.
- Klein 2-Geometry VIII (Dec 1, 2006)
- Continuing Klein 2-geometry
- NIPS 2006 (Nov 27, 2006)
- NIPS 2006 conference, Vancouver
- Philosophy as Stance (Nov 21, 2006)
- Philosophy and taking a stance.
- MacIntyre on Rational Judgment (Nov 16, 2006)
- How explicit must rational reasoning be?
- The Tasks of Philosophy (Nov 10, 2006)
- What should philosophy study?
- Mathematics Under the Microscope (Nov 9, 2006)
- Book about mathematics
- Infinite-Dimensional Exponential Families (Nov 6, 2006)
- Information geometry for kernel methods in machine learning.
- Academic Commons (Nov 2, 2006)
- Enclosure of Academic Commons
- Klein 2-Geometry VII (Nov 1, 2006)
- Continuing to categorify the Erlanger Program
- Foundations (Oct 30, 2006)
- What are foundations?
- Knowledge of the Reasoned Fact (Oct 23, 2006)
- In a comment I raised the question of what to make of our expectation that behind different manifestations of an entity there is one base account, of which these manifestations are consequences. If I point out to you three…
- The Encyclopaedists' Dream (Oct 15, 2006)
- What is epistemology?
- Wittgenstein and Thurston on Understanding (Oct 11, 2006)
- What Wittgenstein might have said about the famous Jaffe-Quinn debate - and what Thurston
*did*say. - Euler Characteristic of a Category (Oct 11, 2006)
- Baez and Dolan defined the cardinality of a groupoid. Now Tom Leinster has defined a more general concept: the Euler characteristic of a category!
- Philosophy of Physics (Oct 9, 2006)
- Publication of ‘Philosophy of Physics’
- So Irigaray was Right? (Oct 6, 2006)
- Navier-Stokes solution
- Emulating Aristotle (Oct 4, 2006)
- How to emulate Aristotle
- The Consolation of n-Categories (Oct 1, 2006)
- What has mathematics meant to people through the ages?
- Klein 2-Geometry VI (Oct 1, 2006)
- Resuming the categorification of Kleinian Geometry
- Toleration (Sep 27, 2006)
- Toleration and the ends of conversation
- Our Raison D'être (Sep 26, 2006)
- Marni Sheppeard reports from the AustMS2006 conference, which, as anyone who knows about Australian mathematics might expect, is holding a category theory session. Dominic Verity is giving one of the talks, in which he considers the raison d’être for higher…
- Mathematical Kinds (Sep 23, 2006)
- Do mathematical entities belong to kinds?
- Categorification in Uppsala (Sep 21, 2006)
- Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are only a handful of participants’ notes available (Scott Morrison’s are…
- The Why and Wherefore of History (Sep 21, 2006)
- Here are some notes for my talk at the Berlin workshop. Fortunately I was upgraded to a 45-minute talk. Even so, I didn’t manage to reach the last part where I discuss David Carr’s ideas. I would be interested in…
- Searching for a New Epistemology in Berlin (Sep 18, 2006)
- Reporting from a workshop in Berlin.
- Mathematics and Virtual Reality (Sep 9, 2006)
- Is Mathematics a Massively-Multiplayer Online Role-Playing Game?
- Category Theory and Philosophy (Sep 8, 2006)
- The place of category theory in philosophy
- Mathematical Circuit Components (Sep 7, 2006)
- What mathematics and radio circuits might have in common.
- The History of n-Categories (Sep 4, 2006)
- How to write the history of mathematics.
- Klein 2-Geometry V (Sep 4, 2006)
- We resume the attempt to categorify Kleinian geometry

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