### Top Posts

### Recent comments

### Blogroll

- Alexander Konovalov
- Annoying precision
- Astronomy Picture of the Day
- Azimuth
- Bad science
- Bob Walters
- British Combinatorial Committee
- CIRCA tweets digest
- CoDiMa
- Coffee, love, and matrix algebra
- Comfortably numbered
- Computational semigroup theory
- DC's Improbable Science
- Diamond Geezer
- Exploring East London
- From hill to sea
- Gödel's lost letter and P=NP
- Gil Kalai
- Haris Aziz
- Intersections
- Jane's London
- Jon Awbrey
- LMS blogs page
- Log24
- London Algebra Colloquium
- London Reconnections
- Marie Cameron's blog
- MathBlogging
- Micromath
- Neill Cameron
- neverendingbooks
- Noncommutative geometry
- numericana hall of fame
- Paul Goldberg
- Robert A. Wilson's blog
- Sheila's blog
- Since it is not …
- Spitalfields life
- St Albans midweek lunch
- Stubborn mule
- Sylvy's mathsy blog
- SymOmega
- Tangential thoughts
- Terry Tao
- The Aperiodical
- The De Morgan Journal
- The ICA
- The London column
- The Lumber Room
- The matroid union
- Theorem of the day
- Tim Gowers
- Vynmath
- XKCD

### Find me on the web

### Cameron Counts: RSS feeds

### Meta

# Tag Archives: Peano arithmetic

## Infinity and Foundation

After the reviving effect of a week’s holiday, I have been thinking about Zermelo–Fraenkel set theory, inspired by a very nice student project I supervised (about which I hope to say something here sometime soonish). I have come across a … Continue reading

## On foundations

Jack Edmonds stayed in my house for two and a half weeks, while giving his two courses on polyhedral combinatorics in London (I reported on the second one here). Whenever we spend time together, we have a robust discussion about … Continue reading

Posted in Uncategorized
Tagged Alan Turing, commutative law, Gauss, Jack Edmonds, Peano arithmetic, Poincare, Ron Aharoni, words, Zermelo-Fraenkel set theory
3 Comments

## The commutative law

Everybody believes the commutative law for multiplication of natural numbers: for any two natural numbers m and n, we have m × n = n × m. But even professional mathematicians have heated debates about exactly what counts as a proof of this law. Here are … Continue reading