Blogs I Follow
- Not Even Wrong
- More Quantum
- Shtetl-Optimized
- Mathematics without Apologies, by Michael Harris
- Windows On Theory
- Thoughts
- ThatsMaths
- Tobias J. Osborne's research notes
- What Immanuel Kant teach you
- Quantum Frontiers
- MyCQstate
- Neil Barton
- Computational Semigroup Theory
- Math ∩ Programming
- ErdosNinth
- in theory
- Anurag's Math Blog
- Annoying Precision
- njwildberger: tangential thoughts
- Combinatorics and more
- What's new
- Bits of DNA
- Turing Machine
- My Brain is Open
- Gödel's Lost Letter and P=NP
- Mathematical Formalities
-
Recent Posts
- Blackbox oracles and function classes December 23, 2025
- Am I an engineer? December 23, 2024
- Proving formal definitions of informal concepts November 4, 2023
- Getting started without a pre-existing understanding of non-standard natural numbers September 9, 2022
- True randomness and ontological commitments February 28, 2022
- Why mathematics? February 19, 2022
- Incredibly awesome, but with overlength September 3, 2021
- Fields and total orders are the prime objects of nice categories January 30, 2021
- Prefix-free codes and ordinals May 11, 2020
- Isomorphism of labeled uniqueness trees April 20, 2020
- Defining a natural number as a finite string of digits is circular August 17, 2019
- Theory and practice of signed-digit representations April 16, 2019
- A list of books for understanding the non-relativistic QM — Ajit R. Jadhav’s Weblog November 25, 2018
- I’m not a physicist April 29, 2018
- ALogTime, LogCFL, and threshold circuits: dreams of fast solutions November 2, 2017
- A subset interpretation (with context morphisms) of the sequent calculus for predicate logic September 24, 2017
- Logic without negation and falsehood December 11, 2016
- Logic without truth September 3, 2016
- Learning category theory: a necessary evil? April 3, 2016
- A canonical labeling technique by Brendan McKay and isomorphism testing of deterministic finite automata November 15, 2015
- On Zeros of a Polynomial in a Finite Grid: the Alon-Furedi bound September 19, 2015
- Groupoids August 3, 2015
- Reversibility of binary relations, substochastic matrices, and partial functions March 22, 2015
- Algebraic characterizations of inverse semigroups and strongly regular rings December 6, 2014
- Gentzen’s consistency proof is more impressive than you expect December 5, 2013
Recent Comments
- gentzen on Am I an engineer?
- gentzen on Am I an engineer?
- Peter Morgan on I’m not a physicist
- Peter Morgan on True randomness and ontological commitments
- gentzen on Fields and total orders are the prime objects of nice categories
- Proving formal definitions of informal concepts | Gentzen translated on Incredibly awesome, but with overlength
- gentzen on Getting started without a pre-existing understanding of non-standard natural numbers
- vegafrank on Getting started without a pre-existing understanding of non-standard natural numbers
- Christopher on Getting started without a pre-existing understanding of non-standard natural numbers
- gentzen on True randomness and ontological commitments
- none on True randomness and ontological commitments
- True randomness and ontological commitments | Gentzen translated on Why mathematics?
- Fields and total orders are the prime objects of nice categories | Gentzen translated on Defining a natural number as a finite string of digits is circular
- Fields and total orders are the prime objects of nice categories | Gentzen translated on Algebraic characterizations of inverse semigroups and strongly regular rings
- gentzen on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
Author Archives: gentzen
Blackbox oracles and function classes
After spending a long time to work out the function classes for bounded alternating Turing machines, I felt stupid that it took me so long to see the obvious: They are the functions computable by deterministic machines (with appropriate resource … Continue reading
Posted in complexity, computability, partial functions
Leave a comment
Am I an engineer?
The public libraries in Munich once were great. The academic bookshops too. Corona killed off what remained of the bookshops, after Amazon and the move of large parts of TUM to Garching had made them unprofitable. I liked the Studentenbibliothek. … Continue reading
Proving formal definitions of informal concepts
It’s been a long time since my last post. Thanks to Shin’ichi Mochizuki and Peter Woit, I found some interesting reflections. That was end of August, but now we have beginning of November. In fact, it is much worse. In … Continue reading
Getting started without a pre-existing understanding of non-standard natural numbers
I’d always taken it as a given that, if you don’t have a pre-existing understanding of what’s meant by a “finite positive integer,” then you can’t even get started in doing any kind of math without getting trapped in an … Continue reading
Posted in computability, logic, philosophy
3 Comments
True randomness and ontological commitments
AbstractAn attempted definition of true randomness in the context of gambling and games is defended against the charge of not being mathematical. That definition tries to explain which properties true randomness should have. It gets defended by explaining some properties … Continue reading
Why mathematics?
The question of “why” is also important for mathematics: One does not only want to know the theorem, but also why it holds. Therefore one proves the theorem. But a proof has two different aspects. On the one hand, it … Continue reading
Posted in philosophy, physics, Uncategorized
1 Comment
Incredibly awesome, but with overlength
Joel David Hamkins answering Daniel Rubin’s questions is incredible. I just had to write this post. Both are great, Joel is friendly and explains extremely well, and Daniel is direct, honest, and engaging in a funny way. And they really … Continue reading
Posted in Uncategorized
1 Comment
Fields and total orders are the prime objects of nice categories
A field is also a commutative ring, so it is an object in the category of commutative rings. A total order is also a partial order, so it is an object in the category of partially ordered sets. Neither are … Continue reading
Prefix-free codes and ordinals
Originally posted on What Immanuel Kant teach you:
Consider the problem of representing a number in computer memory, which is idealized as a sequence of zeros and ones. The binary number system is a well-known solution to this problem —…
Posted in Uncategorized
Leave a comment
Isomorphism of labeled uniqueness trees
The paper Deep Weisfeiler Leman by Martin Grohe, Pascal Schweitzer, Daniel Wiebking introduces a framework that allows the design of purely combinatorial graph isomorphism tests that are more powerful than the well-known Weisfeiler-Leman algorithm. This is a major achievement, see … Continue reading
Gentzen translated 
