Category Archives: Philosophy


Posted in Philosophy, Popular | 3 Comments

Intellectual Lazyness

My friend gives private mathematics lessons to young pupils, mostly high school students who need some help in their curriculum math. Here is a story about a student of him. My friend asks him: how much is 5+6? The guy … Continue reading

Posted in Education, Philosophy, Popular | 4 Comments

Douglas Hofstadter: I Am a Strange Loop.

Two weeks ago I finished reading Douglas Hofstadter‘s 2007-book I Am a Strange Loop. I haven’t read other Hofstadter’s books and I want to write this review before I read any. My next Hofstadter-book is going to be Gödel Escher … Continue reading

Posted in Book & Article Reviews, Logic, Philosophy, Popular | 2 Comments

0.999999….. = 1?

The question in the title is constantly discussed on web forums and at our department’s corridors; sometimes even by professional mathematicians and is in fact already quite seen and banal. In our department this question is often raised by the … Continue reading

Posted in Calculus, Education, Mathematics, Philosophy, Popular | 5 Comments

I am back!

Now I can blog again: the ‘publish’ button returned to the user interface. Let me start the new era of Walks on Math by: * Changing the name of the blog into Walks on Mind * Posting an interview of … Continue reading

Posted in Education, Meta, Philosophy, Popular | Leave a comment

Five groups

Mathematicians are divided into five groups: those who can count to 2, those who can count to 3, those who can count to 4 and logicians.

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Can Mathematics Solve Philosophical Problems?

This post is not an attempt to answer the question of the subject, but merely to discuss related topics. The idea dates back to the time when I first learned what is the likelihood function in probability theory. When one … Continue reading

Posted in Philosophy | 2 Comments

Prisoners’ Problem 5

There is a famous class of problems concerning public announcements. There is a philosophical (sociological) appeal in these problems. Can a public announcement change the behaviour of the citizens? Of course, if it is for example a news article about … Continue reading

Posted in Combinatorics, Mathematics, Philosophy, Recreation | Tagged | Leave a comment

The Most Important Relation In Mathematics 1

Part 1: Basics In this and few following posts I will argue that not only in mathematics, but in all human reasoning, the role of equivalence relations is crucial. The notion of an equivalence relation is the key to any … Continue reading

Posted in Education, Foundations, Mathematics, Philosophy | 3 Comments

LHC And Artifial Inteligence Going Beyond Us

Two days ago, people of the CERN Control Centre and many other scientists in the world celebrated the successful collisions of LHC. LHC is a device mainly to obtain physical data about the microscopic world, but in fact also mathematicians … Continue reading

Posted in Meta, Philosophy | 1 Comment

Pinocchio Is Omnipotent

Please visit my new website at to find more about mathematics, science, cognitive science and art!  

Posted in Logic, Mathematics, Philosophy, Recreation | 15 Comments

Continuum Hypothesis III

Suppose you pick randomly a real number. What is the probability that it equals to 1? The probability is zero. Suppose [tex]X\subset [0,1][/tex] is a countable subset of the unit interval. What is the probability that a randomly picked real … Continue reading

Posted in Foundations, Mathematics, Philosophy, Probability, Set Theory | Tagged | 2 Comments

Continuum Hypothesis I

This is the first part of the forthcoming trilogy in four parts. The trilogy will be devoted to the understanding of the Continuum Hypothesis by looking at some statements that are equivalent to it. In this post I just expose … Continue reading

Posted in Foundations, Mathematics, Philosophy, Set Theory | Tagged | Leave a comment

The Monkey and the Balls

I heard this story here at Mittag-Leffler institute from someone who heard it from someone else, who probably also heard it from someone else. (And so on.) What is the probability that I heard it from someone else? Just kidding. … Continue reading

Posted in Mathematics, Philosophy, Probability | 2 Comments

A liar’s paradox

I will hereby argue that I am the Pope. Consider the following sentence: If this sentence is true, then I am the Pope. It is an implication, i.e. a sentence of the form [tex](A\to B)[/tex], where A is “this sentence … Continue reading

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