This blog post from August 2019 now includes an update with regard to a result that is now revoked. Research has its ups and downs… I would like to share with you a brief description of what I have been doing at Oxford for the past eight months. Since my adviser has already written about […]Read More Modal model theory
Allow me to tell you about an interesting construction I learned from the Stewart’s Calculus book. Start with a square of area one. Next, extend your current rectangle, alternately, on top or beside, by another rectangle of area one. The first 500 steps of this construction are shown below. If you watch the animation carefully, you […]Read More A half-pie ratio
I learned a fascinating fact a few weeks ago at the Philosophy of Mathematics, graduate lecture seminar at the University of Oxford. That week’s discussion was led by Professor Hamkins and concerned a remarkable book Defending the Axioms: On the Philosophical Foundations of Set Theory written by Penelope Maddy, logic and philosophy of science Distinguished […]Read More Think you have a choice? Vitali’s revenge
There is an ongoing debate among mathematicians and philosophers on the nature of the realm where all mathematical activities are performed. But, before I pose the problem, we need to answer a pertinent question: “A realm? Do you mean like… our minds or what?” No. I mean metaphysical entity mathematicians are studying just like physicists […]Read More What complex numbers can tell us about the Multiverse?
This was a talk for “Academic English: Spoken Communication 2” that I gave last Thursday. Please note that this presentation was aimed for non-mathematicians and non-philosophers. Thus, I concealed any anxiety about the topic for clarity’s sake. There is a short clip on the second slide and a GIF on the third one. Unfortunately, these […]Read More Liar’s Paradox
I shall take up a place as a Recognised Student in the Faculty of Philosophy at the University of Oxford starting 7th January 2019. I shall be undertaking research on the topic of “the philosophical consequences of recent advancements in ‘Multiverse inspired mathematics.” My academic adviser will be Professor Joel David Hamkins. I anticipate this […]Read More University of Oxford
One of the first astonishments I faced as an undergraduate mathematics student was that chaos prevails. What do I mean by that? Well, there are more irrational numbers than rational numbers, there are more non-computable functions than computable, and, finally, there are more continuous functions devoid of a derivative than those which have one. In the […]Read More Chaos does not always prevail
Yesterday we had Mother’s Day in Poland. Since my girlfriend and I are parents of our cute pug called Delta, we decided to help her with a gift for mommy. She decided to give her mother a curve. Delta wanted to learn how to make Wolfram|Alpha style person curves like this: You can easily generate […]Read More Making face-curves in Mathematica