I got a letter (excerpt quoted below), and I wonder what the best reply would be. I usually reply, respectfully and to the point. I once found a bug in a two-page proof of Fermat's theorem by a person who wrote math competently but made an honest error involving gcd's. He couldn't get anyone to look at his proof. He thanked me for putting him out of his misery. The present case seems more difficult. Perhaps that video of Vi Hart would help? What do you usually do?
"Respected sir, Here I am representing different method than others so please go through it. ....[stuff omitted].... The whole world assumes that pi is transcendental number but I want to prove that pi is not transcendental. If you keep this concept apart from your brain & read the whole proof you will also get that assurance. If pi is transcendental then 1 = 0.99999… which is not exact? .... [stuff omitted] ....Thus I found that the value of π is (17 -8√3)."
Well, Gašper is one of those people who could write a fast program even if he had only clay tables and a toothpick. So I think when he says that C++ code is "readable" you need to understand that correctly. Urs is teasing, but as a teacher I am really proud of Gašper.
It is my pleasure to announce a second PhD position in Ljubljana! A position is available for a PhD student at the University of Ljubljana in the general research area of modelling and reasoning about computational effects. The precise topic is somewhat flexible, and will be decided in ...
I am trying to understand why certain math problems are difficult for our freshmen. In the "Logic and sets" course we had the following question, which turns out to be difficult:
"Is there an uncountable family of uncountable subsets of the plane such that any two of them intersect in a countably infinite set?"
They did countable and uncountable sets in our course as well as in the analysis course. We did Cantor's theorem, they know that rationals are countable and reals uncountable, and the midterm had the following question: "Are there two uncountable subsets of the line which intersect in a countably infinite set?"
If anyone wants to perform experiments on their students, I'd love to hear the results.
I am looking for a PhD student in mathematics. Full tuition & stipend will be provided for a period of three years, which is also the official length of the programme. The topic of research is somewhat flexible and varies from constructive models of homotopy type theory to development of a ...
The evil publishers are dying slowly but surely. Here is another nail in the coffin. The important thing is not the book itself, but the technology around it (it's a configurable textbook where you get to choose what to include and what notation it should use!) and the fact that it has been done at all.
We’ve kept this on the down-low long enough, I think: together with Aldo Antonelli, Jeremy Avigad, Nicole Wyatt, and Audrey Yap, I’ve been working on an open source advanced logic textbook for a little while; Andy Arana and Gillian Russell are also on the…
Suppose we have a triangular mesh in 3D. I would like to "flatten it out" onto a plane, assuming this is possible, for instance because I took a mesh of a torus and cut it along a longitude and a meridian. The mesh is "stretchy" in the sense that we need not preserve the distances between the nodes. What would be a good phisical model for accomplishing this? It does not have to work in all cases, only fairly reasonable ones.
Here's one attempt: put equal electric charges into the vertices of the mesh so that they repel each other, and make all the edges into springs obeying Hook's law (with some natural length). This is not good enough yet, I think.
Thanks to the #TEDx University of Ljubljana team for a great event yesterday. I am releasing the code, the images, and all the animations from my talk, plus some extra animations not shown in the talk. Enjoy!
I spoke about the Beauty of Roots as described by +John Baez on his web page. I calculated the roots of polynomials with coefficients ±1 up to degree 26 and beat the current record by +Sam Derbyshire by 2 degrees. The race is on!