Mathematicians know that mathematics is beautiful, but they have hard time explaining to others why is it so. In fact, most of the time they give up on this task. My friend Tuomas Tuomiranta hasn’t. I met Tuomas at the University of Helsinki when we both studied mathematics around 10 years ago. Several years later it came to me as a surprise to find out that he became a visual artist! In 2010 Tuomas had created simulations of liquid dynamics based on the Navier-Stoke’s and turned them into artistic animations. Another one was based on the theory of conformal mappings in the complex plane – a common topic at the University of Helsinki. Some links:

http://www.batsandseahorses.com/wp-content/uploads/2017/06/X-ray.jpg10241024Vadimhttp://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.pngVadim2017-06-08 17:35:182017-06-11 19:52:35From Mathematics to Art: an interview with Tuomas Tuomiranta

I am fascinated by the combinations of mathematics and art for several reasons; one reason is that it is so difficult to show the beauty of mathematics to non-experts. As a mathematician I am often frustrated that my work cannot be understood by many people that are important to me. Using mathematics to create Read more

http://www.batsandseahorses.com/wp-content/uploads/2017/06/fractal2.jpg844936Vadimhttp://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.pngVadim2017-06-04 02:43:522017-06-04 14:55:15Mathemat-ART-ical Fract-ART Augumented with Deep Learning

Two weeks ago Adam Neely published a mind blowing video where he introduces fractal music. This is a perfect topic for my blog as well, because it is a mixture between science and art, and this is what Bats and Seahorses is mainly after (apart from the related topic of how to lead a creative life whether in science or art). Before jumping into mathematcs, first of all, here is the video:

I played around a little bit with generating the Penrose tiling and especially how to get knot ornaments out of it. I used algorithm explained at preshing.com as a basis. It generates the Penrose tiling by subdividing triangles. It has two types of triangles which are labeled red and blue and they are subdivided like this:

http://www.batsandseahorses.com/wp-content/uploads/2017/04/coloured_big_.jpg5002000Vadimhttp://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.pngVadim2017-04-16 18:30:242017-04-27 06:36:09Knot ornaments out of Penrose tiling

An interactive animation programmed in JavaScript illustrating the isomorphism from the quotient of the additive groups of reals by intergers to the unit circle on the complex plane defined by the formula:

http://www.batsandseahorses.com/wp-content/uploads/2017/04/e2pixi.jpg204204Vadimhttp://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.pngVadim2017-04-08 08:20:292017-04-18 18:53:55An Interactive Animation Visualising a Group Isomorphism

What tricks do you use in your teaching or have found useful while studying? Comment below!

A couple of months ago I wrote about my eccentric first algebra lecture. I am lecturing Algebra I in this semester which is in fact split into two parts. The teaching methodology this course is being taught in (and has been taught a couple years before me) is already of interest to people outside of our department. I have additionally experimented with some extra stuff such as magic tricks and YouTube videos and below I summarise all that.

http://www.batsandseahorses.com/wp-content/uploads/2017/03/VadimLuennoi1.jpg8161415Vadimhttp://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.pngVadim2017-03-21 21:37:572017-03-22 12:28:31More on my Algebra teaching

What is mathematics? How is mathematics produced, understood and learned by the human brain? Do infinities exist or are they a product of our minds? Whether or not they exist, mathematicians’ minds can conceptualise infinity. What does this mean and how is this possible? Is mathematics limited and shaped by human brain and body or is it completely independent of the agent doing it? Would extraterrestrial aliens have the same mathematics as we do?

http://www.batsandseahorses.com/wp-content/uploads/2017/03/brain_cogsci_math.png20481716Vadimhttp://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.pngVadim2017-03-18 21:04:042017-04-03 17:04:01Cognitive Science of Philosophy of Mathematics - workshop

This semester I am lecturing an introductory course to abstract algebra at the University of Helsinki where I work. For me this is an exercise in mathematics education and public speaking. This is the biggest audience I have ever had in a course: a little short of 200 students. In order to give an exciting first impression of the lectures and maximise future attendance I decided to give a somewhat flashy first lecture. I dressed up in a white suit a hat and a bright red scarf. I dedicated the first lecture to “intuition pumps” which were:

When I met Sir Roger Penrose at the centenary conference of Alan Turing in Manchester in 2012 I told him that Penrose tiling is now featuring as a tiling of Keskuskatu, a central street in Helsinki, he was upset. He said “They should always ask me before they use it!” I was a little dumbfounded. “Can you show a picture?” he continued. I googled it with my smart phone and showed him:

He stared at it for 30 seconds and said “It seems alright.” Sir Roger Penrose is a physicist, mathematician and a philosopher of mind. His ideas are often controversial. He believes that Gödel’s incompleteness implies that the human mind cannot be simulated by a Turing machine which in turn would imply that the human mind radically depends on quantum mechanics which in turn… requires revision according to Penrose, who doesn’t believe in the Schrödinger’s cat. Despite being controversial, he has written numerous books which are excellent at popularizing mathematics, physics and philosophy of mind thereby attracting numerous students to these areas whether they agree with him or not.

[EDIT: I have now heard that Penrose was asked for the permission about Keskuskatu and he gave one. Apparently he either didn’t remember that or he didn’t realize it was the same thing.]

http://www.batsandseahorses.com/wp-content/uploads/2016/12/tiling_feature.jpg249230Vadimhttp://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.pngVadim2016-12-15 23:01:422016-12-16 18:36:10Finnish Artist Makes Progress in Geometry

The size of the wing of a bee in proportion to her body size seems to be virtually identical to that of a penguin. The length of the wing in both animals is around half their height. Why does the bee fly effortlessly while the penguin has absolutely no chance of even slowing down his free fall to save his life? If you read my earlier post about giant grasshoppers, you probably guess the answer…

http://www.batsandseahorses.com/wp-content/uploads/2016/11/beepenguin_cc.png395614Vadimhttp://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.pngVadim2016-11-08 00:01:592016-11-12 00:18:40Bees vs Penguins

Before you continue reading, I would like you to participate in a small poll. Ready? Imagine a giant grasshopper which is otherwise identical to a normal insect grasshopper, but is 50 cm (20 inches) of height. It is like a 20-fold zoomed-in version of the grasshopper, all body parts increased proportionally. Regular tiny grasshoppers can jump up to twenty times times their own body height. The question is:

Big Friendly Giant (2016)

In this post I will explain which is the right answer to the poll and why the giants in the giant country in the movie Big Friendly Giant violate the laws of physics. My aim is not to critisise the movie, but to point out that physics in it is flawed (which is not necessarily a downside artistically speaking). I will also try to give an impression of what the physics of the giant folks should look like which would give the reader an intuition why Read more

http://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.png00Vadimhttp://www.vadimkulikov.org/wp-content/uploads/2016/11/icon-1-300x300.pngVadim2016-08-17 08:23:182016-11-04 14:09:19Big Friendly Giant and Square to Cube Ratio