Welcome back! In my last article Formal Truth and Logic we introduced many fundamental concepts (e.g. “What precisely is a ‘statement’?” or “How can we compose logic statements?”) of logic in Mathematics. If you require extra context on the notations or definitions used throughout this article, I highly recommend reading the previous article in case you have […]
This article flows out of a video conversation between the YouTubers and mathematicians Grant Sanderson and Matt Parker (references below) and an email conversation between myself and a friend of mine: Peter Gaffney as we explored our own solutions to this beguiling puzzle. Exploring different approaches to this seemingly impossible problem reveals some interesting connections […]
In the late 1800s, mathematics was undergoing a radical shift. Led by David Hilbert (among others), a new group of mathematicians became more interested in abstracting ideas rather than solving problems. Initially criticized for lacking practicality, this difference in philosophy has led to a vast amount of interesting results, one of them being Category Theory. […]
If you haven’t read part 1, you can find it here. The general gist of it is that we look at our data and have a guess at what sort of model would fit it best, then we find the parameters for that model that are the most likely to have generated our data. As promised, […]
Fibonacci numbers are one of the most captivating things in mathematics. They hold a special place in almost every mathematician’s heart. Throughout history, people have done a lot of research around these numbers, and as a result, quite a lot of interesting facts have been discovered. Let us see how they look like – Any number […]
Electromagnetism as compared to gravitoelectromagnetism (GEM) was formulated by the proponents through painstaking observations on the behavior of real objects, i.e. magnets and inductors in their respective electric and magnetic fields. A similar observation on a gravitational field, while it would seemingly be easy, is on the contrary counterintuitive, especially when the supposed objects possesses […]
I recently started a job in which I, trained as a mathematician, am working with a number of colleagues who were trained as physicists. At lunch, this situation led to a discussion of the connections between the two fields, which in turn led to a discussion of Eugene Wigner’s article “The Unreasonable Effectiveness of Mathematics […]
This is part one of a small series of articles meant to describe the most interesting results of complex analysis in an understandable way. Even if you have not had any course in complex function theory, you should be able to get some valuable understanding of this fantastic field. If you are studying mathematics or […]
Using Newton’s Approximation to find the roots of polynomials is commonly taught. However, this can involve repeated iterations to achieve the required level of accuracy. This post shows how to achieve high accuracy in a single application. The method exploits the amazing symmetry of cubic polynomials around their Inflection Point, (Xip,Yip), to find an optimal […]
Last time we followed Eristarchus’ steps of measuring the circumference of the Earth. Today, we will push forward in our investigation of how big the universe is. Because, again, we are hungry for knowledge. We know what the size of the Earth is. So let us go up there and see the one of the closest […]
Most physics textbooks are similar. They differ (little) for the sequence and for the choice of the mathematical details with which topics are presented. Most authors and teachers do not even ask themselves why they illustrate topics that way. Apparently, there is only one way to introduce something. I believe this is not true. At […]
“Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e. there are statements of the language of F which can neither be proved nor disproved in F.” Gödel’s 1931 paper containing the proof of his first incompleteness theorem is difficult to read. It is 26 pages long, contains 46 […]
Suppose, as we all do on a Friday evening, you are looking at data of all the heights of people attending a university. You can plot a histogram of all the data and it might look something like this: You hear that there will be a new person arriving tomorrow and you want to find […]
These days all your devices are encrypted. Apple boasts about their secure systems, most companies have encrypted servers, even your own laptop probably has some level on encryption going on. However, all of these systems are subject to fault. Of course, this all depends on the type of encryption you’re using. While many agree that […]