After hearing about Eugene Wigner’s article, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” for many years, I recently decided to read and digest the article for myself. (If you’re so inclined, you can read about the results here.) Continuing this exploration of the philosophy of mathematics led me to Mario Livio’s intriguing book, Is God […]
My intention for this article is to provide a look into how the decimal expansion of some fractions yields the Fibonacci sequence. Let us first take a look at the decimal expansion of 1/89: Now, for a quick refresher on the Fibonacci sequence. You start with the numbers 0 and 1, and every number after […]
Understanding Pierre de Fermat’s observation about prime numbers If p is a prime and a is any integer not divisible by p, then p divides aᵖ⁻¹ – 1. This property of numbers discovered by Pierre de Fermat in 1640 essentially says the following: Take any prime p and any number a not divisible by that […]
Cantor’s Archive is an official directory of stories published in Cantor’s Paradise, a community-driven publication of math-, science- and technology-related essays. Why Cantor’s Archive? Cantor’s Archive includes stories published in Cantor’s Paradise which are older than 1 years old. The Story Medium ceased supporting publications in mid-2021. Medium’s founder and CEO Ev Williams resigned from […]
As I finished reading The Fault in Our Stars by John Green, perhaps what stood out the most was the phrase, “Some infinities are bigger than other infinities.” As Hazel Grace looked back at the time that Augustus Waters and her had left together, she had struck a reference to a seemingly enigmatic idea — that there […]
Many philosophers and logicians have analysed the forms of arguments and shown us that the same forms occur across many different cases. They’ve also shown us that when it comes to what are called argument-forms, the semantic content of the premises doesn’t (really) matter as long as the argument-form (which involves the proper use of the symbols for the premises […]
If you are looking for the answer to the question “which one is best suited philosophy of mathematics?” I’m afraid this article can’t give it to you. But I do encourage you to work on it. In fact, to develop a good answer to the question “what the entire mathematical reasoning is about?” you will […]
I was born on the 2nd of August, exactly 33 years before my father was born. I always taught the fact of sharing the birthday with my dad was something really unique. I don’t even have two friends who were born on the same day. I never really thought about the math of two people […]
From the Big bang to the Heat death of the universe It’s not because you’re stupid or weren’t concentrating in school Two envelopes with different amounts of money in them. Choose the better one with a higher chance than fifty-fifty! Natural numbers were created by God, everything else is the work of men — Kronecker […]
“When we met, was I walking to the faculty club or away from it? I’m wondering, because in the latter case I’ve already had my lunch” American mathematician Norbert Wiener (1894–1964) was by all accounts, a very peculiar man. After graduating from high school at 11 years old, he entered Tufts College and within three years was awarded […]
In 1896, Becquerel had registered the very first spontaneous radioactivity while working on x-rays. A mere accident allowed him to detect remarkable, not-seen-before phenomenon. To some degree, all discoveries are like rolling a dice. What, once thought out, is kind of funny; because all initial conditions must be met, without any knowledge about them. Like […]
I have a habit of throwing into the air whatever I hold. I do it so often that some call it as my addiction, yeah, it is so common to me. Depending on initial conditions, on how it left my hand, I make bare predictions: how many rotations it will make, what hight it will […]
Raymond Louis Wilder was born 1896 and died in 1982. He was an American mathematician who specialised in algebraic topology and the theory of manifolds. Wilder was professor at the University of Texas, Ohio State University and at the University of Michigan. He was also vice president of the American Mathematical Society and its president from 1955 to 1956. (He was […]
I am a student myself and not (yet) a professional mathematician. This article and the following ones go along as I am learning myself. I follow the script of my lectures and attempt to rephrase in my own words as much as possible. For more information and resources, please see the concluding notes at the […]