Fabula spatium

Countless hours of learning more

Countless hours of knowing less

The next installation focuses on the mathematicians of Europe weaving a new face of mathematics. Let’s start with Piero della Francesca from the early Renaissance where his masterpieces of both art and mathematics are well known. In his painting, “Flagellation of Christ”, a technique was used and that is perspective. It’s quite interesting if used properly like present three dimensional paintings to a two dimensional canvas. Parallel lines meet at a vanishing point. His works record a mathematical revelation, a new way or language to understand geometry.

In 17^th century, who would have thought that René Descartes thought that the bed is the best place for the meditative state of thinking shapes and patterns? :)) His philosophical, scientific and mathematical ideas fit together. He was a mercenary working for those who paid him, taking no sides. Cool Descartes has philosophy as his favorite subject. Ha! He built philosophy with facts of mathematics such that an appendix in a dictionary became controversial because he links algebra and geometry. With this, he unlocks the possibility of navigating geometry in higher dimensions

He needed one vital ingredient, though. This is found by Marin Mersenne, a Parisian monk, who discovered prime numbers and correspondence. Publicized works of Pierre de Fermat, who discovered modern number theory and a magistrate mind you, include several new patterns in prime numbers where two squared numbers added together to the same prime number provided that the division of that prime number by 4 has a remainder of 1 and that is for however big the number is. He wanted a proof that this pattern exists forever.

Well, that was for France in. Another dish in this European buffet is from Britain where prestigious universities like Oxford and Cambridge produced very brilliant mathematicians. I’m sure Isaac Newton is on top of the list! Whooo. He was greatest of them but people knew his physics mostly. You know that gravity and acceleration stuff? I know it’s hard but his discovery of Calculus allows us to find the exact speed and the precise distance traveled at any moment in time. Seriously? That’s all? Yes, he led us to mathematics of motion and change so that we are able to understand the movement of planets and more complexities of this ever changing world. Sure, the Royal Society gave Newton credit for being first to discover calculus with Gottfried Leibniz credited for first publication but Leibniz was accused of plagiarism in the second decision. But even though Leibniz discovered calculus shortly after Newton, his contributions to logic and philosophy paved way for building practical calculating machines that worked in a binary system. Unlike Newton’s clumsy and illegible writings, mathematicians today prefer Leibniz’s notations and way of writing because it shows the spirit of calculus. He was just so good at capturing a vision by producing the right language to revolutionize mathematics. Sorry Isaac, I still love your say on apples falling on anyone’s head.

Let’s go to Basel, Switzerland back in 18^th century where a family by the name of Bernoulli made calculus known by spreading it over Europe. They distributed Leibniz’s work if I’m not mistaken but that’s not where their history ends. They are masters of calculus and with this, they discovered calculus of variation. Applications of this include maximizing profits, minimizing energy and construction optimization. Leonhard Euler, star pupil of Johannes Bernoulli, studied during 1730’s in St. Petersburg State University on the side of Russia. He was good with modern mathematics, topology, analysis and all. An amazing feat of his is the equation where E to the power of i x pi = -1. In 1735, Euler discovered pi squared divided by 6 is equal to the sum of the inverted squared positive integers.

Hallo Germany! The Prince of Mathematics, a prodigy, is names Carl Friedrich Gauss. For those who watched Game of Thrones, Gauss has a stone mason for a father. Hey Arya. So anyway, here’s why we should be embarrassed of his bragging rights. At 12, he was criticizing Euclid’s geometry. At 15, he discovered a new pattern of prime numbers that eluded mathematicians for 2000 years. At 19, construction of a 17-sided figure nobody had known during his time. He also had a diary in Latin. This is found in Gottingen University. He discovered theory of elliptic functions and imaginary numbers which helped us understand radio waves, quantum physics and more. You must know that the imaginary number line lies perpendicular to the traditional number line where positive numbers go right and negative numbers go left. He was the first person to explain clearly how the imaginary numbers works. However, as his fame develops, his character deteriorates. While he failed to follow up some of his great insights, another mathematician though has no such fears.

Transylvanian mathematical prodigy, János Bolyai, lived to publish his work in 1831 of imaginary and hyperbolic geometry only to find out that exactly the same idea was also published two years before him by Nikolai Lobachevsky. Include Gauss’s decline of tutoring him and other disheartening gestures. It was all downhill for Bolyai when Gauss lent support to very few mathematicians. But there’s one exception, Bernhard Riemann. A lecture in 1852 on the foundations of geometry took placed when he focused on higher dimensional geometry and multi-dimensional space. He was only 26 years old then. His works continue to perplexed and amazed that his results are everywhere. Hyperspace is no longer a science fiction but a science fact. Imagine all these people imagining imaginary mathematics building an imaginary world. Nah, I salute another batch of mathematicians, European men for this matter. Their works blew away the cobwebs of doubts, allowing us to see the world as it really is today. Du Sautoy said, our world is stranger than we ever thought.

Stranger than fiction it seems but I was able to prove and see what Europe already have. Not just their great views and their great mathematicians’ great views. They also have the same share of unprinted names. Nevertheless, speculations in space and higher dimensions keep us wandering on how we see the world. It’s another perspective. It’s another continent. It’s another achievement. It’s another story but it’s the same yin and yang of historical leaps in mathematics history. It’s getting closer to infinite new sets of possibilities.