“Math is an essential tool for physics and physics is a rich source of inspiration in maths” |Researcher|MS Maths|Email: areeba@math.qau.edu.pk
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Hungarian-born Paul Erdős (1913–1996) was a legendary mathematician of the 20th century. He is famous for having published more research papers than anyone since Euler. Both of his parents used to teach mathematics.

At 16, his father made him familiar with two of his lifetime favorite subjects; set theory and infinite series. Erdős always remembered his parents with great affection and love. At 17, he started university in Budapest then he left for the US during the pre-war years. At 20, he was successful in constructing an elegant proof of famous Bertrand’s postulate in number theory. …


A closer look at their concerns about the Starlink broadband constellation.

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A SpaceX Falcon 9 rocket heads into the clouds carrying 60 Starlink satellites, on November 11, 2019. Photo by SpaceX on Unsplash

The Starlink satellite constellation is an ambitious project initiated by SpaceX’s CEO Elon Musk to provide high-speed internet anywhere around the globe.

They have launched nearly 600 satellites in low-Earth-orbit (LEO) so far and are planning to extend it to the interconnected network of about 12,000 small satellites. The network of satellites is connected by space lasers. The main concern they have is global connectivity through the world’s largest Low-Earth-orbit broadband constellation.

The service is foreseen to be available in North America and Canada in the following year. This will likely change our rough and ready ways to connect to the internet nowadays in a tremendous way. Musk speaks about it as a grand innovation that could change the way we view and access the world around us. …


Abel was done to death by poverty, Galois by stupidity

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The portrait of Évariste Galois as a teen

Abel was done to death by poverty, Galois by stupidity. In all the history of science, there is no completer example of the triumph of crass stupidity over untamable genius than is afforded by the all too brief life of Évariste Galois. The record of his misfortunes might well stand as a sinister monument to all self-assured pedagogues, unscrupulous politicians, and conceited academicians. Galois was no “ineffectual angel,” but even his magnificent powers were shattered before the massed stupidity aligned against him, and he beat his life out fighting one unconquerable fool after another.”

— Men of mathematics by E. T. …


A theorem which is simple yet remained unsolved for a long time

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The four-colored map of the United Staes

Historical context

The origin of the four-color map theorem dates back to 1852. Its emergence is quite captivating. Once a person named Francis Guthrie was trying to color the Britain countries on the map, he then suspected that he is able to do that by using only four colors. Little did he knew that his thinking will be going to pose a genuine problem that will remain unanswered for such a long time.

He had a discussion about that problem with his brother Frederick who was a student of the famous mathematician Augustus De Morgan at University College London. …


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Perspective is the most critical aspect associated with every impossible shape.

Impossible shapes are the ones that form in an inconsistent way to create a spooky optical illusion. That deceives our brain on a very first impression by creating a false reality. A few of them are discussed in this article.

Penrose Triangle

The Penrose triangle or the impossible triangle (Penrose tribar) was first designed by a Swedish artist Oscar Reutersvärd in 1934. He was known as the “father of the impossible figures”. He created that picture at the age of 18 while drawing randomly in his Latin class.

The triangle gained more widespread attention in the 1950s when a psychiatrist Lionel Penrose and his son Sir Roger Penrose, who is now a prominent Nobel Prize-winning mathematician, independently expressed it as a “pure impossibility”. They published a paper entitled “IMPOSSIBLE OBJECTS: A SPECIAL TYPE OF VISUAL ILLUSION” in The British Journal of Psychology in 1958. Moreover, the objects with impossible geometry are also featured in the works of Dutch graphic artist M. C. …


The general theory of relativity was pieced together by many renowned people

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Einstein with Marcel Grossmann (left) and Michele Besso (right)

The emergence of the General Theory of Relativity is a subject that has been written and gained extensive attention with the well-defined focus of Albert Einstein’s role in it. This article will enlighten the part played by Marcel Grossmann in generalizing gravity and a little bit about other people who served as building blocks in the completion of the theory.

Firstly I will review the biography of Marcel Grossmann (1878–1936) and his intellectual contributions to the field of geometry. Later I will discuss the collaboration which resulted in Einstein-Grossmann's theory in 1913. …


Making use of the byproduct of cosmic rays from distant galaxies

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The Egyptian pyramids

The elementary particles — Muons

Muons were first discovered by Carl D. Anderson and Seth Neddermeyer in 1936 at Caltech while studying the cosmic rays. Muons are produced in the Earth’s upper atmosphere by cosmic rays from distant galaxies colliding with atomic nuclei of different molecules in the air.

They observed the particles which showed a slight distinct behavior from electrons and other elementary particles e.g they curved differently while passing through a magnetic field. Their properties were quite similar to electrons but they are slightly more massive. Their existence was confirmed one year later in the cloud chamber experiment by J. C. Street and E. C. …


The genius himself had his scientific masters too

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Albert Einstein is known as one of the most brilliant minds of the 20th century. Everyone in today’s world is more or less familiar with his most famous equation E=mc², though they don't understand the actual meaning behind it. He was invariably fond of talking about physics problems, whether with fellow-workers of his age or with people much younger than him. He never bothered much about teaching courses. No student was ever awarded a doctorate degree while working with him. Yet his public lectures were naturally attended and enjoyed by the huge audience. …


Even his tombstone bears the inscription of a spiral

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Illustration of the logarithmic spiral

Biography

Jacob Bernoulli (1655–1705) was a very prominent Swiss mathematician. He belonged to the Bernoulli family, which included a bunch of well-known mathematicians. His father wanted him to peruse theology but in disagreement with his father, he changed his path and learned about mathematics and astronomy.

He was first introduced to the subject of calculus by G.W Leibniz. After that, he has made significant contributions to the subject.

  • The word ‘integral’ was first used by him to analyze the area underneath the curve.
  • His collaboration with his brother Johann Bernoulli resulted in a new field of study ‘the calculus of variations’. …


The darkest mysteries of the cosmos are revealed

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I’m feeling overjoyed upon hearing the news about the Nobel laureates this year. The reason behind my excitement is that this year’s prize has finally been awarded in my own research field i.e specifically in the advancement of our understanding of black holes. I cheerfully pay my heartiest congratulations to the brilliance of these geniuses.

It’s a moment of excitement for all the astronomy and astrophysics community. Because there is a long-running joke about awarding prizes in astronomy and astrophysics that the Nobel community doesn't bother about these observational subjects.

In these fields, it was last awarded in 2006 for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiationand in 2011 for the discovery of the accelerating expansion of the Universe through observations of distant supernovae”. Now it's been two years in a row, in 2019 for the discovery of an exoplanet orbiting a solar-type star and for theoretical discoveries in physical cosmology and now finally in astronomy for long-running mysteries i.e

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