Mathematics With Nanshin

03/08/2025

12/06/2025

(9 Nov. 1970) --- The Apollo 14 (Spacecraft 110/Lunar Module 8/Saturn 509) space vehicle arrives at Pad A, Launch Complex 39, during the Apollo 14 roll out from the Kennedy Space Center's Vehicle Assembly Building. The Saturn V stack and its mobile launch tower atop a huge crawler-transporter. The three members of the Apollo 14 prime crew are in the foreground. They are (left to right) astronauts Edgar D. Mitchell, lunar module pilot; Alan B. Shepard Jr., commander; and Stuart A. Roosa, command module pilot.

13/05/2025

Can 26 pages change the world?
The story of John Nash proves that genius isn’t measured in quantity—but in clarity and courage.

In 1950, a 22-year-old mathematician named John Forbes Nash Jr. submitted a doctoral thesis that was only 26 pages long. It contained just two references—one of which was his own previous paper.

That short thesis introduced an idea that would revolutionize:
✔️ Economics
✔️ Political strategy
✔️ Evolutionary biology
✔️ Artificial intelligence
✔️ Algorithmic systems

It was the foundation of Game Theory.
At its heart: the famous Nash Equilibrium — a mathematical proof that even in competitive situations, there’s always a balance point where no one can improve their outcome without making someone else worse off.

Imagine two companies competing for the same market. If both lower prices, profits suffer. If both raise them, they risk losing customers.
The Nash Equilibrium is that sweet spot where neither benefits from changing strategy unless the other does too.

🔹 Nash’s work now explains:

— How nations negotiate in war
— Why animals sometimes cooperate instead of compete
— How AI systems make strategic decisions
— How online auctions and digital marketplaces operate

But recognition didn’t come easily.
For decades, Nash’s theory was seen as an academic curiosity.
Only in 1994, over 40 years later, did he receive the Nobel Prize in Economic Sciences.

And in the years between?

He battled schizophrenia.
He spent decades isolated from academia, fighting his own mind while the world forgot his brilliance.
But he never gave up.

His life became the basis for the film “A Beautiful Mind”, which won four Academy Awards and reintroduced the world to one of its quietest geniuses.

His legacy isn’t just mathematical.
It’s a reminder that depth matters more than volume.

In a world obsessed with word counts, data overload, and endless presentations, Nash showed that a single, elegant idea can change the course of history.

“Ideas are fleeting.

12/05/2025

Men writing equations for a satellite orbit on a chalkboard at Systems Lab Corp. in California - 1957.

(📷 J.R. Eyerman/LIFE Picture Collection)

26/04/2025

Remembering Srinivasa Ramanujan , an Indian mathematician and autodidact , on his 105th death anniversary on 26th April.

He with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions.

Ramanujan initially developed his own mathematical research in isolation; it was quickly recognized by Indian mathematicians.

When his skills became apparent to the wider mathematical community, centred in Europe at the time, he began a famous partnership with the English mathematician G. H. Hardy.

He rediscovered previously known theorems in addition to producing new theorems.

During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations).

Nearly all his claims have now been proven correct, although some were already known.

He stated results that were both original and highly unconventional, such as the Ramanujan prime and the Ramanujan theta function, and these have inspired a vast amount of further research.

The Ramanujan Journal, an international publication, was launched to publish work in all areas of mathematics influenced by his work.

07/04/2025

Dennis Gaitsgory has spent 30 years on a monumental, groundbreaking proof of the geometric Langlands conjecture in characteristic 0. He receives the 2025 Breakthrough Prize in Mathematics.

03/04/2025

"Mathematics is an experimental science, and definitions do not come first, but later on."

- Oliver Heaviside

Oliver Heaviside was an English mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vector calculus, and rewrote Maxwell's equations in the form commonly used today. He significantly shaped the way Maxwell's equations are understood and applied in the decades following Maxwell's death. His formulation of the telegrapher's equations became commercially important during his own lifetime, after their significance went unremarked for a long while, as few others were versed at the time in his novel methodology. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science.

16/01/2025

Terence Tao is widely regarded as one of the greatest mathematicians of our era.

At just 8 years old, he scored over 700 on the SAT math section.

He went on to become the youngest tenured professor in UCLA history and has since authored more than 300 research papers and 17 books.

Tao is known for proving the Green–Tao theorem, which showed that it is always possible to find, somewhere in the infinity of integers, a progression of prime numbers of equal spacing and any length. He also resolved the Erdős discrepancy problem and proved the probabilistic claim that almost all Collatz orbits attain almost bounded values.

Among his many accolades, Tao has been awarded the prestigious Fields Medal and the MacArthur Fellowship.

Learn more: https://www.sciencefocus.com/science/who-has-the-highest-iq

30/12/2024

ISAAC NEWTON AND CONTROVERSIES
Isaac Newton, one of the greatest scientists in history, was no stranger to conflict. When he presented his revolutionary ideas on light and color to the Royal Society in 1672, he faced sharp criticism from Robert Hooke, a leading figure of the time. Hooke, who saw himself as an authority on optics, dismissed Newton’s work with condescension. For most people, criticism might have been a chance for debate, but for Newton, it was deeply personal. The dispute escalated into a bitter feud, with Newton eventually withdrawing from public discussions for years.
This wasn’t an isolated event. Newton had a knack for turning professional disagreements into personal vendettas. He later clashed with Gottfried Wilhelm Leibniz over who invented calculus, a dispute so fierce that their supporters waged a pamphlet war that lasted decades. Yet, amid these controversies, Newton produced some of the most important scientific discoveries of all time, reshaping our understanding of the universe.

Despite his difficult childhood, Newton showed extraordinary intelligence. He loved tinkering, building mechanical models of windmills and clocks as a child. When it became clear he wasn’t cut out to manage the family farm, he was sent back to school. Eventually, he made his way to Trinity College, Cambridge, in 1661, where he began exploring the ideas that would make him famous.

Newton’s most productive period came during the Great Plague of 1665–1666, when Cambridge closed, and he returned to his family home. In this quiet solitude, Newton developed calculus, made groundbreaking discoveries in optics, and began formulating his law of universal gravitation.

Newton’s discoveries in optics, particularly his experiments with prisms, fundamentally changed our understanding of light. He showed that white light is made up of different colors, challenging centuries of belief that light was simple and uniform.

However, his ideas weren’t universally accepted. When he shared them with the Royal Society, Hooke and others criticized his methods and conclusions. Newton’s inability to handle criticism made the situation worse. He responded with anger, withdrew from public life, and avoided sharing his work for years.

Despite these setbacks, Newton eventually published his most famous work, Philosophiae Naturalis Principia Mathematica (Principia), in 1687. This book laid out his three laws of motion and the law of universal gravitation, providing a mathematical framework for understanding how the universe works.

Source :Britannica

30/12/2024

Water Ice Has Officially Been Found On Mars:

This image, captured by ESA’s Mars Express, showcases the Korolev crater, an 82-kilometer-wide structure located in the northern lowlands of Mars.

Korolev crater on Mars resembles a vast field of snow but is actually filled with ice. The crater, located in Mars’ northern lowlands near the Olympia Undae dune fields, spans 82 kilometers and has a central ice mound up to 1.8 kilometers thick that remains year-round due to a unique “cold trap” phenomenon.

This occurs because the crater’s floor, two kilometers deep, cools the air above the ice, creating a stable layer of cold air that prevents the ice from melting. This effect is heightened as air is a poor heat conductor, keeping the crater permanently icy.

The images, captured by the Mars Express High Resolution Stereo Camera (HRSC), mark 15 years since the spacecraft began its mission, having entered Mars’ orbit on 25 December 2003.

Korolev crater is named after Sergei Korolev, a pioneer of Soviet space technology, known for his work on the Sputnik and Vostok programs, as well as early interplanetary missions.

Other missions, such as ESA’s ExoMars program, have also shown interest in this region to explore the possibility of past life on Mars. The ExoMars Trace Gas Orbiter, operating since April 2018, captured a detailed image of the crater’s northern rim, highlighting its unique icy landscape.

IMAGE CREDIT: ESA/DLR/FU Berlin

30/12/2024

BREAKING: CERN discovers antihyperhelium-4, the heaviest antimatter particle yet

Scientists at CERN’s Large Hadron Collider have discovered the heaviest antimatter particle ever observed: antihyperhelium-4.

This exotic particle, the antimatter counterpart of hyperhelium-4, contains two antiprotons, an antineutron, and an antilambda particle. The breakthrough offers insights into the extreme conditions of the early universe and sheds light on the baryon asymmetry problem — why our universe is dominated by matter despite matter and antimatter being created in equal amounts during the Big Bang.

The discovery was made using lead-ion collisions at the LHC, recreating the hyper-hot environment of the newborn universe. Machine learning models analyzed the data, identifying antihyperhelium-4 particles and precisely measuring their masses.

While the experiment confirmed that matter and antimatter are created in equal portions, the mystery of what tipped the cosmic balance remains unsolved. With ongoing upgrades to the LHC, more groundbreaking discoveries in antimatter research could be on the horizon.