Math Files

Life is nonlinear.
So handle it using Math.

[Math Files @Math_files]

Two engineering students happen to be very close friends.

One day, while sitting in a restaurant and having coffee, one friend asked the other: "How is your relationship with that new girlfriend going?"

Student: I forgot to mention, yesterday she came to my house.
Friend: WOW!!! What happened then? Tell me the full story.
Student: Well, I played her favorite music and we danced.
Friend: Then what happened??
Student: As we were dancing together, we kissed...
Friend: Then what? Keep going!
Student: I picked her up in my arms and sat her on the table next to my new laptop...
Friend: You got a New Laptop? When???
Student: Just last week. My parents gifted me one...
Friend: WOW! What configuration?
Student: 500 GB harddisk, 8 GB RAM, 2.3GHz processor...
Friend: Does it have an HDMI port?
Student: Yes!
Friend: A blu-ray burner?
Student: Yes.
Friend: AWESOME, DUDE!!

[Math Files @Math_files]

Richard Feynman was known for an unusual habit when reading research papers.

He would take the latest issue of Physical Review, read the abstract and opening of each article, and then try to guess how the paper would conclude. Only after forming his own prediction would he check the result. If his guess matched, he would move on; if not, he would read the paper in full.

This wasn’t just about efficiency—it was a way of thinking. By actively predicting outcomes, he turned reading into a process of testing intuition and deepening understanding.

Later in life, time likely made this practice less feasible, and like many scientists, he relied more on discussions with colleagues to keep up with new ideas.

It’s a simple but powerful lesson: don’t just read—engage, predict, and learn from being wrong.

[Math Files @Math_files]

On August 10, 1937, a quiet 21-year-old named Claude Shannon submitted an 85-page thesis at MIT. No headlines. No applause. Just another paper that seemed destined to be forgotten. But inside those pages was a revolutionary idea: machines could think using simple logic, 1s and 0s, ON and OFF. By linking Boolean algebra with electrical circuits, Shannon transformed switches into decision-makers. That single insight became the foundation of the digital world. Every computer, smartphone, and algorithm traces back to it. History did not roar that day. It whispered. And from that whisper, the modern world was born, one bit at a time.

[Math Files @Math_files]

https://t.co/WejZhgpm8B

[Math Files @Math_files]

She must be some maths genius!!

[Math Files @Math_files]

“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.”

-Terence Tao

[Math Files @Math_files]

The building that housed the Scottish Café, where a group of mathematicians met in the late 1930s, is still standing in Lwów (left, photo by Stanisław Kosiedowski). Copies of the Scottish Book, containing the original entries by Banach and Ulam, are on display at the Library of the Mathematical Institute of the Polish Academy of Sciences in Warsaw (right, photo from PIWiki, uploaded by Stako).

The original book remains in the custody of the Banach family, who took it with them after Banach’s death and the end of the war, when they were required to resettle in Warsaw. Steinhaus kept in touch with the family and, after the war, copied the book by hand to send to Ulam at Los Alamos in 1956. Ulam later translated the book into English and had 300 copies printed at his own expense.

As requests for the book grew, another edition was printed in 1977. Following a Scottish Book Conference in 1979, in which Ulam participated, the book was reissued once again, this time with updated material and additional papers.

Source: The BEST WRITING ON MATHEMATICS, 2019
Editor: Mircea Pitici

[Math Files @Math_files]

(a + b)² = a² + 2ab + b²

[Math Files @Math_files]

While mathematics geniuses such as Newton, Leibniz and Euler deserve to be acclaimed for their voluminous ground-breaking achievements, we should not forget the signal contributions of some of their predecessors in mathematics.

François Viète (1540–1603) was a French lawyer, politician, diplomat and amateur mathematician. One of his many mathematical contributions is the expression of π as an infinite product involving only the integer 2, in an infinite nesting of square roots.

Viète’s expression marked a milestone in the history of mathematics. It was the first equation incorporating the concept of an infinite process, even though it was not explicitly spelt out as such. The dots (…) in the equation denotes continuing the process indefinitely.

If we think that the expression looks difficult, remember Viète published it in 1593, more than four hundred years ago!

[Math Files @Math_files]

A mathematics professor once discovered that the sink in his kitchen had broken. He called a plumber, who arrived the next day, tightened a few fittings, and quickly fixed the problem.

The professor was pleased—until he saw the bill.

“This is a third of my monthly salary!” he exclaimed.

Still, he paid it. As the plumber was leaving, he said, “I understand your situation. Why not join our company? You could earn much more than you do now. Just one thing—when you apply, say you only finished elementary school. They prefer that.”

The professor, intrigued, followed the advice. To his surprise, he was hired. The work was simple—occasional repairs, tightening pipes—and his income improved dramatically.

Some time later, the company introduced a new rule: all employees had to attend evening classes to complete basic schooling. The professor had no choice but to attend.

On the first day, the subject was mathematics. The instructor asked a student to write the formula for the area of a circle on the board. The professor was chosen.

He walked up confidently—but then hesitated. He couldn’t recall the formula.

Determined, he began deriving it from scratch. The board quickly filled with integrals, derivatives, and complex expressions. After several minutes of work, he arrived at a result:

−πr²

Unsatisfied with the negative sign, he tried again. And again. Each time, the same result appeared.

Frustrated, he turned to the class. Behind him, the other plumbers were whispering to one another:

“Switch the limits of the integral.”

[Math Files @Math_files]

In 1971, Matijasevich devised an explicit method to construct such a formula but did not carry it through to completion.

The first fully written explicit formula appeared in 1976 and used 26 variables (A to Z). It works like a computer program: assign numbers to the variables and evaluate the expression. If the result is positive, it is a prime number.

By systematically trying all possible assignments, the formula generates every prime number, though some inputs give negative values, which are simply ignored.

[Math Files @Math_files]

And it worked