Math Files

Life is nonlinear.
So handle it using Math.

[Math Files @Math_files]

In 1978, John McKay noticed something that looked almost embarrassingly trivial.

But the two sides came from mathematical worlds that seemed unrelated.

196883 is the smallest nontrivial irreducible representation dimension of the Monster group, while 196884 appears as the first nonconstant coefficient of the modular-function.

[Math Files @Math_files]

Can you jump straight to a distant digit of π?

The Bailey–Borwein–Plouffe formula (1995) extracts hexadecimal digits without calculating the preceding ones.

In 2022, Simon Plouffe proposed a Bernoulli-number approach to decimal digits.

[Math Files @Math_files]

In 1902, a puzzle showed that an equilateral triangle could be cut into just four pieces and rearranged into a perfect square.

Could three pieces suffice?

A proof published in 2026 by Demaine, Kamata and Uehara established that four is the minimum for polygonal pieces rearranged without flipping.

A 124-year-old geometric question, settled.

[Math Files @Math_files]

Add 2 to the sum of the first 2, 4, 6, ... primes. The first TEN results are all prime: 7, 19, 43, 79, 131, 199, 283, 383, 503, 641. Then the 11th result breaks the pattern: 793 = 13 × 61.

[Math Files @Math_files]

In 1891, David Hilbert described a remarkable mathematical object: a continuous curve that
fills an entire square.

At its nth finite approximation, the curve has length,

Lₙ = 2ⁿ − 2⁻ⁿ.

As n → ∞, its length diverges, yet every point remains inside a square of area 1.

In the limit, the curve passes through every point of that square.

A beautiful surprise from the mathematics of infinity.

[Math Files @Math_files]

Solving a 4D Rubik's Cube (4 × 4 × 4 × 4 Tesseract).

A normal cube has 6 square faces and 3 rotation planes (XY, XZ, YZ).
A 4D tesseract has 8 cubic cells and 6 rotation planes (XY, XZ, XW, YZ, YW, ZW) across 4⁴ = 256 lattice positions.

[Math Files @Math_files]

https://t.co/K5xp21WN5D

[Math Files @Math_files]

AI may have settled an 18-year-old quantum conjecture. PSI reports a proof of the Aaronson–Ambainis conjecture using an unreleased Anthropic model, checked in Lean. It limits exponential quantum query speedups on random, unstructured inputs. Expert review continues.

[Math Files @Math_files]

In 1959, Paul Erdős met a Hungarian boy who was not yet twelve years old. His name was Lajos Pósa.

During lunch, Erdős gave him a problem that had once taken him about ten minutes to solve.

Choose any n + 1 distinct positive integers from 1 to 2n. Prove that at least two must be relatively prime.

Pósa continued eating his soup.

Then he noticed something wonderfully simple.

Arrange the integers into pairs:

(1, 2), (3, 4), (5, 6), ..., (2n − 1, 2n).

There are only n pairs. If you select n + 1 distinct integers, at least one pair must be selected completely.

And any two consecutive integers are relatively prime.

Problem solved.

According to an account reproduced by David Wells, Pósa saw the idea in about half a minute.

Erdős was so impressed that he compared the boy's insight to Gauss's celebrated childhood arithmetic feat.

What makes this story memorable is the contrast. A problem that appears to demand number theory yields to one elementary observation and the pigeonhole principle.

Sometimes a beautiful mathematical proof is simply the right way to look at the numbers.

And sometimes that insight arrives before the soup is finished.

[Math Files @Math_files]

https://t.co/WsR6qfszjP

[Math Files @Math_files]

G. H. Hardy, one of Britain's greatest mathematicians, once devised a rather unusual insurance policy against drowning.

Hardy was a convinced atheist, but he enjoyed joking that God was his personal enemy.

During a visit to Denmark, he spent time with his friend Harald Bohr, a distinguished mathematician and the younger brother of physicist Niels Bohr.

When it was time to return to England, Hardy faced a dangerous journey across the North Sea.

The weather was dreadful, and only a small boat was available.

So Hardy came up with an extraordinary idea.

Before boarding, he sent a postcard announcing:

"I have proved the Riemann Hypothesis."

This was completely untrue.

The Riemann hypothesis was one of mathematics' most celebrated unsolved problems. Anyone who proved it would achieve extraordinary recognition.

Hardy's reasoning was delightfully mischievous.

If his boat sank, people might believe that he had solved the problem but died before revealing the proof.

That would give Hardy enormous posthumous mathematical glory.

And surely God, whom Hardy jokingly regarded as his enemy, would never allow that!

Therefore, God would have to prevent the ship from sinking.

Hardy survived the voyage.

The story is recounted in David Wells's The Penguin Book of Curious and Interesting Mathematics and in George Pólya's reminiscences.

It captures Hardy's peculiar combination of mathematical ambition, skepticism, and humor.

For a man who did not believe in God, he had invented a wonderfully elaborate way of trying to outwit Him.

[Math Files @Math_files]

Born on 7 November 1867, Marie Skłodowska Curie remains the only person to win Nobel Prizes in two different scientific disciplines.

1903: Physics, for research on radiation phenomena.

1911: Chemistry, for the discovery of radium and polonium, and the isolation and study of radium.

The first woman Nobel laureate, Curie helped establish the experimental foundations of radioactivity research.

[Math Files @Math_files]

At 16, June Huh left high school to write poetry. He took six years to graduate from college.

In his final year, a course by Fields Medalist Heisuke Hironaka changed his path.

In 2022, Huh won the Fields Medal for bringing Hodge theory into combinatorics.

[Math Files @Math_files]

On 18 June 1980, Indian mental calculator Shakuntala Devi achieved an extraordinary feat at Imperial College London.

She multiplied two randomly selected 13-digit numbers:

7,686,369,774,870 × 2,465,099,745,779

Her correct 26-digit answer:

18,947,668,177,995,426,462,773,730

Time taken: just 28 seconds.

Guinness World Records recognizes this achievement as the fastest human computation, a remarkable demonstration of mental arithmetic.

[Math Files @Math_files]

https://t.co/a68JYShAZe

[Math Files @Math_files]

Gilbert Strang transformed how generations of students learn linear algebra.

His MIT 18.06 lectures (Spring 2005) are freely available, covering vector spaces, eigenvalues, least squares, matrix factorizations and singular value decomposition.

His central teaching insight: understand the geometry behind matrix operations.

A complete university-level mathematics course, accessible to anyone.

[Math Files @Math_files]

Born on 7 November 1888, C. V. Raman discovered in 1928 that light scattered by molecules can undergo a change in frequency through energy exchange.

This Raman shift reveals molecular vibrations and rotations, providing a spectral fingerprint of matter.

His discovery earned him the 1930 Nobel Prize in Physics and became the foundation of Raman spectroscopy, now widely used in chemistry, physics and materials science.

[Math Files @Math_files]

Mathematics Is Everywhere