Beautiful Mathematics

This question was asked by Toeplitz in 1911 and remains unsolved to this day

ℹ The chemical element Berkelium was originally named after the University of California Berkeley ➡️ which is named after the city of Berkeley ➡️ which is named after the philosopher George Berkeley, who didn't believe in the existence of a physical world!

Universe
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10²⁴
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🌌 Milky Way
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10¹⁸
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10¹⁵
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💫 Solar System
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☀️ Sun
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🌍 Earth
10⁶
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🏔 Mountains
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🐋 Whales
👫 Humans
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🐞 Ladybug
10⁻³
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10⁻⁶
🦠 Virus
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🧬 DNA
⚛️ Atoms
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10⁻¹²
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10⁻¹⁵
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⚡️ Electrons
⚫️ Quarks

“We should not be ashamed to acknowledge the truth or to acquire it, wherever it comes from.” ~ Al-Kindi, Arabic mathematician and philosopher, c 800–873

❝If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?❞ — David Hilbert

Googol = 10¹⁰⁰

A Googol is a 1 followed by 100 zeroes. Other names for googol include ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale.

The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of U.S. mathematician Edward Kasner.

Kasner popularized the concept in his 1940 book Mathematics and the Imagination.

Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics.

A googol has no special significance in mathematics.

However, it is useful when comparing with other very large quantities such as the number of subatomic particles in the visible universe or the number of hypothetical possibilities in a chess game.

To give a sense of how big a googol really is, the mass of an electron, just under 10−30 kg, can be compared to the mass of the visible universe, estimated at between 1050 and 1060 kg.[3] It is a ratio in the order of about 1080 to 1090, or only about one ten-billionth of a googol (0.00000001% of a googol).

Carl Sagan pointed out that the total number of elementary particles in the universe is around 1080 (the Eddington number) and that if the whole universe were packed with neutrons so that there would be no empty space anywhere, there would be around 10128.

He also noted the similarity of the second calculation to that of Archimedes in The Sand Reckoner.

By Archimedes's calculation, the universe of Aristarchus (roughly 2 light years in diameter), if fully packed with sand, would contain 1063 grains. If the much larger observable universe of today were filled with sand, it would still only equal 1095 grains.

Another 100,000 observable universes filled with sand would be necessary to make a googol.

The decay time for a supermassive black hole of roughly 1 galaxy-mass (1011 solar masses) due to Hawking radiation is on the order of 10100 years.

Therefore, the heat death of an expanding universe is lower-bounded to occur at least one googol years in the future.

In 1683 the Swiss mathematician Jacob Bernoulli found the first approximation of the mathematical constant e while studying continuous compound interest. e is a number of great importance alongside 0, 1, π and i.

2⁴ = 4² is the only positive integer solution of aᵇ=bᵃ assuming that a≠b.

Memory Test

Everything Turns, Rotates, Spins, Circles, Loops, Pulsates, Resonates, And Repeats.

Circles Of life, Born from Pulses Of light, Vibrate To Breathe, While Spiraling Outwards For Infinity Through lens Of time, And into A sea Of stars And Lucid Dreams.

Poetry by Suzy Kassem

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Times Tables, Mandelbrot and the Heart of Mathematics

Credits: Mathologer

John T. Tate, Familiar Name in the World of Numbers, Dies at 94

RIP John Tate, an esteemed mathematician and recipient of the Abel Prize.

nytimes.com Many of his explanations of fundamental ideas now bear his name, a much-honored one among mathematicians.

Happy Birthday C.V. Raman

On This Day - 28 February 1928 - Sir C. V. Raman discovered the famous Raman Effect about the scattering of light.

❝Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.❞ — Bertrand Russell

TechScie

Nobel Prize in Physiology or Medicine 2019 has been awarded jointly to William G. Kaelin Jr, Sir Peter J. Ratcliffe and Gregg L. Semenza “for their discoveries of how cells sense and adapt to oxygen availability.”

The researchers discovered how cells can sense and adapt to changing oxygen availability. They identified molecular machinery that regulates the activity of genes in response to varying levels of oxygen.

Their discoveries have also paved the way for promising new strategies to fight anaemia, cancer and many other diseases.

(Credit: The Nobel Assembly at Karolinska)

SQUARED NUMBERS - Staggered Diagonal Array

The spiral of natural counting numbers, beginning with "1" in the centre, and spiralling around this clockwise on squared tiling cells or graph paper, effortlessly reveals the sequence of squared numbers:
1 - 4 - 9 - 16 - 25 - 36 - ... - 361 - 400 (20 squared) in the unusual form of a staggered diagonal. This is not a true diagonal running from corner to opposing corner, but is off-centered by a small amount, though the unusual symmetry is still visible and apparent. This is yet another hint of Nature's hidden code, revealing hidden patterns in apparent simple arrays like the natural counting order of numbers whirling around a centre.

When we examine the other unmarked true diagonal, (not staggered) the sequence of numbers
1 - 3 - 7 - 13 - 21 - 31 - 43 - 57 - 73 - ...
are all Odd Numbers, and the difference between each successive pair is the sequence of Even Numbers
2 - 4 - 6 - 8 - 10 - 12- 14 - ... etc.

(Jain 108)

TechScie

The most intelligent picture ever taken: Participants of the 5th Solvay Conference on Quantum Mechanics, 1927. 17 of the 29 attendees were or became Nobel Prize winners.

Front: Irving Langmuir, Max Planck, Marie Curie, Hendrik Lorentz, Albert Einstein, Paul Langevin, Charles-Eugène Guye, CTR Wilson, Owen Richardson.

Middle: Peter Debye, Martin Knudsen, William Lawrence Bragg, Hendrik Anthony Kramers, Paul Dirac, Arthur Compton, Louis de Broglie, Max Born, Niels Bohr.

Back: Auguste Piccard, Émile Henriot, Paul Ehrenfest, Édouard Herzen, Théophile de Donder, Erwin Schrödinger, JE Verschaffelt, Wolfgang Pauli, Werner Heisenberg, Ralph Fowler, Léon Brillouin.

Proof with Picture

“No human investigation can be called real science if it cannot be demonstrated mathematically.” ~ Leonardo da Vinci, Trattato della Pittura (Treatise on Painting)

Evariste Galois

Évariste Galois, born on 25 October 1811, was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem standing for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. He died at age 20 from wounds suffered in a duel.

TechScie

❝Since her death in 1979, the woman who discovered what the universe is made of has not so much as received a memorial plaque. Her newspaper obituaries do not mention her greatest discovery. […] Every high school student knows that Isaac Newton discovered gravity, that Charles Darwin discovered evolution, and that Albert Einstein discovered the relativity of time. But when it comes to the composition of our universe, the textbooks simply say that the most abundant atom in the universe is hydrogen. And no one ever wonders how we know.❞ — Jeremy Knowles, discussing the complete lack of recognition Cecilia Payne gets, even today, for her revolutionary discovery. (via alliterate)

OH WAIT LET ME TELL YOU ABOUT CECILIA PAYNE

• Cecilia Payne’s mother refused to spend money on her college education, so she won a scholarship to Cambridge.

• Cecilia Payne completed her studies, but Cambridge wouldn’t give her a degree because she was a woman, so she said to heck with that and moved to the United States to work at Harvard.

• Cecilia Payne was the first person ever to earn a Ph.D. in astronomy from Radcliffe College, with what Otto Strauve called “the most brilliant Ph.D. thesis ever written in astronomy.”

• Not only did Cecilia Payne discover what the universe is made of, she also discovered what the sun is made of (Henry Norris Russell, a fellow astronomer, is usually given credit for discovering that the sun’s composition is different from the Earth’s, but he came to his conclusions four years later than Payne — after telling her not to publish).

• Cecilia Payne is the reason we know basically anything about variable stars (stars whose brightness as seen from earth fluctuates). Literally every other study on variable stars is based on her work.

• Cecilia Payne was the first woman to be promoted to full professor from within Harvard, and is often credited with breaking the glass ceiling for women in the Harvard science department and in astronomy, as well as inspiring entire generations of women to take up science.

• Cecilia Payne is awesome and everyone should know her.

(OP: Matthew Gardner)

In 1939, L. E. Dickson proved that all positive integers can be represented as the sum of at most 9 positive cubes. Interestingly, only two numbers exist that require all 9 cubes: 23 and 239

François Viète was the first person to uncover an infinite product formula for π in the 16th century. The formula involves just a single number: 2

Goro Shimura, 89, Mathematician With Broad Impact, Is Dead

Goro Shimura, a mathematician whose insights provided the foundation for the proof of Fermat’s Last Theorem and led to tools widely used in modern cryptography, died on May 3 at his home in Princeton, N.J. He was 89.

His work on the Taniyama–Shimura conjecture guided Andrew Wiles in making the proof for Fermat's Last Theorem. He was also a collector of Imari porcelain!

"Goro Shimura, a mathematician whose insights provided the foundation for the proof of Fermat’s Last Theorem and led to tools widely used in modern cryptography.

He worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the Taniyama–Shimura conjecture which ultimately led to the proof of Fermat's Last Theorem.

He wrote more than 100 papers and books. One book was not about mathematics but about Imari porcelain, which he collected for three decades.

He wrote almost all of his mathematical papers alone. Dr. Sarnak of Princeton recalled visiting Dr. Shimura’s house and seeing two desks in his office. In the morning, Dr. Shimura would work at one, exploring new ideas. In the afternoon, he would work at the second, polishing papers for publication. Once he made a breakthrough and finished a draft of a paper at the morning desk, he would place it in a drawer in the second desk and not return to it for about a year."

nytimes.com His insights provided the foundation for the proof of Fermat’s Last Theorem and led to tools widely used in modern cryptography.

Every math quiz on social media ever 😁