Why are numbers beautiful?

[Guest]

FYI: On research directed at resolving conjectures or advancing existing mathematical theory, please note the difference between thesis and hypothesis:

'Difference Between Thesis and Hypothesis',

https://pediaa.com/difference-between-thesis-and-hypothesis/.

[Guest]

Hmm. Some Food for Thought:

"Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty, spiritual formulas are discovered primarily for the deeper penetration into the laws of nature." -- Albert Einstein.

[Guest]

Hmm. On the Nature of Things:

Two of the most important fundamental ideas in science are the Periodic Table of Elements and the Fundamental Theorem of Arithmetic.

Stable matter is made of atoms, and integers are made of primes. Matter is described by its wave-particle nature, and integers are also described their wave (zeros of the Riemann Zeta Function)-particle (primes) nature. And spectrum analysis detects unique atoms as well as distinct primes... Go figure!

Relevant Reference Link:

'Prime Numbers: A Particle in a Box and the Complex Wave Model' by Prof. Sousa,

https://www.researchgate.net/publication/283321542_Prime_Numbers_A_Particle_in_a_Box_and_the_Complex_Wave_Model.

[Guest]

Hmm. On the Nature of Things:

Two of the most important fundamental ideas in science are the Periodic Table of Elements and the Fundamental Theorem of Arithmetic.

Stable matter is made of atoms, and integers are made of primes. Matter is described by its wave-particle nature, and integers are also described their wave (zeros of the Riemann Zeta Function)-particle (primes) nature. And spectrum analysis detects unique atoms as well as distinct primes... Go figure!

Relevant Reference Link:

'Prime Numbers: A Particle in a Box and the Complex Wave Model' by Prof. Sousa,

https://www.researchgate.net/publication/283321542_Prime_Numbers_A_Particle_in_a_Box_and_the_Complex_Wave_Model.

Hmm. Please view, 'Physics All Around Us with Prof. Neil deGrasse Tyson',

https://www.youtube.com/watch?v=EkZuVHw8FXc since it is entertaining and informative about science matters... Hmm.

[Guest]

Hmm. 'Prof. Neil Turok Public Lecture: The Astonishing Simplicity of Everything', https://www.youtube.com/watch?v=f1x9lgX8GaE, is also good!

[Guest]

Some Food for Thought:

"Thinking in the sense of programs instead of equations opens up a new kind of science." -- Stephen Wolfram, 2002.

"The deepest and most elementary and therefore still unresolved problem in mathematics today has nothing to do with geometry or integers: it's about the calculation." -- Christos H. Papadimitriou, 2007.

Relevant Reference Links:

'From Newton and Turing to Cyber-Physical Systems: Exploring Fundamental Problems of Theoretical Computer Science',

https://www.mpg.de/11867550/mpi-sws_jb_2018?c=155640;

'An algorithm developed to study the structure of galaxies helps explain a key feature of embryonic development',

https://phys.org/news/2019-07-algorithm-galaxies-key-feature-embryonic.html.

[Guest]

Hmm. 'How the Universe Works - From The Big Bang To The Present Day - Space Discovery Documentary',

https://www.youtube.com/watch?v=dMYmzeZXxMM.

[Guest]

On Human Genius:

“Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius — and a lot of courage to move in the opposite direction.”
― E.F. Schumacher.

“The only genius that's worth anything is the genius for hard work.”
― Kathleen Winsor.

“The true genius shudders at incompleteness — imperfection — and usually prefers silence to saying the something which is not everything that should be said.”
― Edgar Allan Poe, Marginalia.

“Neither a lofty degree of intelligence nor imagination nor both together go to the making of genius. Love, love, love, that is the soul of genius.”
― Wolfgang Amadeus Mozart.

“The most tragic thing in the world is a man of genius who is not a man of honor.”
― George Bernard Shaw.

"I have witnessed living geniuses at work, and in all cases, they were my best teachers."
― David Cole.

[Guest]

'A New Book (The Universe Speaks in Numbers: How Modern Math Reveals Nature's Deepest Secrets) Examines the Relationship between Math and Physics',

https://www.scientificamerican.com/article/a-new-book-examines-the-relationship-between-math-and-physics/.

[Guest]

FYI: Nova's 'The Great Math Mystery',

https://www.youtube.com/watch?v=mpcpzXuzdQk.

[Guest]

Nature is a grand optimizer, and therefore, one and only one critical line, (Re(z) = 1/2, the Riemann Hypothesis), is enough to define all primes and all nontrivial zeros of the Riemann Zeta Function. Hmm.

Wow!! Grand optimization implies grand unification, and grand unification implies grand optimization. Go figure! And Go Blue!

[Guest]

Nature is a grand optimizer, and therefore, one and only one critical line, Re(z) = 1/2 (the Riemann Hypothesis), is enough to define all primes and all nontrivial zeros of the Riemann Zeta Function. Hmm.

Wow!! Grand optimization implies grand unification, and grand unification implies grand optimization. Go figure! And Go Blue!

[Guest]

Some Food for Thought: 'There’s Beauty in Numbers',

https://www.nytimes.com/2008/06/08/nyregion/nyregionspecial2/08artsli.html

FYI: 'People can see beauty in complex mathematics, study shows',

https://phys.org/news/2019-09-people-beauty-complex-mathematics.html.

[Guest]

Some Food for Thought: 'There’s Beauty in Numbers',

...

FYI: 'People can see beauty in complex mathematics, study shows',

...

Wow! 'Images: (Some of) The World's Most Beautiful Equations',

https://www.livescience.com/26681-most-beautiful-mathematical-equations.html

Euler's Equation: [tex]e^{i\pi} + 1 = 0[/tex] is very beautiful!

FYI: 'Euler’s Identity: 'The Most Beautiful Equation',

https://www.livescience.com/51399-eulers-identity.html

[Guest]

FYI: 'THE MATHEMATICAL KNOWLEDGE CHILDREN BRING TO SCHOOL',

https://www.nap.edu/read/9822/chapter/7.

[Guest]

Was the great scientist, R. P. Feynman, wrong about truth and beauty in science?

Relevant Reference Link:

'Richard Feynman was wrong about beauty and truth in science',

https://aeon.co/ideas/richard-feynman-was-wrong-about-beauty-and-truth-in-science.

"To those who do not know mathematics, it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she (nature) speaks in." -- Richard Feynman.


The beautiful and grand nature of things demands beautiful and grand mathematics to describe her (nature). The great Richard Feynman was right about the beauty and truth in science!

Dave.

[Guest]

Nature is a grand (complete) optimizer, and therefore, one and only one critical line, Re(z) = 1/2 (the Riemann Hypothesis), is enough to define all primes and all nontrivial zeros of the Riemann Zeta Function. Hmm.

Wow!! Grand (complete) optimization implies grand (complete) unification, and grand (complete) unification implies grand (complete) optimization. Go figure! And Go Blue!

FYI: 'The Riemann Hypothesis (Part 1)',

https://golem.ph.utexas.edu/category/2019/09/the_riemann_hypothesis_part_1.html

[Guest]

Hmm. FYI: 'The Prime Number Conspiracy: The Biggest Ideas in Math from QUANTA', https://mitpress.mit.edu/books/prime-number-conspiracy, is highly recommended...

[Guest]

"A sound mathematical theory should always point in the direction of truth." Hmm.

For the strong nonbelievers (those who strongly disbelieve the existence of Lord GOD or who strongly believe that Lord GOD is irrelevant...), please ponder and take to heart the following quote by Immanuel Kant,

"... there is a GOD precisely because Nature itself, even in chaos, cannot proceed except in an orderly and regular manner."

Dave.

[Guest]

"The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." -- G. H. Hardy, a great mathematician.

Relevant Reference Link:

' EXTRACT FROM A MATHEMATICIAN’S APOLOGY BY G. H. HARDY',

https://www.cranleigh.org/culture/issue-1/archives-extract-mathematicians-apology-g-h-hardy/