1. ## Fermat's last theorem

Note by Bill: this was originally an off-topic reply to Did You See Them's post on The Voynich Manuscript: now solved after 600 years thread. That, and Fermat's last theorem, seemed very indirectly related!

After Peter UK's reply to that (post #2 below), it seemed clear that a separate thread was needed, as I might have a little more to say about this.

~~~

Posted by Did You See Them (here)
It's marvelous to see a mystery unravel before your eyes !
Like Fermat's Last Theorem. That was famously claimed to have been proved by the brilliant mathematician Pierre de Fermat, in the 17th century. He wrote by hand in the margin of one of his math textbooks:
"I have discovered a truly remarkable proof of this theorem which this margin is too small to contain."
What he'd discovered, assuming he wrote it down elsewhere, was never found. Some said it was like he'd buried a magnificent treasure, but never left anyone a map.

His handwritten notes in the same textbook made many other similar claims. And Fermat was always 100% right: everything else he stated was later proved by mathematicians, gradually and systematically, in the centuries that followed.

But not his 'Last' Theorem. The 'missing proof' kept the world's finest minds busy for generations. No-one could figure out what Fermat had found.

Eventually, the English mathematician Andrew Wiles, who'd been obsessed with the challenge since he was a child, solved the enigma — 358 years later. It was highly complex, and took up 129 very dense pages. The math was so abstruse, advanced and conceptual that very few other mathematicians in the world were qualified to understand it.

Now, what we need is Fermat's original "truly remarkable" proof... just a little too long for him to note down with his quill pen in the narrow margin of his book.

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3. ## Re: Fermat's last theorem

Posted by Bill Ryan (here)
Eventually, the English mathematician Andrew Wiles, who'd been obsessed with the challenge since he was a child, solved the enigma — 358 years later. It was highly complex, and took up 129 very dense pages. The math was so abstruse, advanced and conceptual that very few other mathematicians in the world were qualified to understand it.
It was a 20th c. proof which means that the mathematical resources and discoveries since the time of Fermat would not have been available to him.

Now that really does make it a mystery.

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5. ## Re: Fermat's last theorem

Posted by Peter UK (here)
Posted by Bill Ryan (here)
Eventually, the English mathematician Andrew Wiles, who'd been obsessed with the challenge since he was a child, solved the enigma — 358 years later. It was highly complex, and took up 129 very dense pages. The math was so abstruse, advanced and conceptual that very few other mathematicians in the world were qualified to understand it.
It was a 20th c. proof which means that the mathematical resources and discoveries since the time of Fermat would not have been available to him.

Now that really does make it a mystery.

Yes. This has all been a source of friendly disagreement between mathematicians.

Some insist that Fermat must have been wrong in his belief that he had a proof. Others say that maybe we shouldn't be so arrogant and presumptuous, as Fermat was clearly an extraordinary genius.

Many have continued to search for a proof that would only feature the non-modern math that Fermat was familiar with.

Interestingly, there have been some proposals. I've looked at a couple of them, and can't find any errors. But that doesn't mean anything at all!

Here's one, published in 2016 at the University of Kelaniya (Sri Lanka).
Another interesting proof, that I also can't fault, was proposed in a blog comment on this page by Jimmy A. M. Kazmi, Hyderabad, India.
And intriguingly, on this page, there's a reference to a 3-page proof devised by Herbert S. Riddle, an MIT graduate, specifically using the math of Fermat's day. (Riddle was dissatisfied with a long, highly complex modern proof that was light years beyond Fermat's knowledge.) Apparently, he later condensed it down to one page — but I've been totally unable to find it anywhere to take a look.
On the same page, there's a reference to a 6-page proof by an Italian, Onofrio Gallo, which I can't find anywhere either.

This all brings to mind the most marvelous 2015 film The Man Who Knew Infinity, about the life and work of Srinivasa Ramanujan.

Ramanujan was an Indian who lived 100 years ago, and worked as a lowly clerk, with little formal education. But while he himself was an unquestioned self-taught genius, he had astonishing mathematical insights that he insisted were gifted to him by a Hindu Goddess when he was in prayer or meditation.

He filled three notebooks with dense formulae that shocked and astounded the great English mathematician G. H. Hardy, who brought him to Cambridge to study (and to learn from him).

The discovery of his third ('lost') notebook, in 1976, long after he had died in 1920 aged only 32, was regarded rather as if Beethoven's unfinished symphony had been found in its entirety.

The moral of the story? If someone who is quite unknown (like the father-and-son team who finally solved the riddle of the Yoynich Manuscript) claims to achieved what recognized academics have failed to do for centuries, maybe we might just pay them the courtesy of listening carefully.

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7. ## Re: Fermat's last theorem

Here's something else to consider.

I sense there's a distinct possibility, maybe even likelihood, given the unusual obsession with the problem from a young age, that this is a past life.

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9. ## Re: Fermat's last theorem

Fermat's last theorem story sound like John Dee's alchemy formula story.

Angel Alphabets-John Dee and Shakespeare by Vincent Bridges, Stars and Stones
(1:20:23 hrs.)

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11. ## Re: Fermat's last theorem

Posted by Bill Ryan (here)
https://topdocumentaryfilms.com/fermats-last-theorem

On this page, there's a reference to a 6-page proof by an Italian, Onofrio Gallo, which I can't find anywhere either.
Well, I got curious, and after some searching I found this on an Italian web page about his town of birth.

This is a series of posts in the comments section, which (apart from the first) I've translated from the Italian. I tidied up the worst typos in the first post.

My main purpose in posting this all here is just in case there's anything to this (which seems very unlikely!) — and just maybe, someone formally connected in the world of mathematics might also be searching for the mysterious Gallo. In which case, they might find this post, and it might be helpful.

Either Onofrio Gallo is an extraordinary unheralded eccentric genius (and there are some! Ramanujan would have been one such, barely known to this day if G.H. Hardy hadn't realized that the long handwritten letter he received from India wasn't a prank) — or the person promoting him is delusional.

It does seem like the latter, I have to say. One clue lies in the reference to the "Sailors and the Coconuts" problem below. (See this page for reference, and many others too, which are easy to find) The problem is interesting but mathematically trivial, and the solutions are well known and quite easy to find.

Archimedes' Cattle Problem is similar: not quite so easy to calculate, but it's fully understood.

His claims also to have proven the Riemann Hypothesis, Goldbach's Conjecture, and the Twin Prime Conjecture, if true (and the chances are practically zero!), would place him at the topmost pinnacle of the mathematical pyramid of all-time super-geniuses.

Whatever the truth, it has to be said that in the academic world, one will not be recognized, whatever one's achievements, unless one's work is formally published and peer-reviewed.
~~~

Umberto Esposito
, 10 January 2010: (original post here, which was in rather poor English)

ONOFRIO GALLO (brief bio-bibliographical note) Mathematician, poet and polymath born May 13 1946 in Cervinara (Avellino) (Valle Caudina).

He studied in Maracaibo (Venezuela) (College “L Gonzaga “Jesuit fathers), in Pozzuoli (Naples) (College of the Archbishop ‘S. Paul”), in Maddaloni (Caserta) (Convitto Nazionale “G. Bruno”), in Naples (Liceo Scientifico Statale “V. Cuoco”), in Naples (University “Federico II”, including a Masters in Mathematics ( Faculty of Sciences) with an original thesis in Abstract Algebra (Sui quasigruppi commutativi, mediali, idempotenti), then specializing in theories and techniques for the use and application of computers (Faculty of Engineering) and attending, post graduate, the School of PhD in Theoretical Physics and Nuclear (Mostra d’Oltremare), attached to the Faculty of Physics of the same University.

Unpublished works in mathematics: the treaty Mathematics (on the prediction of future discrete random events); in the Number Theory the Treaty on Diophantine Equations, in which appears the Gallo’s Fundamental Theorem FPG on the Fermat-Pell–Gallo equations of degree k ≥ 2.

Over thirty articles published and the original core and memories:
Sulla risolubilità delle equazioni diofantee del tipo (F) xn+yn=zn (On the solvability of the diophantine equations (F) xn + yn = zn (Gallo’s Mirabilis Theorem) (Rome, 1993).

Sur la résolubilté des équations du type de Diophante (F) xn + yn = zn (Gottingen, 1994)
New On The Number Theory (Oslo, 2004)

From Fermat’s Last Theorem To Riemann’s Hypothesis (Oslo, 2004)
The Gallo’s PSI Theorem or The Riemann-Gallo’s Theorem (Oslo, 2004) on the equivalence of the infinite zeros of complex Gallo’s function ψ (psi) (real part = 1) and the infinite zeros of the Riemann’s Ϛ (zeta) function (real part = 1/2)

Original and general resolutions of its known and difficult mathematical problems, such as the Cattle’s Problem of Archimedes (in 1995), resolved on the basis of his Theorem FPG / N (which, after nearly three millennia, is used to calculate the k- root of any positive integer N (with N≠ nk and n positive integers) has resolved in various ways, providing Diophantine solutions unknown to his predecessors, even when it is necessary to take account of new and difficult conditions (conditions of Gallo).

Even the well-known problem of the Sailors and Coconuts has been solved by him, for the first time in the world, including in the general case without solving any Diophantine equation!

Onofrio Gallo has developed several original and important chapters of Mathematics, as TTIE or the Theory of the Transformations of the Identities in Equations (1989), the General Theory of p-diophantine equations, Theory of Generalized Fermat-Pell equations, the Theory of Random Hermitian Structures of order 3, Theory of the ψ (psi) function.

Onofrio Gallo has settled, after some four millennia, so comprehensive and definitive, and the problem of the calculation of primitive Pythagorean terns (Gallo’s General Theorem on Primitive Pythagorean Terns, 1994), as well as chapters on the problems of squares congruenti ( PSC) and the problems of the area-congruo numbers (PAC), dating back to Arab mathematicians, to Italian Magistri of Abaco and at the same Fibonacci.

Its also the first demonstration general and original world of Fermat’s Last Theorem (FLT) (Rome, 1993; Gottingen 1994) and the first general and original demonstrations of the Goldbach Conjecture (1994) and the Conjecture of Twin Primes (1994), unpublished.

The FLT is the particular case of the Gallo’s Mirabilis Theorem that, for the first time in the history of mathematics, to solve for symmetry (without trial and without radicals and without the use of continued fractions) Diophantine and algebraic equations of any degree n (finished), the problems solved by Ramanujan with the use of continued fractions and, for n = 2, to calculate – over Pythagoras - two sides of a right triangle, known only the third side, the discrete with continuous and to solve many other difficult problems.

His Non Standard Theory of Transformations of Identity in Equations (1989) go beyond Euclid and logical principles and semi-logical underpinning of his fundamental unpublished treatise Mathematics or TMPECF or Mathematical Theory for the Forecast of Future Random Events; (NP = not probabilistic and NQ = not qualitative), defined by some.

Works in the literary field: Canti autobiografici (Autobiographical songs), MI, 1972), I Violini del Cosmo (The Violins of the Cosmos ; CZ, 1979), Saggi letterari sul Novecento (Literary Essays on the Twentieth Century, 2005, unpublished).

Winning in the Capitol (Rome)for the Poetry and Fiction, among the absolute winners of the prestigious Prize for Poetry CE.SI (Award of Culture of the Presidency of the Council of Ministers), co-founder of the monthly Science and Culture Oltre il 2000 (Beyond 2000), he participated in numerous books and his essays, stories and poems appear in numerous anthologies, magazines, dictionaries, diaries, calendars and almanac, along with the most illustrious names of Literature and Poetry Italian classical and contemporary.

He has published several critical essays on literary characters (from Borges to Garcia Lorca), science (from Einstein to Majorana) and politics (from Cossiga to Bush).

By Umberto Esposito, friend and great admirer of Onofrio Gallo, authorized to disseminate on the WEB news and notes and results of his CODEX CERVINARENSIS related to its very original and innovative research in Mathematics, Physics, and Letters (Poetry, Essays and Fiction), which - for tune - this is very difficult not to bring his own words.

~~~

Andreas, 19 January 2010: (original post here)
I find no information about the Italian mathematician Onofrio Gallo (b. 1946 in Cervinara, Valle Caudina) author of many important theorems, such as the Theorem Mirabilis of Gallo, and of the first original direct proof of Fermat's Last Theorem. How is this possible? I would like to know more about his biography and his works. Thanks. Andreas.

~~~

Francesco Santosuosso, 17 May 2010: (original post here)
I would like to have a copy of the Codex Cervinarensis. I am a professor of physics from Benevento. Thanks.

~~~

Umberto Esposito, 17 June 2010: (original post here)
Dear Prof. Francesco Santosuosso, thank you for your interest in the omnia “Codex Cervinarensis” by Onofrio Gallo. Unfortunately, I must tell you that your request cannot be satisfied as it is a very large work (about eight thousand pages) and because, at present, it is a work still unpublished in almost all of its various sections. This in no way precludes obtaining information on the contents that the undersigned, curator of the work in question, will have occasion to highlight periodically on the web, when the occasion will arise. In the event of possible publication of the Codex, your name will be kept in mind. Thanking you for the interest shown for the scientific work of Onofrio Gallo, I cordially greet you. Umberto Esposito.

~~~

Dr.Kathrine Martinez-Martignoni, 8 July 2010: (original post here)
You could at least make available a simple photograph of this "mysterious and fantastic" mathematician Onofrio Gallo. It does not seem to me such an impossible request to satisfy. Best regards to all. Dr.Kathrine M. (Switzerland).

~~~

Umberto Esposito, 25 July 2010: (original post here)
Dear Dr. Kathrine Martinez-Martignoni, in reference to your request of 08/07/2010, at the moment, beyond the photos appeared in some poetic anthologies ("Città Eterna" Award, Rome 1972, etc.) the only photo currently available of the mathematician Onofrio Gallo whom you rightly define as "mysterious and fantastic" - for obvious reasons of privacy - is the following "essential" photo.

Brain: Principle of Identity - Second General Principle of Knowledge - TTIE Theory - TMPECF Theory of Mathematics
Eyes: Fermat's Last Theorem - Riemann Hypothesis
Nose: FPG Theorem (k-diophantine equations)
Mouth: Codex Cervinarensis
Vague physical resemblance: actor Richard Gere
Foreign languages: Spanish - French - English
Preferred classical language: Latin
Culture of at least fifty disciplines, among them: Literature and Poetry, Philosophy, Analysis of History and Philosophy, Linguistic Research, Science of Earth and Life, Music of each epoch and of every type, etc.
Hobbies: from poetic composition to the creation of novels and thrillers; from artistic design to architecture; from musical compositions to directing and making recurrent films; from publishing to bibliophilia, to the regeneration of paintings, books and ancient objects; from mechanical inventions to futuristic projects of means of transport and housing, etc.)
Sports practiced: Baseball - Roller skates - Soccer - Motoring
Private collection: Video library of over 7000 hours ("everything and more")
Among the projects for the near future: Creation and management of an IRPEC or World Agency for the Forecast of Future Random Events.
Edited by U. Esposito, courtesy of the Author.

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13. ## Re: Fermat's last theorem

Posted by Bill Ryan (here)
Posted by Bill Ryan (here)
https://topdocumentaryfilms.com/fermats-last-theorem

On this page, there's a reference to a 6-page proof by an Italian, Onofrio Gallo, which I can't find anywhere either.
Well, I got curious, and after some searching I found this on an Italian web page about his town of birth.

This is a series of posts in the comments section, which (apart from the first) I've translated from the Italian. I tidied up the worst typos in the first post.

My main purpose in posting this all here is just in case there's anything to this (which seems very unlikely!) — and just maybe, someone formally connected in the world of mathematics might also be searching for the mysterious Gallo. In which case, they might find this post, and it might be helpful.

Either Onofrio Gallo is an extraordinary unheralded eccentric genius (and there are some! Ramanujan would have been one such, barely known to this day if G.H. Hardy hadn't realized that the long handwritten letter he received from India wasn't a prank) — or the person promoting him is delusional.

It does seem like the latter, I have to say. One clue lies in the reference to the "Sailors and the Coconuts" problem below. (See this page for reference, and many others too, which are easy to find) The problem is interesting but mathematically trivial, and the solutions are well known and quite easy to find.

Archimedes' Cattle Problem is similar: not quite so easy to calculate, but it's fully understood.

His claims also to have proven the Riemann Hypothesis, Goldbach's Conjecture, and the Twin Prime Conjecture, if true (and the chances are practically zero!), would place him at the topmost pinnacle of the mathematical pyramid of all-time super-geniuses.

Whatever the truth, it has to be said that in the academic world, one will not be recognized, whatever one's achievements, unless one's work is formally published and peer-reviewed.
~~~

Umberto Esposito
, 10 January 2010: (original post here, which was in rather poor English)

ONOFRIO GALLO (brief bio-bibliographical note) Mathematician, poet and polymath born May 13 1946 in Cervinara (Avellino) (Valle Caudina).

He studied in Maracaibo (Venezuela) (College “L Gonzaga “Jesuit fathers), in Pozzuoli (Naples) (College of the Archbishop ‘S. Paul”), in Maddaloni (Caserta) (Convitto Nazionale “G. Bruno”), in Naples (Liceo Scientifico Statale “V. Cuoco”), in Naples (University “Federico II”, including a Masters in Mathematics ( Faculty of Sciences) with an original thesis in Abstract Algebra (Sui quasigruppi commutativi, mediali, idempotenti), then specializing in theories and techniques for the use and application of computers (Faculty of Engineering) and attending, post graduate, the School of PhD in Theoretical Physics and Nuclear (Mostra d’Oltremare), attached to the Faculty of Physics of the same University.

Unpublished works in mathematics: the treaty Mathematics (on the prediction of future discrete random events); in the Number Theory the Treaty on Diophantine Equations, in which appears the Gallo’s Fundamental Theorem FPG on the Fermat-Pell–Gallo equations of degree k ≥ 2.

Over thirty articles published and the original core and memories:
Sulla risolubilità delle equazioni diofantee del tipo (F) xn+yn=zn (On the solvability of the diophantine equations (F) xn + yn = zn (Gallo’s Mirabilis Theorem) (Rome, 1993).

Sur la résolubilté des équations du type de Diophante (F) xn + yn = zn (Gottingen, 1994)
New On The Number Theory (Oslo, 2004)

From Fermat’s Last Theorem To Riemann’s Hypothesis (Oslo, 2004)
The Gallo’s PSI Theorem or The Riemann-Gallo’s Theorem (Oslo, 2004) on the equivalence of the infinite zeros of complex Gallo’s function ψ (psi) (real part = 1) and the infinite zeros of the Riemann’s Ϛ (zeta) function (real part = 1/2)

Original and general resolutions of its known and difficult mathematical problems, such as the Cattle’s Problem of Archimedes (in 1995), resolved on the basis of his Theorem FPG / N (which, after nearly three millennia, is used to calculate the k- root of any positive integer N (with N≠ nk and n positive integers) has resolved in various ways, providing Diophantine solutions unknown to his predecessors, even when it is necessary to take account of new and difficult conditions (conditions of Gallo).

Even the well-known problem of the Sailors and Coconuts has been solved by him, for the first time in the world, including in the general case without solving any Diophantine equation!

Onofrio Gallo has developed several original and important chapters of Mathematics, as TTIE or the Theory of the Transformations of the Identities in Equations (1989), the General Theory of p-diophantine equations, Theory of Generalized Fermat-Pell equations, the Theory of Random Hermitian Structures of order 3, Theory of the ψ (psi) function.

Onofrio Gallo has settled, after some four millennia, so comprehensive and definitive, and the problem of the calculation of primitive Pythagorean terns (Gallo’s General Theorem on Primitive Pythagorean Terns, 1994), as well as chapters on the problems of squares congruenti ( PSC) and the problems of the area-congruo numbers (PAC), dating back to Arab mathematicians, to Italian Magistri of Abaco and at the same Fibonacci.

Its also the first demonstration general and original world of Fermat’s Last Theorem (FLT) (Rome, 1993; Gottingen 1994) and the first general and original demonstrations of the Goldbach Conjecture (1994) and the Conjecture of Twin Primes (1994), unpublished.

The FLT is the particular case of the Gallo’s Mirabilis Theorem that, for the first time in the history of mathematics, to solve for symmetry (without trial and without radicals and without the use of continued fractions) Diophantine and algebraic equations of any degree n (finished), the problems solved by Ramanujan with the use of continued fractions and, for n = 2, to calculate – over Pythagoras - two sides of a right triangle, known only the third side, the discrete with continuous and to solve many other difficult problems.

His Non Standard Theory of Transformations of Identity in Equations (1989) go beyond Euclid and logical principles and semi-logical underpinning of his fundamental unpublished treatise Mathematics or TMPECF or Mathematical Theory for the Forecast of Future Random Events; (NP = not probabilistic and NQ = not qualitative), defined by some.

Works in the literary field: Canti autobiografici (Autobiographical songs), MI, 1972), I Violini del Cosmo (The Violins of the Cosmos ; CZ, 1979), Saggi letterari sul Novecento (Literary Essays on the Twentieth Century, 2005, unpublished).

Winning in the Capitol (Rome)for the Poetry and Fiction, among the absolute winners of the prestigious Prize for Poetry CE.SI (Award of Culture of the Presidency of the Council of Ministers), co-founder of the monthly Science and Culture Oltre il 2000 (Beyond 2000), he participated in numerous books and his essays, stories and poems appear in numerous anthologies, magazines, dictionaries, diaries, calendars and almanac, along with the most illustrious names of Literature and Poetry Italian classical and contemporary.

He has published several critical essays on literary characters (from Borges to Garcia Lorca), science (from Einstein to Majorana) and politics (from Cossiga to Bush).

By Umberto Esposito, friend and great admirer of Onofrio Gallo, authorized to disseminate on the WEB news and notes and results of his CODEX CERVINARENSIS related to its very original and innovative research in Mathematics, Physics, and Letters (Poetry, Essays and Fiction), which - for tune - this is very difficult not to bring his own words.

~~~

Andreas, 19 January 2010: (original post here)
I find no information about the Italian mathematician Onofrio Gallo (b. 1946 in Cervinara, Valle Caudina) author of many important theorems, such as the Theorem Mirabilis of Gallo, and of the first original direct proof of Fermat's Last Theorem. How is this possible? I would like to know more about his biography and his works. Thanks. Andreas.

~~~

Francesco Santosuosso, 17 May 2010: (original post here)
I would like to have a copy of the Codex Cervinarensis. I am a professor of physics from Benevento. Thanks.

~~~

Umberto Esposito, 17 June 2010: (original post here)
Dear Prof. Francesco Santosuosso, thank you for your interest in the omnia “Codex Cervinarensis” by Onofrio Gallo. Unfortunately, I must tell you that your request cannot be satisfied as it is a very large work (about eight thousand pages) and because, at present, it is a work still unpublished in almost all of its various sections. This in no way precludes obtaining information on the contents that the undersigned, curator of the work in question, will have occasion to highlight periodically on the web, when the occasion will arise. In the event of possible publication of the Codex, your name will be kept in mind. Thanking you for the interest shown for the scientific work of Onofrio Gallo, I cordially greet you. Umberto Esposito.

~~~

Dr.Kathrine Martinez-Martignoni, 8 July 2010: (original post here)
You could at least make available a simple photograph of this "mysterious and fantastic" mathematician Onofrio Gallo. It does not seem to me such an impossible request to satisfy. Best regards to all. Dr.Kathrine M. (Switzerland).

~~~

Umberto Esposito, 25 July 2010: (original post here)
Dear Dr. Kathrine Martinez-Martignoni, in reference to your request of 08/07/2010, at the moment, beyond the photos appeared in some poetic anthologies ("Città Eterna" Award, Rome 1972, etc.) the only photo currently available of the mathematician Onofrio Gallo whom you rightly define as "mysterious and fantastic" - for obvious reasons of privacy - is the following "essential" photo.

Brain: Principle of Identity - Second General Principle of Knowledge - TTIE Theory - TMPECF Theory of Mathematics
Eyes: Fermat's Last Theorem - Riemann Hypothesis
Nose: FPG Theorem (k-diophantine equations)
Mouth: Codex Cervinarensis
Vague physical resemblance: actor Richard Gere
Foreign languages: Spanish - French - English
Preferred classical language: Latin
Culture of at least fifty disciplines, among them: Literature and Poetry, Philosophy, Analysis of History and Philosophy, Linguistic Research, Science of Earth and Life, Music of each epoch and of every type, etc.
Hobbies: from poetic composition to the creation of novels and thrillers; from artistic design to architecture; from musical compositions to directing and making recurrent films; from publishing to bibliophilia, to the regeneration of paintings, books and ancient objects; from mechanical inventions to futuristic projects of means of transport and housing, etc.)
Sports practiced: Baseball - Roller skates - Soccer - Motoring
Private collection: Video library of over 7000 hours ("everything and more")
Among the projects for the near future: Creation and management of an IRPEC or World Agency for the Forecast of Future Random Events.
Edited by U. Esposito, courtesy of the Author.
I'm not sure,but I think that:
1- (the simple one) or Gallo and Esposito are the same person;
2- (the complex one) or Gallo and Esposito are the imagination of a third person.

In any case I found some informations which looks very elaborated on an other blog.It's a lot of reading and translated.
IL PRINCIPIO DI DISIDENTITA’ DI GALLO E IL SECONDO PRINCIPIO GENERALE DELLA CONOSCENZA
Nel Codex Cervinarensis del matematico italiano Onofrio Gallo (n. 1946 a Cervinara, Valle Caudina), l’Autore, in alcune pagine relative all’analisi dell’unità immaginaria e ad altri argomenti matematici, si sofferma sul cosiddetto Principio di Disidentità di Gallo ( lasciamo proseguire l’Autore)
…………………………………………………………………………….A LOT OF POINTS
Nel caso che p e q siano del tipo 4n+ 3, delle due equazioni congruenziali
(5) x^2≡ 19 (mod 11) e (6) x^2≡ 11 (mod 19) è risolubile solo la (6) che ammette le infinite soluzioni: x=7, 26, 45, 64, 83, 102, ….., infatti risulta:
72=49=2×19+11
262=676=35×19+11
452=2025=106×19+11
642=4096=215×19+11
832=6889=362×19+11
1022= 10404=547×19+11
……………………………....................................... ......................................;
mentre nel caso delle (7) x^2≡ 19 (mod 31) e (8) x^2≡ 31 (mod 19) solo la (7) ammette infinite soluzioni: x=9, 40, 71, 102….., mentre la (8) non è risolubile in quanto non esiste alcun n intero positivo tale che n^2= 19h + 31.
Di applicazioni inconsce del Secondo Principio della Conoscenza nella Fisica della Materia che hanno condotto un celebre fisico al Premio Nobel diremo in un prossimo scritto”
News a cura di Umberto Esposito, per gentile concessione dell’Autore.

Postato martedì, 6 luglio 2010 alle 7:19 pm da umberto esposito

14. ## The Following 2 Users Say Thank You to EFO For This Post:

Bill Ryan (5th November 2019), Frank V (5th November 2019)

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