"The number 108 is actually the average distance that the sun is in terms of its own diameter from the earth; likewise, it is also the average distance that the moon is in terms of its own diameter from the earth. It is owing to this marvelous coincidence that the angular size of the sun and the moon, viewed from the earth, is more or less identical. It is easy to compute this number. The angular measurement of the sun can be obtained quite easily during an eclipse. The angular measurement of the moon can be made on any clear full moon night. An easy check on this measurement would be to make a person hold a pole at a distance that is exactly 108 times its length and confirm that the angular measurement is the same. Nevertheless, the computation of this number would require careful observations. Note that 108 is an average and due to the ellipticity of the orbits of the earth and the moon the distances vary about 2 to 3 percent with the seasons. It is likely, there- fore, that observations did not lead to the precise number 108, but it was chosen as the true value of the distance since it is equal to 27 x 4, because of the mapping of the sky into 27 naksatras. The diameter of the sun is roughly 108 times the diameter of the earth, but it is unlikely that the Indians knew this fact."

"I John... was in the isle that is called , for the word of God, and for the testimony of Jesus Christ. I was in the Spirit on the Lord's day, and heard behind me a great voice, as of a trumpet, Saying, I am Alpha and Omega, the first and the last: and, What thou seest, write in a book, and send it unto the seven churches... And I turned to see the voice that spake with me. And being turned, I saw seven golden candlesticks; And in the midst of the seven candlesticks one like unto the Son of man... His head and his hairs were white like wool, as white as snow; and his eyes were as a flame of fire... and his voice as the sound of many waters. And he had in his right hand seven stars: and out of his mouth went a sharp two-edged sword: and his countenance was as the sun shineth in his strength. And when I saw him, I fell at his feet as dead. And he laid his right hand upon me, saying... I am he that liveth, and was dead; and, behold, I am alive for evermore, Amen; and have the keys of hell and of death. Write the things which thou hast seen... The mystery of the seven stars which thou sawest in my right hand, and the seven golden candlesticks. The seven stars are the angels of the seven churches: and the seven candlesticks which thou sawest are the seven churches."

"And I saw another mighty angel come down from heaven, clothed with a cloud: and a rainbow was upon his head, and his face was as it were the sun, and his feet as pillars of fire: And he had in his hand a little book open: and he set his right foot upon the sea, and his left foot on the earth, And cried with a loud voice, as when a lion roareth: and when he had cried, seven thunders uttered their voices. And when the seven thunders had uttered their voices, I was about to write: and I heard a voice from heaven saying unto me, Seal up those things which the seven thunders uttered, and write them not. And the angel which I saw stand upon the sea and upon the earth lifted up his hand to heaven, And sware by him that liveth for ever and ever, who created heaven, and... the earth... and the sea, and the things which are therein, that there should be time no longer: But in the days of the voice of the seventh angel, when he shall begin to sound, the mystery of God should be finished, as he hath declared to his servants the prophets."

"Strange, indeed, that you should not have suspected that your universe and its contents were only dreams, visions, fiction! Strange, because they are so frankly and hysterically insane—like all dreams: a God who could make good children as easily as bad, yet preferred to make bad ones; who could have made every one of them happy, yet never made a single happy one; who made them prize their bitter life, yet stingily cut it short; who gave his angels eternal happiness unearned, yet required his other children to earn it; who gave his angels painless lives, yet cursed his other children with biting miseries and maladies of mind and body; who mouths justice, and invented hell—mouths mercy, and invented hell—mouths Golden Rules and forgiveness multiplied by seventy times seven, and invented hell; who mouths morals to other people, and has none himself; who frowns upon crimes, yet commits them all; who created man without invitation, then tries to shuffle the responsibility for man's acts upon man, instead of honorably placing it where it belongs, upon himself; and finally, with altogether divine obtuseness, invites his poor abused slave to worship him!"

"The folly of Interpreters has been, to foretell times and things by this Prophecy, as if God designed to make them Prophets. By this rashness they have not only exposed themselves, but brought the Prophecy also into contempt. The design of God was much otherwise. He gave this and the Prophecies of the Old Testament, not to gratify men's curiosities by enabling them to foreknow things, but that after they were fulfilled they might be interpreted by the event, and his own Providence, not the Interpreters, be then manifested thereby to the world. For the event of things predicted many ages before, will then be a convincing argument that the world is governed by providence. For, as the few and obscure Prophecies concerning Christ’s first coming were for setting up the Christian religion, which all nations have since corrupted; so the many and clear Prophecies concerning the things to be done at Christ’s second coming, are not only for predicting but also for effecting a recovery and re-establishment of the long-lost truth, and setting up a kingdom wherein dwells righteousness. The event will prove the Apocalypse; and this Prophecy, thus proved and understood, will open the old Prophets, and all together will make known the true religion, and establish it. For he that will understand the old Prophets, must begin with this; but the time is not yet come for understanding them perfectly, because the main revolution predicted in them is not yet come to pass. In the days of the voice of the seventh Angel, when he shall begin to sound, the mystery of God shall be finished, as he hath declared to his servants the Prophets: and then the kingdoms of this world shall become the kingdom of our Lord and his Christ, and he shall reign for ever, Apoc. x. 7. xi. 15. There is already so much of the Prophecy fulfilled, that as many as will take pains in this study, may see sufficient instances of God’s providence: but then the signal revolutions predicted by all the holy Prophets, will at once both turn men’s eyes upon considering the predictions, and plainly interpret them. Till then we must content ourselves with interpreting what hath been already fulfilled. Amongst the Interpreters of the last age there to scarce one of note who hath not made some discovery worth knowing; and thence I seem to gather that God is about opening these mysteries. The success of others put me upon considering it; and if I have done any thing which may be useful to following writers, I have my design."

"There are Seven Seals to be opened, that is to say, Seven mysteries to know, and Seven difficulties to overcome, Seven trumpets to sound, and Seven cups to empty. The Apocalypse is, to those who receive the nineteenth degree, the of that Sublime Faith which aspires to God alone, and despises all the pomps and works of Lucifer. ...[T]raditions are full of Divine Revelations and Inspirations: and Inspiration is not of one Age nor of one Creed. Plato and Philo, also, were inspired."

"The tree that thou sawest, which grew, and was strong, whose height reached unto the heaven, and the sight thereof to all the earth; Whose leaves were fair, and the fruit thereof much, and in it was meat for all; under which the beasts of the field dwelt, and upon whose branches the fowls of the heaven had their habitation: It is thou, O king, that art grown and become strong: for thy greatness is grown, and reacheth unto heaven, and thy dominion to the end of the earth. And whereas the king saw a watcher and an holy one coming down from heaven, and saying, Hew the tree down, and destroy it; yet leave the stump of the roots thereof in the earth, even with a band of iron and brass, in the tender grass of the field; and let it be wet with the dew of heaven, and let his portion be with the beasts of the field, till seven times pass over him; This is the interpretation, O king, and this is the decree of the most High, which is come upon my lord the king: That they shall drive thee from men, and thy dwelling shall be with the beasts of the field, and they shall make thee to eat grass as oxen, and they shall wet thee with the dew of heaven, and seven times shall pass over thee, till thou know that the most High ruleth in the kingdom of men, and giveth it to whomsoever he will. And whereas they commanded to leave the stump of the tree roots; thy kingdom shall be sure unto thee, after that thou shalt have known that the heavens do rule. Wherefore, O king, let my counsel be acceptable unto thee, and break off thy sins by righteousness, and thine iniquities by shewing mercy to the poor; if it may be a lengthening of thy ."

"Number mysticism was not original with the Pythagoreans. The number seven, for example, had been singled out for special awe, presumably on account of the seven wandering stars or planets from which the week (hence our names for the seven days of the week) is derived. The Pythagoreans were not the only people who fancied that the odd numbers had male attributes and the even female... Many early civilizations shared various aspects of numerology, but the Pythagoreans carried number worship to its extreme..."

"ARTS, Liberal, or Seven Liberal. The distinction between the liberal arts and the practical arts on the one hand, and philosophy on the other, originates in Greek education and philosophy. In the Republic (Bk. xi.) of Plato, and the Politics (viii. 1) of Aristotle, the 'liberal arts' are those subjects that are suitable for the development of intellectual and moral excellence, as distinguished from those that are merely useful or practical. The distinction was always made, by the Greek theorists, between music, literature in the form of grammar and rhetoric, and the mathematical studies, and that higher aspect of the liberal discipline termed philosophy. Philosophy was sometimes called the liberal art par excellence."

"[W]hile these patterns, the constellations, remained unchanging over time, there were seven objects, or ‘heavenly bodies’, that seemed to move across the skies with a life of their own. They were given the name ‘planet’... ‘wanderer’... These... were the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn... The number seven has long been held to have a certain mystical significance. There are seven days of the week reflecting the seven days of creation in the Bible. The Seven Deadly Sins are balanced by the Seven Heavenly Virtues. In Islam there are seven levels in heaven and the same number in hell. Rome was founded upon Seven Hills. It has been said that Isaac Newton divided the rainbow into seven colours in order to imitate the seven notes in a musical scale. Over time, each of the seven heavenly bodies came to be associated with a particular day of the week and with one of the gods from ancient mythology..."

"Give me a child till he is seven years old, and I will make him what no one will unmake. ...Give me a child until he is 7 and I will show you the man."

"In regard to Philolaus, we are told... that he derived geometrical determinations (the point, the line, the surface, the solid) from the first four numbers, so he derived physical qualities from five, the soul from six; reason, health, and light, from seven; love, friendship, prudence, and inventive faculty from eight. Herein (apart from the number schematism) is contained the thought that things represent a graduated scale of increasing perfection; but we hear nothing of any attempt to prove this in detail, or to seek out the characteristics proper to each particular region."

"The expression artes liberales, chiefly used during the Middle Ages, does not mean arts as we understand the word at this present day, but those branches of knowledge which were taught in the schools of that time. They are called liberal (Latin liber, free), because they serve the purpose of training the free man, in contrast with the artes illiberales, which are pursued for economic purposes; their aim is to prepare the student not for gaining a livelihood, but for the pursuit of science in the strict sense of the term, i.e. the combination of philosophy and theology known as . They are seven in number and may be arranged in two groups, the first embracing grammar, rhetoric, and dialectic, in other words, the sciences of language, of oratory, and of logic, better known as the artes sermocinales, or language studies; the second group comprises arithmetic, geometry, astronomy, and music, i.e. the mathematico-physical disciplines, known as the artes reales, or physicae."

"The seven liberal arts do not adequately divide ; but, as says, seven arts are grouped together (leaving out certain other ones), because those who wanted to learn philosophy were first instructed in them. And the reason why they are divided into the and is that "they are as it were paths (viae) introducing the quick mind to the secrets of philosophy.""

"I have now established... that the human encephalos does not increase after the age of seven, at highest. This has been done, by measuring the heads of the same young persons, from infancy to adolescence and maturity; for the slight increase in the size of the head, after seven (or six) is exhausted by the development to be allowed in the bones, muscles, integuments, and hair."

"Seven scores, seven scores, seven hundreds of saints, And seven thousands and seven ten scores, November a number implored, Though martyrs good they came."

"And said unto , Build me here seven altars, and prepare me here seven oxen and seven rams."

"Mathematicians have constructed a very large number of different systems of geometry, Euclidean or non-Euclidean, of one, two, three, or any number of dimensions. All these systems are of complete and equal validity. They embody the results of mathematicians' observations of their reality, a reality far more intense and far more rigid than the dubious and elusive reality of physics. The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real. ...There may be three dimensions in this room and five next door. As a professional mathematician, I have no idea; I can only ask some competent physicist to instruct me in the facts."

"He (Gilgamesh) crossed the first mountain with him (), but the cedars were not revealed to his heart. The second mountain, the third mountain, the fourth mountain, the fifth mountain, (and) the sixth mountain. When he was crossing the seventh mountain, the cedars were revealed to his heart."

"A person who circumambulates this House (the Ka’bah) seven times and performs the two Rak’at Salat (of Tawaaf) in the best form possible will have his sins forgiven."

"Writers differ with respect to the apophthegms of the Seven Sages, attributing the same one to various authors."

"Peter came to Jesus and asked, "Lord, how many times shall I forgive my brother when he sins against me? Up to seven times?" Jesus answered, "I tell you, not seven times, but seventy-seven times (or seventy times seven).""

"My money 360, you only 180. Line complete."

"In the tenth book Euclid deals with certain irrational magnitudes; and since the Greeks possessed no symbolism for surds, he was forced to adopt a geometrical representation. Propositions 1 to 21 deal generally with incommensurable magnitudes. The rest of the book, namely, propostions 22 to 117, is devoted to the discussion of every possible variety of lines which can be represented by \sqrt{(\sqrt{a} \pm \sqrt{b})}, where a and b denote commensurable lines. There are twenty-five species of such lines, and that Euclid could detect and classify them all is in the opinion of so competent an authority as Nesselmann the most striking illustration of his genius. No further advance in the theory of incommensurable magnitudes was made until the subject was taken up by Leonardo and Cardan after the interval of more than a thousand years. In the last proposition of the tenth book [prop. 117] the side and diagonal of a square are proved to be incommensurable. The proof is so short and easy that I may quote it. If possible let the side be to the diagonal in a commensurable ratio, namely, that of two integers, a and b. Suppose this ratio reduced to its lowest terms so that a and b have no common divisor other than unity, that is, they are prime to one another. Then (by Euc. I, 47) b^2 = 2a^2; therefore b^2 is an even number; therefore b is an even number; hence, since a is prime to b, a must be an odd number. Again, since it has been shown that b is an even number, b may be represented by 2n; therefore (2n)^2 = 2a^2; therefore a^2 = (2n)^2; therefore a^2 is an even number; therefore a is an even number. Thus the same number a must be both odd and even, which is absurd; therefore the side and the diagonal are incommensurable. Hankel believes that this proof is due to Pythagoras, and this is not unlikely. This proposition is also proved in another way in Euc. X, 9, and for this and other reasons it is now usually believed to be an interpolation by some commentator on the Elements."

"Fermat's Last Theorem is to the effect that no integral values of x, y, z can be found to satisfy the equation xn+yn=zn if n is an integer greater than 2. ...It is possible that Fermat made some... erroneous supposition, though it is perhaps more probable that he discovered a rigorous demonstration. At any rate he asserts definitely that he had a valid proof—demonstratio mirabilis sane—and the fact that no theorem on the subject which he stated he had proved has been subsequently shown to be false must weigh strongly in his favour; the more so because in making the one incorrect statement in his writings (namely, that about binary powers) he added that he could not obtain a satisfactory demonstration of it. … [I]t took more than a century before some of the simpler results which Fermat had enunciated were proved, and thus it is not surprising that a proof of the theorem which he succeeded in establishing only towards the close of his life should involve great difficulties. ...I venture however to add my private suspicion that continued fractions played a not unimportant part in his researches, and as strengthening this conjecture I may note that some of his more recondite results—such as the theorem that a prime of the form 4n+1 is expressible as the sum of two squares—may be established with comparative ease by properties of such fractions."

"The thorough analysis of even simple problems in arithmetic may require the application of advanced mathematics. A striking example is that of the distribution of prime numbers. The solution of this problem lies in finding a general formula which tells us the number of primes that lie in any given numerical interval. ...Edmund Landau ...wrote two large volumes analyzing this problem without solving it, using the most advanced mathematics known at the time. Even in the elementary aspects of mathematics we are thus dealing with complex topics which make great demands on our mathematical skills."

"Although I firmly believe that there is no such thing as a stupid question, there can indeed be stupid answers. 42 is an example. Not only is this a poor ripoff of Doug Adams' Hitchhiker's Guide, but it isn't even a prime number. Everyone surely knows that numerical answers to profound questions are always prime. (The correct answer is 37.)"

"Prime numbers belong to the exclusive world of intellectual conceptions. We speak of those marvelous notions that enjoys simple, elegant description, yet lead to extreme—one might say unthinkable—complexity in the details. The basic notion of primality can be accessible to a child, yet no human mind harbors anything like a complete picture. In modern times... vast toil and resources have been directed toward the computational aspect, the task of finding, characterizing, and applying the primes..."

"There is another lesser-known "quote" of Erdos that I know first-hand he did not say, since I made it up! ... I gave a talk about Erdos and number theory, and I tried to explain how marvelous the Erdos--Kac theorem is... [Overhead Slide] Einstein: "God does not play dice with the universe." I then said orally: "I would like to think that Erdos and Kac replied..." [Overhead Slide] Erdos and Kac: Maybe so, but something is going on with the primes. ...Somehow, the San Diego newspaper picked this up the next day, and attributed it as a real quote of Erdos."

"And this proposition is generally true for all progressions and for all prime numbers; the proof of which I would send to you, if I were not afraid to be too long. Et cette proposition est généralement vraie en toutes progressions et en tous nombres premiers; de quoi je vous envoierois la démonstration, si je n'appréhendois d'être trop long."

"The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. … Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated."

"In the spring of 1997, Connes went to Princeton to explain his new ideas to the big guns: Bombieri, Selberg and Sarnak. Princeton was still the undisputed Mecca of the Riemann Hypothesis... Selberg had become godfather to the problem... a man who had spent half a century doing battle with the primes. Sarnak... [had] recently joined forces with ... one of the undisputed masters of the mathematics developed by Weil and Grothendieck. Together they had proved that the strange statistics of random drums that we believe describe the zeros in Riemann's landscape are definitely present in the landscapes considered by Weil and Grothendieck. ...It was Katz who, some years before, had found the mistake in Wiles's first erroneous proof of Fermat's Last Theorem. And finally there was Bombieri... the undisputed master of the Riemann Hypothesis. He had earned his for the most significant result to date about the error between the true number of primes and Gauss's guess - a proof of... the 'Riemann Hypothesis on average'. ...Bombieri, like Katz, has a fine eye for detail."

"Hodge cohomology, algebraic de Rham cohomology, crystalline cohomology, the étale ℓ-adic cohomology theories for each prime number ℓ ... A strategy to encapsulate all the different cohomology theories in algebraic geometry was formulated initially by Alexandre Grothendieck, who is responsible for setting up much of this marvelous cohomological machinery in the first place. Grothendieck sought a single theory that is cohomological in nature that acts as a gateway between algebraic geometry and the assortment of special cohomological theories, such as the ones listed above—that acts as the motive behind all this cohomological apparatus."

"Leonhard Euler stated that mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind would never penetrate."

"Maybe we have become so hung up on looking at the primes from Gauss's and Riemann's perspective that what we are missing is simply a different way to understand these enigmatic numbers. Gauss gave an estimate for the number of primes, Riemann predicted that the guess is at worst the square root of N off its mark, Littlewood showed that you can't do better than this. Maybe there is an alternative viewpoint that no one has found because we have become so culturally attached to the house that Gauss built."

"Riemann's insight followed his discovery of a mathematical looking-glass through which he could gaze at the primes. ...[I]n the strange mathematical world beyond Riemann's glass, the chaos of the primes seemed to be transformed into an ordered pattern as strong as any mathematician could hope for. He conjectured that this order would be maintained however far one stared into the never-ending world beyond the glass. His prediction of an inner harmony... would explain why outwardly the primes look so chaotic. The metamorphosis... where chaos turns to order, is one which most mathematicians find almost miraculous. The challenge that Riemann left the mathematical world was to prove that the order he thought he could discern was really there."

"In... 1859 Bernhard Riemann... presented a paper to the [Berlin] Academy... "On the Number of Prime Numbers Less Than a Given Quanitity." ...Riemann tackled the problem with the most sophisticated mathematics of his time... inventing for his purposes a mathematical object of great power and subtlety. ...[H]e made a guess about that object, and then remarked:One would of course like to have a rigorous proof of this, but I have put aside the search for such a proof after some fleeting vain attempts because it is not necessary for the immediate objective...That ... guess lay almost unnoticed for decades. Then... gradually seized... imaginations... until it attained the status of an overwhelming obsession. ...The Riemann Hypothesis... remained an obsession all through the twentieth century and remains one today, having resisted every attempt at proof and disproof. [It is] now the great white whale of mathematical research."

"Gauss liked to call [number theory] 'the Queen of Mathematics'. For Gauss, the jewels in the crown were the primes, numbers which had fascinated and teased generations of mathematicians."

", eleven years younger than Archimedes, was a native of Cyrene. He... measured the obliquity of the ecliptic and invented a device for finding prime numbers. ...In his old age he lost his eyesight, and on that account is said to have committed suicide by voluntary starvation."

"A prime number is one (which is) measured by a unit alone. Πρῶτος ἀριθμός ἐστιν ὁ μονάδι μόνῃ μετρούμενος."

"The primes are the atoms of arithmetic, the indivisible building blocks from which all other numbers are constructed. In their chaotic distribution lies a profound order, a secret language waiting to be deciphered. To study them is to chase the fundamental rhythm of mathematics itself."

"Fermat died with the belief that he had found a long-sought-for law of prime numbers in the formula 2^{2^n} + 1 = a prime, but he admitted that he was unable to prove it rigorously. The law is not true, as was pointed out by Euler in the example 2^{2^5} + 1 = 4,294,967,297 = 6,700,417 times 641. The American lightning calculator Zerah Colburn, when a boy, readily found the factors but was unable to explain the method by which he made his marvellous mental computation."

"Armed with his prime number tables, Gauss began his quest. As he looked at the proportion of numbers that were prime, he found that when he counted higher and higher a pattern started to emerge. Despite the randomness of these numbers, a stunning regularity seemed to be looming out of the mist."

"I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe. Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers."

"The present work is inspired by Edmund Landau's famous book, Handbuch der Lehre von der Verteilung der Primzahlen, where he posed two extremal questions on cosine polynomials and deduced various estimates on the distribution of primes using known estimates of the extremal quantities. Although since then better theoretical results are available for the error term of the prime number formula, Landau's method is still the best in finding explicit bounds. In particular, Rosser and Schonfeld used the method in their work "Approximate formulas for some functions of prime numbers"."

"We don't naturally have some magic formula to try and find these prime numbers. In fact trying to find where the next prime number is represents one of the biggest mysteries in the whole of mathemaics. ...The challenge if the primes is somehow of the ultimate puzzle in the whole of mathematics."

"It has the very commendable aim of contributing towards stressing the cultural side of mathematics. ...there appears the widespread interchange of the definitions of excessive and defective numbers. ...it is stated that Euclid contended that every perfect number is of the form 2n-1(2n -1). It is true that Euclid proved that such numbers are perfect whenever 2n - 1 is a prime number but there seems to be no evidence to support the statement that he contended that no other such numbers exist. ...it is stated that the arithmetization of mathematics began with Weierstrass in the sixties of the last century. The fact that this movement is much older was recently emphasized by H. Wieleitner... it is stated that the arithmos of Diophantus and the res of Fibonacci meant whole numbers, and... we find the statement that in the pre-Vieta period they were committed to natural numbers as the exclusive field for all arithmetic operations. On the contrary, operations with common fractions appear on some of the most ancient mathematical records."

"(a + b) \times (a - b) = a^2 - b^2...The difference of two square numbers is always a product, and divisible both by the sum and by the difference of the roots of those two squares; consequently the difference of two squares can never be a prime number."

"I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras... I have no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as "startling". ...Very recently I came across a tract published by you styled Orders of Infinity in page 36 of which I find a statement that no definite expression has been as yet found for the number of prime numbers less than any given number. I have found an expression which very nearly approximates to the real result, the error being negligible. I would request that you go through the enclosed papers. Being poor, if you are convinced that there is anything of value I would like to have my theorems published. I have not given the actual investigations nor the expressions that I get but I have indicated the lines on which I proceed. Being inexperienced I would very highly value any advice you give me. Requesting to be excused for the trouble I give you. I remain, Dear Sir, Yours truly..."