Leonhard Euler ~ Sakinorva Databank

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Leonhard Euler

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Leonhard Euler ~ Sakinorva Databank

Leonhard Euler

Mathematician

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	nicotineseries 2025/07/23 (Wed) 06:17:15 #10203
	6.) Quotes about Euler: (cite: https://en.m.wikiquote.org/wiki/Leonhard_Euler?searchToken=4ksauftzw0wiksimssnoeuwmm) Frederick the Great, Letters of Voltaire and Frederick the Great (1927), translated by Richard Aldington, letter 221 from Frederick to Voltaire (25 November 1777): "Euler calculated the force of the wheels necessary to raise the water in a reservoir … My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry!" Carl Friedrich Gauss, as quoted by Louise Grinstein, Sally I. Lipsey, Encyclopedia of Mathematics Education (2001) p. 235: "The study of Euler's works will remain the best school for the different fields of mathematics and nothing else can replace it." George Pólya, Induction and Analogy in Mathematics (1954) Vol. 1 Of Mathematics and Plausible Reasoning: "Euler's step was daring. In strict logic, it was an outright fallacy... Yet it was justified by analogy, by the analogy of the most successful achievements of a rising science that he called... "Analysis of the Infinite." Other mathematicians, before Euler, passed from finite differences to infinitely small differences, from sums with a finite number of terms to sums with an infinity of terms, from finite products to infinite products. And so Euler passed from equations of a finite degree (algebraic equations) to equations of infinite degree, applying the rules made for the finite... This analogy... is beset with pitfalls. How did Euler avoid them? ...Euler's reasons are not demonstrative. Euler does not reexamine the grounds for his conjecture... only its consequences. ...He examines also the consequences of closely related analogous conjectures... Euler's reasons are, in fact, inductive". William Whewell, History of the Inductive Sciences (1859) Vol. 1, pp. 363-363: "As analysis was more cultivated, it gained a predominancy over geometry; being found to be a far more powerful instrument for obtaining results; and possessing a beauty and an evidence, which, though different from those of geometry, had great attractions for minds to which they became familiar. The person who did most to give to analysis the generality and symmetry which are now its pride, was also the person who made Mechanics analytical; I mean Euler." 7.) Another eulogy of Euler in 1783 by Nicolas Fuss: Website: http://eulerarchive.maa.org/historica/fuss.html By Marquis de Condorcet: Website: http://eulerarchive.maa.org/historica/condorcet.html 8.)?: For another you that wanna searching or research or even know in deep about the man is now right now isn't that difficult there are many on the website, you can search if you have any intention to know it. 9.) So another problem when he with Voltaire. I confused, so summary on he was a target of Voltaire wit right? 10.) Wow you guys read his letter to German princesses? But natural philosophy are. Ow I have a pdf of it. https://drive.google.com/file/d/16sIGvRWlQp1YypXfKUBzVaGD1QzAzpnm/view?usp=drivesdk 11.) Guys I found there is something that really interesting! Wait, okay here is it. https://myhero.com/leonhard-euler-the-catalyst-behind-the-revolution-of-mathematics 12.) If you want some book of his biography that I recommend to reads for. I definitely have an pdf on it so you can read. https://drive.google.com/file/d/1dEnKzINjAFUMIzRZjujfl0PiRIXzf32A/view?usp=drive_link 13.) About his mistakes: https://drive.google.com/file/d/1YLGD2fUGLRn3VTeEijjLm7QHpXpKAzLu/view?usp=drivesdk 14.) A little bit out of context is this "Mathematicians are People, Too!" Is the book I recommend to read about: https://drive.google.com/file/d/1YMD6HTCr1YsPsKPL9XnUfoQKsb8pbYD9/view?usp=drivesdk

Editing post #10203 by nicotineseries 6.) Quotes about Euler: (cite: https://en.m.wikiquote.org/wiki/Leonhard_Euler?searchToken=4ksauftzw0wiksimssnoeuwmm) Frederick the Great, Letters of Voltaire and Frederick the Great (1927), translated by Richard Aldington, letter 221 from Frederick to Voltaire (25 November 1777): "Euler calculated the force of the wheels necessary to raise the water in a reservoir … My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry!" Carl Friedrich Gauss, as quoted by Louise Grinstein, Sally I. Lipsey, Encyclopedia of Mathematics Education (2001) p. 235: "The study of Euler's works will remain the best school for the different fields of mathematics and nothing else can replace it." George Pólya, Induction and Analogy in Mathematics (1954) Vol. 1 Of Mathematics and Plausible Reasoning: "Euler's step was daring. In strict logic, it was an outright fallacy... Yet it was justified by analogy, by the analogy of the most successful achievements of a rising science that he called... "Analysis of the Infinite." Other mathematicians, before Euler, passed from finite differences to infinitely small differences, from sums with a finite number of terms to sums with an infinity of terms, from finite products to infinite products. And so Euler passed from equations of a finite degree (algebraic equations) to equations of infinite degree, applying the rules made for the finite... This analogy... is beset with pitfalls. How did Euler avoid them? ...Euler's reasons are not demonstrative. Euler does not reexamine the grounds for his conjecture... only its consequences. ...He examines also the consequences of closely related analogous conjectures... Euler's reasons are, in fact, inductive". William Whewell, History of the Inductive Sciences (1859) Vol. 1, pp. 363-363: "As analysis was more cultivated, it gained a predominancy over geometry; being found to be a far more powerful instrument for obtaining results; and possessing a beauty and an evidence, which, though different from those of geometry, had great attractions for minds to which they became familiar. The person who did most to give to analysis the generality and symmetry which are now its pride, was also the person who made Mechanics analytical; I mean Euler." 7.) Another eulogy of Euler in 1783 by Nicolas Fuss: Website: http://eulerarchive.maa.org/historica/fuss.html By Marquis de Condorcet: Website: http://eulerarchive.maa.org/historica/condorcet.html 8.)?: For another you that wanna searching or research or even know in deep about the man is now right now isn't that difficult there are many on the website, you can search if you have any intention to know it. 9.) So another problem when he with Voltaire. I confused, so summary on he was a target of Voltaire wit right? 10.) Wow you guys read his letter to German princesses? But natural philosophy are. Ow I have a pdf of it. https://drive.google.com/file/d/16sIGvRWlQp1YypXfKUBzVaGD1QzAzpnm/view?usp=drivesdk 11.) Guys I found there is something that really interesting! Wait, okay here is it. https://myhero.com/leonhard-euler-the-catalyst-behind-the-revolution-of-mathematics 12.) If you want some book of his biography that I recommend to reads for. I definitely have an pdf on it so you can read. https://drive.google.com/file/d/1dEnKzINjAFUMIzRZjujfl0PiRIXzf32A/view?usp=drive_link 13.) About his mistakes: https://drive.google.com/file/d/1YLGD2fUGLRn3VTeEijjLm7QHpXpKAzLu/view?usp=drivesdk 14.) A little bit out of context is this "Mathematicians are People, Too!" Is the book I recommend to read about: https://drive.google.com/file/d/1YMD6HTCr1YsPsKPL9XnUfoQKsb8pbYD9/view?usp=drivesdk
Replying to post #10203 by nicotineseries

	nicotineseries 2025/07/23 (Wed) 06:16:30 #10202
	5.) Presenting the explicit versions of his quotes from Berx 1.) Euler: "Since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear." =>introduction to De Curvis Elasticis, Additamentum I to his Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes 1744; translated on pg10-11, "Leonhard Euler's Elastic Curves", Oldfather et al 1933. "All the greatest mathematicians have long since recognized that the method presented in this book is not only extremely useful in analysis, but that it also contributes greatly to the solution of physical problems. For since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear. Wherefore there is absolutely no doubt that every effect in the universe can be explained as satisfactorily from final causes, by the aid of the method of maxima and minima, as it can from the effective causes themselves. Now there exist on every hand such notable instances of this fact, that, in order to prove its truth, we have no need at all of a number of examples; nay rather one's task should be this, namely, in any field of Natural Science whatsoever to study that quantity which takes on a maximum or a minimum value, an occupation that seems to belong to philosophy rather than to mathematics. Since, therefore, two methods of studying effects in Nature lie open to us, one by means of effective causes, which is commonly called the direct method, the other by means of final causes, the mathematician uses each with equal success. Of course, when the effective causes are too obscure, but the final causes are more readily ascertained, the problem is commonly solved by the indirect method; on the contrary, however, the direct method is employed whenever it is possible to determine the effect from the effective causes. But one ought to make a special effort to see that both ways of approach to the solution of the problem be laid open; for thus not only is one solution greatly strengthened by the other, but, more than that, from the agreement between the two solutions we secure the very highest satisfaction." 2.) Euler: "The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful." =>Opera Omnia, ser. 1, vol. 2, p. 459 Spcimen de usu observationum in mathesi pura, as quoted by George Pólya, Induction and Analogy in Mathematics Vol. 1, Mathematics and Plausible Reasoning (1954) "It will seem a little paradoxical to ascribe a great importance to observations even in that part of the mathematical sciences which is usually called Pure Mathematics, since the current opinion is that observations are restricted to physical objects that make impression on the senses. As we must refer the numbers to the pure intellect alone, we can hardly understand how observations and quasi-experiments can be of use in investigating the nature of numbers. Yet, in fact, as I shall show here with very good reasons, the properties of the numbers known today have been mostly discovered by observation, and discovered long before their truth has been confirmed by rigid demonstrations. There are many properties of the numbers with which we are well acquainted, but which we are not yet able to prove; only observations have led us to their knowledge. Hence we see that in the theory of numbers, which is still very imperfect, we can place our highest hopes in observations; they will lead us continually to new properties which we shall endeavor to prove afterwards. The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful."

Editing post #10202 by nicotineseries 5.) Presenting the explicit versions of his quotes from Berx 1.) Euler: "Since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear." =>introduction to De Curvis Elasticis, Additamentum I to his Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes 1744; translated on pg10-11, "Leonhard Euler's Elastic Curves", Oldfather et al 1933. "All the greatest mathematicians have long since recognized that the method presented in this book is not only extremely useful in analysis, but that it also contributes greatly to the solution of physical problems. For since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear. Wherefore there is absolutely no doubt that every effect in the universe can be explained as satisfactorily from final causes, by the aid of the method of maxima and minima, as it can from the effective causes themselves. Now there exist on every hand such notable instances of this fact, that, in order to prove its truth, we have no need at all of a number of examples; nay rather one's task should be this, namely, in any field of Natural Science whatsoever to study that quantity which takes on a maximum or a minimum value, an occupation that seems to belong to philosophy rather than to mathematics. Since, therefore, two methods of studying effects in Nature lie open to us, one by means of effective causes, which is commonly called the direct method, the other by means of final causes, the mathematician uses each with equal success. Of course, when the effective causes are too obscure, but the final causes are more readily ascertained, the problem is commonly solved by the indirect method; on the contrary, however, the direct method is employed whenever it is possible to determine the effect from the effective causes. But one ought to make a special effort to see that both ways of approach to the solution of the problem be laid open; for thus not only is one solution greatly strengthened by the other, but, more than that, from the agreement between the two solutions we secure the very highest satisfaction." 2.) Euler: "The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful." =>Opera Omnia, ser. 1, vol. 2, p. 459 Spcimen de usu observationum in mathesi pura, as quoted by George Pólya, Induction and Analogy in Mathematics Vol. 1, Mathematics and Plausible Reasoning (1954) "It will seem a little paradoxical to ascribe a great importance to observations even in that part of the mathematical sciences which is usually called Pure Mathematics, since the current opinion is that observations are restricted to physical objects that make impression on the senses. As we must refer the numbers to the pure intellect alone, we can hardly understand how observations and quasi-experiments can be of use in investigating the nature of numbers. Yet, in fact, as I shall show here with very good reasons, the properties of the numbers known today have been mostly discovered by observation, and discovered long before their truth has been confirmed by rigid demonstrations. There are many properties of the numbers with which we are well acquainted, but which we are not yet able to prove; only observations have led us to their knowledge. Hence we see that in the theory of numbers, which is still very imperfect, we can place our highest hopes in observations; they will lead us continually to new properties which we shall endeavor to prove afterwards. The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful."
Replying to post #10202 by nicotineseries

	nicotineseries 2025/07/23 (Wed) 06:14:30 #10201
	So when I read it carefully and I think it reservedly. Now I'll do an opinion, and my resume of all what I read about this person. Yet I know if all of my presentations about the comment that I write are wrong and not consistent with. So this is the list of my reasons: 1.) Thanks for @Berx and his knowledge for writing of his topology and @watcher. But really? If I know if it was true he has Ti/Fe axis function but why? Well I'm open to any argument for opposing me but I think that was he is not think of something about "harmony"? Pre-establised harmony? Euler turns away from the monistic philosophy in his time and from monadology, and he returns to the Cartesian dualism of body and soul, but he does not accept the Cartesian concept of body. He refuses also the opinion that animals are mere automatic machines, and he reproaches the Wolffians for considering human beings in the same way. In letter No. 81 Euler explains “There is a special place in the brain where all the nerves come to an end, and just there the soul is seated or there it feels all its impressions which are effected on it by the senses.” In letter No. 92 he says that an hour is not bound to a place. Then he continues: “Similarly I may say that my soul is neither in my head nor outside my head nor elsewhere, ... Therefore my soul does not exist at any place, but it operates at a certain place ...” (What did it mean to that?) In letter No. 83 he tries to ridicule pre-established harmony by the fiction of a connection between his soul and the body of a rhinoceros in Africa, but in letter No. 93 he argues for a stationary soul, and he thinks it is possible that immediately after death God could connect his soul with a body on the moon. (what else could you possibly want? Huh, Fe again?) Since Euler returns to dualism, to him those problems that provoked the monistic philosophy return, along with the system of pre-established harmony for either resolving them or avoiding them. He is well acquainted with these difficulties, and he refers to them in the letters again and again: If body and mind are based on two completely distinct substances, how could it be possible that the perceiving soul is able to “assume” something of the material world? Indeed, sensible perception needs the fulfilment of some conditions of the body, but nevertheless the picture on the retina is not yet the object of the seeing soul. The problem of the provenance of sensation, which is a hard problem in every theory of knowledge, especially in the Kantian theory, is treated in letter No. 82. Euler compares the soul with a man sitting in a dark room and seeing the things outside the room via a camera obscura. Similarly the soul is considering the ends of the nerves and receiving the impressions of the sense organs. “Though it is absolutely unknown to us what the similarity is between the impressions on the ends of nerves and the objects causing those impressions, these impressions are appropriate to deliver to us a very adequate idea of the objects.” Descartes had at least endeavoured to argue for the adequacy of that idea, but in Euler’s writings it is merely claimed. Obviously he does not advance to the Kantian question of whether there could be any similarity at all. For Euler it is certain in virtue of God’s omnipotence that a connection between body and mind can exist and, indeed, does exist. The second principal question in the theory of knowledge is “How are they connected?” This question was treated by the atomists of antiquity and it is still discussed by modern brain scientists. Euler’s answer is succinct: It is a great mystery (grand mystére)! (What do you think guys?) 3.) I don't know why you say about this person use Ti while you said "Ti doesn't merely seek a formula that 'works'. It seeks the most elegant version of the formula, i.e. the one that expresses the 'most truth' using the least amount of notation." Did he seems mention that? In 1767 Euler was sixty years old and losing his eyesight. He dictated the book to a servant, a tailor's apprentice, so one might imagine that under such circumstances his account of the rules for the multiplication of roots contained simple mistakes or oversights, in what was otherwise a masterpiece (Ti?). However, neither old age nor blindness slowed Euler's productivity or dulled his sharpness of mind, as is well known. Besides, Euler was increasingly acknowledged as the person who strikingly solved the vexing puzzle of taking logarithms of negative and complex numbers, as the latter eventually became known. So it seems stunning that he would have been confused about elementary multiplication. A passage in his Algebra seems even to state that √-1 x √-4 = 2, ridiculous though it seems. Some historians, Florian Cajori for one [4, p. 127], have suggested that perhaps such errors stemmed merely from typographical printing miscues for which Euler can not be held accountable. Others say that it involved a systematic confusion. Actually, neither is the case. Surprisingly, Euler committed no mistake on the matter. The solution to this puzzle is found buried in history under layers of ambiguous expressions, notations, and changing conventions on the definitions of basic operations. Stranger still, the historical analysis reveals defects and arbitrariness in the approach to this subject that became incorporated into elementary algebra as we know it. (It's it Ti?). As you want to know more again you can check this: https://drive.google.com/file/d/1YLGD2fUGLRn3VTeEijjLm7QHpXpKAzLu/view?usp=drivesdk 4.) Actually, if you read that article that I write in my past comment. In my opinion, He is use his principle to refine and perfecting a few encompassing ideas rather than generate more or more. He is not a someone who seek impartial and universalized foundational principles and he want his formula to proving the other problem that someone probably know are missing. Like did he making a new formula than improving the Newton's second law or a rigid bodies? Or a pioneer of new possibilities did he do that? I know he was being impartial but it was not the way about principle, it was all about his manners, his ethic/moral that he had in his daily life. And I know he is too a pioneer of pure mathematics but did he seek for understand of it's own sake? For the play of being intelligent? He had do saying like "Oh" "my pencil is more intelligent than I am". I think that what his want to be mathemicians is all about his interest and he did that with passion for changing the past principle that not yet completed or repaired by someone. Think that about Fermat's number of theory, is one of his dedicated things to solved the problems. Or Konigsberg bridges? 5.) I highly recommend or totally agree you should read what I said before in my past comment. In there I almost give all of the resources that I collected from many articles, scholars, or even scientific book about his life in generals. Please please I begging you to not close your eyes and your mind about what I wrote in it. Thanks to all of you ♡

Editing post #10201 by nicotineseries So when I read it carefully and I think it reservedly. Now I'll do an opinion, and my resume of all what I read about this person. Yet I know if all of my presentations about the comment that I write are wrong and not consistent with. So this is the list of my reasons: 1.) Thanks for @Berx and his knowledge for writing of his topology and @watcher. But really? If I know if it was true he has Ti/Fe axis function but why? Well I'm open to any argument for opposing me but I think that was he is not think of something about "harmony"? Pre-establised harmony? Euler turns away from the monistic philosophy in his time and from monadology, and he returns to the Cartesian dualism of body and soul, but he does not accept the Cartesian concept of body. He refuses also the opinion that animals are mere automatic machines, and he reproaches the Wolffians for considering human beings in the same way. In letter No. 81 Euler explains “There is a special place in the brain where all the nerves come to an end, and just there the soul is seated or there it feels all its impressions which are effected on it by the senses.” In letter No. 92 he says that an hour is not bound to a place. Then he continues: “Similarly I may say that my soul is neither in my head nor outside my head nor elsewhere, ... Therefore my soul does not exist at any place, but it operates at a certain place ...” (What did it mean to that?) In letter No. 83 he tries to ridicule pre-established harmony by the fiction of a connection between his soul and the body of a rhinoceros in Africa, but in letter No. 93 he argues for a stationary soul, and he thinks it is possible that immediately after death God could connect his soul with a body on the moon. (what else could you possibly want? Huh, Fe again?) Since Euler returns to dualism, to him those problems that provoked the monistic philosophy return, along with the system of pre-established harmony for either resolving them or avoiding them. He is well acquainted with these difficulties, and he refers to them in the letters again and again: If body and mind are based on two completely distinct substances, how could it be possible that the perceiving soul is able to “assume” something of the material world? Indeed, sensible perception needs the fulfilment of some conditions of the body, but nevertheless the picture on the retina is not yet the object of the seeing soul. The problem of the provenance of sensation, which is a hard problem in every theory of knowledge, especially in the Kantian theory, is treated in letter No. 82. Euler compares the soul with a man sitting in a dark room and seeing the things outside the room via a camera obscura. Similarly the soul is considering the ends of the nerves and receiving the impressions of the sense organs. “Though it is absolutely unknown to us what the similarity is between the impressions on the ends of nerves and the objects causing those impressions, these impressions are appropriate to deliver to us a very adequate idea of the objects.” Descartes had at least endeavoured to argue for the adequacy of that idea, but in Euler’s writings it is merely claimed. Obviously he does not advance to the Kantian question of whether there could be any similarity at all. For Euler it is certain in virtue of God’s omnipotence that a connection between body and mind can exist and, indeed, does exist. The second principal question in the theory of knowledge is “How are they connected?” This question was treated by the atomists of antiquity and it is still discussed by modern brain scientists. Euler’s answer is succinct: It is a great mystery (grand mystére)! (What do you think guys?) 3.) I don't know why you say about this person use Ti while you said "Ti doesn't merely seek a formula that 'works'. It seeks the most elegant version of the formula, i.e. the one that expresses the 'most truth' using the least amount of notation." Did he seems mention that? In 1767 Euler was sixty years old and losing his eyesight. He dictated the book to a servant, a tailor's apprentice, so one might imagine that under such circumstances his account of the rules for the multiplication of roots contained simple mistakes or oversights, in what was otherwise a masterpiece (Ti?). However, neither old age nor blindness slowed Euler's productivity or dulled his sharpness of mind, as is well known. Besides, Euler was increasingly acknowledged as the person who strikingly solved the vexing puzzle of taking logarithms of negative and complex numbers, as the latter eventually became known. So it seems stunning that he would have been confused about elementary multiplication. A passage in his Algebra seems even to state that √-1 x √-4 = 2, ridiculous though it seems. Some historians, Florian Cajori for one [4, p. 127], have suggested that perhaps such errors stemmed merely from typographical printing miscues for which Euler can not be held accountable. Others say that it involved a systematic confusion. Actually, neither is the case. Surprisingly, Euler committed no mistake on the matter. The solution to this puzzle is found buried in history under layers of ambiguous expressions, notations, and changing conventions on the definitions of basic operations. Stranger still, the historical analysis reveals defects and arbitrariness in the approach to this subject that became incorporated into elementary algebra as we know it. (It's it Ti?). As you want to know more again you can check this: https://drive.google.com/file/d/1YLGD2fUGLRn3VTeEijjLm7QHpXpKAzLu/view?usp=drivesdk 4.) Actually, if you read that article that I write in my past comment. In my opinion, He is use his principle to refine and perfecting a few encompassing ideas rather than generate more or more. He is not a someone who seek impartial and universalized foundational principles and he want his formula to proving the other problem that someone probably know are missing. Like did he making a new formula than improving the Newton's second law or a rigid bodies? Or a pioneer of new possibilities did he do that? I know he was being impartial but it was not the way about principle, it was all about his manners, his ethic/moral that he had in his daily life. And I know he is too a pioneer of pure mathematics but did he seek for understand of it's own sake? For the play of being intelligent? He had do saying like "Oh" "my pencil is more intelligent than I am". I think that what his want to be mathemicians is all about his interest and he did that with passion for changing the past principle that not yet completed or repaired by someone. Think that about Fermat's number of theory, is one of his dedicated things to solved the problems. Or Konigsberg bridges? 5.) I highly recommend or totally agree you should read what I said before in my past comment. In there I almost give all of the resources that I collected from many articles, scholars, or even scientific book about his life in generals. Please please I begging you to not close your eyes and your mind about what I wrote in it. Thanks to all of you ♡
Replying to post #10201 by nicotineseries

date	username	vote
25/12/31 22:44	nicotineseries	N
23/08/21 05:48	jamelspy	INTJ
23/08/21 05:39	salim	INTJ
19/03/03 16:04	tch	INTJ
19/03/03 02:05	LadyX	INTJ

date	username	vote
23/08/21 05:48	jamelspy	INTJ
23/08/21 05:39	salim	INTJ
20/01/21 17:56	tch	INTP

date	username	vote
19/03/03 02:05	LadyX	1w9