These comments on Shouryya Ray’s work are made on the basis of the posts that I have read on the following websites:
1. //thorehusfeldt.net/2012/05/29/shouryya-ray-and-the-press/
2. //thorehusfeldt.net/2012/06/05/shouryya-ray-closing-remarks/
3. //tu-dresden.de/die_tu_dresden/fakultaeten/fakultaet_mathematik_und_naturwissenschaften/fachrichtung_mathematik/institute/analysis/chill/dateien/CommentsRay.pdf
4. //physics.stackexchange.com/questions/28931/what-are-the-precise-statements-by-shouryya-ray-of-particle-dynamics-problems-po
5. //math.stackexchange.com/questions/150242/teenager-solves-Newton-dynamics-problem-where-is-the-paper
6. //www.reddit.com/r/worldnews/comments/u7551/teen_solves_Newtons_300yearold_riddle_an/
7. //www.physicsforums.com/showthread.php?t=609259
8. //en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Shouryya_Ray
After going through the posts and comments in these websites and following them very carefully, it is apparent that the final comments on most of the websites are made on the basis of the post, “Comments on some recent work by Shouryya Ray” by Prof. Dr. Ralph Chill and Prof. Dr. Jürgen Voigt (Technische Universität Dresden - TUD), dated June 4, 2012.
I am, therefore, writing the following comments on basis of this post (also including partly the history of comments mentioned on the websites above) and I must confess that I am not that fortunate as the TUD professors who were actually shown the work:
1. In the initial stage, most of the posts assumed that the conserved quantity of motion (which the boy displays in his hand in one of the pictures that can be found on the web) is his final solution and concluded that there is nothing new in it since many other researchers (for example Parker, Ref#5 of TUD post) have already found that relation. And of course, most people on these forums seems to have felt relaxed (or happy) about the fact that nothing new has been done by the boy, which they could not do themselves. This apprehension will be repeated throughout the text since the comments that I am going to make here should have come to others’ mind as well, but it happened otherwise.
2. The story (or the investigation) did not end (or stop) there and we came to know more about it. After having a very careful look into his other posters, his final solution was found in the form of series. Thanks to the people who carried out this exercise. And many people commented that series solutions are not considered analytic and hence he did not find any analytical solution! I am not raising the question that if one finds a solution in terms of sine, cosine, exponential, error function, or Bessel function (I can continue with the list, but, I guess the idea will be conveyed with these few examples), whether it would be legitimate to claim that he has an analytical solution. Thanks to the post of the two TUD professors, who unambiguously explained why Shouryya Ray’s solution can be considered as analytical solution.
3. The next obvious question that would come to one’s mind is: Is it the first ever EXPLICIT analytical solution for the problem of projectile motion under quadratic drag? The learned community is in the opinion: it is not, since many people found this solution before! This, according to me, requires a very careful look, on which the EXPERTS clearly think that they already have done it. Consider the work of Parker (Ref#5 of TUD post): he only obtained an implicit expression (Eq.(5) of TUD post) and nobody knows why he could not proceed further. This point, although pointed out by some of the members on these forums, was generally ignored by many others. Perhaps that once again, helps one to feel comfortable!
4. Some people, on different sites, mentioned the work of Yabugarbagea et al. (Ref#8 of TUD post) and commented that the series solution of Shouryya Ray was already found by these authors and his solutions are not new! Once again a point to feel relaxed - nothing new has been done which WE could not do! Some of the posts, however, mentioned that Shouryya Ray has the references of both Parker and Yabugarbagea et al. on his posters and hence he must be aware of and have already gone through them: therefore, he must have done something new. Good thinking! I, however, seriously think that nobody possibly went through the paper of Yabugarbagea et al. Had they gone through it, they would have discovered that Yabugarbagea et al. obtained their solution with the homotopy analysis method and their series converges only for a specific range of homotopy parameter, which on one hand, depends on the problem specification and on the other hand, cannot be determined a priori. Thus, I think, the solution of Yabugarbagea et al. cannot be considered truly analytic. Most importantly, none of the experts ever reported that the solution of Shouryya Ray can be easily derived from the solution of Yabugarbagea et al. (one can try his luck - my best wishes). And still, one has to believe that the boy has done NOTHING new as that makes us feel relaxed!
5. Some other people referred to a book from 1860 (written by Isidore Didion), which is written in French. And I guess, only a very few have really dared to go through it (may be due to the language barrier). If one goes through the book, he will find that there is definitely no explicit solution.
6. Let me now come to the 4th. page of the post by the two TUD professors. Let us focus our attention on the text at the beginning of the page. It says: “In the context of Shouryya Ray’s work it was an unfortunate circumstances, that a recent article from 2007 claims that no analytic solution of problem (1) was known, or that it was known only in special cases, namely for falling objects. This might have misled Shouryya Ray who was also not aware of the classical theory of ordinary differential equations.” While the part of the last sentence is easily understandable that he may not be aware of the classical theory of ODEs (since he is only a 16 year old school boy and it is not expected of him), the first part is completely incomprehensible! It makes you think on the basis of which evidence the authors made this remark! At least, the literature reviews carried out by so many experts on the scientific forums could not find any evidence of explicit yet truly (whose solution or convergence does not depend upon the choice of additional parameter) analytical solution of the problem. Had they found some, they must have reported them! Most importantly, the authors of TUD also could not provide any evidence in support of the statement. Therefore, this makes one to think: what led the authors to make such remarks?
7. Perhaps the answer lies on the two statements, made by the TUD professors. One is on page#3, which reads: “Having these existence theorems at hand, the coefficients ... ... may also be obtained from equation (3) or (4) by successively differentiating the equations and thus obtaining a recursion formula for the higher order derivatives of $\psi$ at 0.” This statement means that the expert mathematicians could find the solution very easily, but, most unfortunately, the available evidence shows that they DID NOT find one, possibly due to the reason best known to them! The second statement is on page#4, which reads: “Actually, many mathematicians have considered the problem of projectile motion in air over a long time.” Once again, that also does not imply that any mathematician has actually solved it explicitly! It must be recognized that there is a BIG difference between “could be solved” and “has been solved”. To that extent, I sincerely think that there is no point in contesting the comments of Yabugarbagea et al. (Ref#9 of TUD post) unless one has the existence of definite evidence; they must have made this statement after carefully going through the literature. I thought that the mathematicians believe on the logic and the proof of existence the most!
8. I strongly believe that on the basis of the evidence available to the authors (two TUD professors) they could only make the following statement: “According to the best of our knowledge (due to whatever reason) Shouryya Ray’s solution appears to be the FIRST EVER, clean, explicit, truly analytical solution for the problem of projectile motion under quadratic drag.”
9. The most dangerous statement comes in the last sentence of the last-but-one paragraph: “Nevertheless, all his steps are basically known to experts, and we emphasize that he did not solve an open problem posed by Newton”. I guess, by the words, “an open problem posed by Newton”, the authors actually meant problem (1) in their text - at least that is the way their statement has been interpreted by the learned scientific community! Wonderful! What a logical conclusion! What an emphatic statement! As if, it came as a natural consequence of the existence of a lot of documentary evidence! This is the most “catchy” statement which has almost immediately caught the attention - once again to feel RELAXED - Nothing has been really done which WE could not do! What assumption could be behind this statement? It must be clear from the statement itself. Since all the steps are basically known to experts, does it necessarily mean that they MUST have solved it? Extending this extremely sophisticated logic (assumption, to be precise), one could easily conclude: No one can solve any unsolved problem using known mathematical tools - as that will be known to the expert mathematicians and if that is known, they must have solved it - it does not require any evidence - this is BY DEFAULT)! Here I really felt annoyed and thought of writing these comments.
10. The TRUTH probably is: although Shouryya Ray did not use any novel method for solution (which can never be proved to be essential for finding a new solution) it does not necessarily imply that he did not find a new solution! Question is then how this statement should be changed? In my opinion it can only read: “We emphasize that he did not use any new mathematical tool that was not known to the experts in order to solve an open problem posed by Newton.” By the way, I believe that problem (1) was not actually posed by Newton - he framed his laws of motion, which forms the basis of problem (1) and also proposed the quadratic drag law - like many of his other extraordinary findings (e.g., law of viscosity, law of cooling, etc.).
11. With all said and done, I feel that the media hype was surely not created by the boy, but, according to the status of the current knowledge, it appears that the boy did not claim anything incorrect. I guess, any senior university professor (other than mathematicians of course!) would have published article(s) on it, if he would have found out the same solution. In the present context, this has been done by a 16 year old school boy - possibly that is the real sensation - not the mathematical complexity of the problem. Hence, I believe, due respect should be given to him even though we understand the sentiment: any expert mathematician could solve his first problem without any trouble. Let us happily forget about the second problem! After all, that will keep us more relaxed and comfortable - NOTHING new has happened! Many of the posts in the scientific forums, including those on Wikipedia page, appear to be YELLOWER than the YELLOWEST journalism on this topic that could have been made by a non-scientific journalist on a scientific topic.
12. Unfortunately, it seems that to know more about the work, we have to really wait for sometime and expect that this boy, along with his supervisor(s), possibly publish articles in archival journals. I am writing this text with a hope that this boy reads this and feels encouraged!
I believe that this SMALL(!) text/ post would help the experts in correcting the wrong and caustic comments made before by them, iff (it is not a spelling mistake - I guess, I am posting it to people who are interested in mathematics) the intention is to serve science and not to belittle or malign the effort of the boy, who probably thought the world of science is really CLEAN (which most of us know is, unfortunately, not the case)! If, however, it is a question of megalomania, no one can possibly help. I am waiting for the corrections to those posts or their removal!
