K. S. SARKARIA

This website is – you guessed it! – “under construction” but in due time you’ll find here practically all my published and unpublished papers. These are for the most part in mathematics because – you guessed correctly again! – I am mostly a mathematician, but there are some exceptions. Just as a sample, here is one from long ago in which I had proved A Trace Formula, and here is a later more whimsical paper of mine which points out and discusses this Paradox : the usual way in which Fluid Mechanics is taught “proves” that the fundamental group of a circle is trivial! And here, finally, is a very recent photograph I took of my shoes as I was doing mathematics in my brother’s beautiful garden in New Jersey:--

My plan, basically, is to just complete the attached incomplete List and upload all its items. In the meantime, see also www.geocities.com/sarkaria_2000 and www.geocities.com/karanbirsarkaria, my previous websites (which too have remained “under construction” only for a very long time, and shall now soon be deconstructed).

Dr. J. S. Sarkaria’s Cactus Book is also now on this website.

Update of April 11, 2010. As I had so astutely – clap! clap! – foreseen, this site is still “under construction” after so many months (and the geocities links have been defunct for almost as many), but, as those fond of avidly perusing this website have no doubt noticed, I have stuck to my basic plan, though perhaps at a less than blistering pace. Besides, starting today – a Happy Birthday to you too! – I’ve started building up another list, of hard-to-find items by other authors that I have liked over the years, which too will be treated, basically, as per the same tried-and-tested (or is it slow-but-steady?) plan.

Update of April 11, 2011. Considering how much more material has been added to it during the last year, this website is now no longer “under construction” in a restricted sense, but then again, considering how much more remains to be uploaded, and even more, how much more by way of new projects I’ve in the pipeline, it seems it is destined to remain happily “under construction” for my lifetime? Anyway, one project of the latter kind which did make it during the previous year was the, by now well-known, paper from which the above photo—which also serves as an entry to a picture gallery!—is extracted.

Update of April 11, 2012. As they say: the more things change, the more they (appear to) remain the same …

Update of April 11, 2013. Chugging along ... and a special word of thanks for all those who have been giving help from far away ... indeed today only I received a scanned pdf of those long seminar notes from 1993-94 on Poincaré’s Analysis Situs ... so these too are now available on this website.

Update of April 11, 2014. Clicking on the above pic will tell you that walking around and around those garden paths can lead one to do funny things ... and there is much else too that is new in List ... but I’ll let you explore for yourself and pick and choose what catches your fancy ...

Update of April 11, 2015. Funny how what I spent almost all of this twelvemonth doing ... very little of that got posted ... while a couple of btw things that happened jlt did ... still, this little should suffice to give, to at least some of you, a pretty good idea of what’s cooking ...

Update of April 11, 2016. The trivial -- but crucial ! -- first paragraph of PG&R had set the above ball rolling three years ago ... besides, to answer some interesting questions that have arisen in its sequels, I’ve been playing with arguments like the one below which uses a bricklaying pattern.

Update of April 11, 2017. Time flew thanks to aliens who can go back in time and some notes on a footnote.

Update of April 11, 2018. “So what is your best work?” Never an easy question to answer, but I’d say what I’ve done after 2009, especially Plain Geometry & Relativity, I-II-III-IV-V, together with its burgeoning off-shoot, a topological reworking of algebra. For the manifesto of the latter click on the first picture below, and for some related rubaiyaan (!) inspired by the prettiest composition of Khayyam on the second. All translations are also available from List, except of the latest installment posted today, of which the translation will be made available as soon as it is ready.

Update of April 11, 2019. It’s all revolving now, around what Baby Algebra is proving in the picture below, as the next and yet-to-be-translated part four posted today further shows.

Update of April 11, 2020. The picture below of an hero of mine clicks to a miscellany of fifty thoughts, the one-sided halo of the cake to the translation of part four, and posted now is the yet-to-be-translated part five.

Update of April 11, 2021. The translation of the interleaved part three and a half, a.k.a. fifty thoughts on everything under the sun, and that of the conclusion of our topological theory of equations, had to wait upon quite a bit of this and that left in its wake, e.g., hobson’s choice, garlands, etc., as well as the fun story contained in the picture below. Which stirred up many old and new results, but happily this segue on spin, theta, etc., has quite naturally circled back into the nik-suk I was doing before, and God willing, hope to continue.

Update of April 11, 2022. Frolicking in the garden of mathematical delights, this orbit found me mostly musing on elves from the eighties and nineties, and there is lotta stuff from the past now added to List, but there is much more on my to-do list that needs to be done ... however, at least the following – my take on a wonderful but ‘secret’ place at a stone’s throw almost from where we live! – I’ve now duly ticked off :-

Update of April 11, 2023. Many old notes, for example mli, were being posted, and work was continuing apace in my miscellany ... but then there was a health setback, post which, there was a pressing need to assure myself that my contributions to mathematics will be remembered till the end of all time! Things steadied en suite: a couple of pending translations were done; also via the two pictures below you can, respectively, enjoy a fun story or historical satire that I wrote during this time, and, muse over a biological-cum-celestial poser which the wise old banyan has posed to bing and bamboo man (this heavenly drawing being imho the most original drawing I have drawn so far). During the last couple of months only have I resumed doing (but hopefully not too seriously) some serious mathematics, but, all I have to show for it so far are some more footnotes in my miscellany.

Update of April 11, 2024. Outlandish though it sounds, it may well be true that, in the modern era, no one has published more original mathematics in any language native to this subcontinent than yours truly! Naturally it is all in my ma-boli Punjabi, but heretofore only in Gurmukhi script. This twelvemonth began with me boning up temporarily on the other main script in which Punjabi is written, enough I hope to transcribe correctly that pretty theorem of mine from Gurmukhi into Shahmukhi script. Then another pending item in my overflowing in-tray took me all the way back to my childhood fascination with maps. What resulted is a unique and heady mix of the geography of Sirsa nadi, the history of a qila, and much much more ... including a mathematical idea seemingly too good to be true, which took me back again to a very beautiful paper, and had at least the merit of keeping me busy for the rest of this orbit ...

Update of April 11, 2025. A pleasant connection was made this year between what I am doing, and what I had discovered sixty years ago. Which lifted nicely to a curious arithmetic that an imaginative primary school student could have discovered, and indeed did in my opinion, and that too not far from where I live! Also I discovered that that early discovery of continuous but never differentiable motion by a brave bohemian—a heroic species of mathematicians which later was even fashionable for a little while in the free world, but alas has again dwindled to extinction in these terrible times—was tied intimately to a lesser known, and decidedly more pacific, version of the fable about the hare and the tortoise, in which the two are good friends and tie their race, even though the former is always running twice as fast as his pal:-

Back in the day then, mathematics too was more heroic, and most of it still coming out in other European languages. It is a no-brainer that (like poetry) a creative pursuit like mathematics is pursued best in one’s own mother tongue, and especially with translation between some languages already much easier now, I see no reason (outside those belonging to the “business of mathematics”) why we mathematicians (again to be distinguished from “mathematicians” who alas are even more abundant now) should not do exactly that! Anyway, you’ll again find added to List some more items in my mother tongue, of which the one written jointly I particularly like; but this time I’ve also posted translations of some beautiful short papers by others; and oh yes, there is there now, rather late in the day, my very first paper in German!