'The Mystery of the Prime Numbers', Secrets of Creation vol. 1 by Matthew Watkins

comments on the number theory and physics archive

The website was featured as one of three "Further Reading" links in the New Scientist Online version of the NS 11/11/00 cover article "Prime Time" by Erica Klarreich. This was the first NS cover article concerning a pure mathematical problem in a very long time, I believe:

See near the bottom of the page http://www.newscientist.com/features/features_226444.html

Similarly, the website was recommended in Marcus du Sautoy's acclaimed book Music of the Primes (Fourth Estate, 2003)

Here is an excerpt from a posting by Andrew Odlyzko to the American Scientist E-print Forum from March 2003:

"The ease of electronic communication has also led to a countervailing trend, namely the rise of new modes of communication that allow us to cope with the increased load of fluff (something that I wrote about in "The rapid evolution of scholarly communication", Learned Publishing, Jan. 2002, available at http://www.dtc.umn.edu/~odlyzko/doc/eworld.html. An outstanding example of that is the Web site maintained by Matthew Watkins listed above, part of an extensive collection of material about the Riemann zeta function available at http://www.maths.ex.ac.uk/~mwatkins. It is not part of the traditional refereed literature, but it is very widely used as a resource by number theory researchers."

J. Baez's "This Weeks Finds in Mathematical Physics (Week 199)" discusses C* algebras and B. Julia's "free Riemann gas" concept, referencing my summary of the original article, and continuing:

"Matthew Watkins has a lot of other fascinating material about prime numbers and physics on his website... so this is the best place to start if you're a beginner wanting to learn more about this stuff."

I was thanked for "very constructive comments" in the 'acknowledgements' section of the recent preprint "On supersymmetric QM, fractal strings and steps towards a proof of the Riemann hypothesis" by Carlos Castro, Alex Granik and Jorge Mahecha

See http://xxx.lanl.gov/abs/hep-th/0107266

(This article is to be published in the Journal of Chaos, Solitons, and Fractals)

The site was also referred to in the article "p-Adic stochastic dynamics, supersymmetry and the Riemann conjecture" by C. Castro

See http://xxx.lanl.gov/abs/physics/0101104

(This is also to be published in the Journal of Chaos, Solitons, and Fractals)

More recently, the site was acknowledged in E. Elizalde, V. Moretti and S. Zerbini's preprint "On recent strategies proposed for proving the Riemann hypothesis" which examines the above work. The authors emailed:

"We are posting a paper on the RH math-ph/0109006. While we are not specialists on the RH, we certainly are versed in zeta functions and can appreciate the effort you have done with your web page."

More recently, Professor Elizalde (of M.I.T.) commented:

"Their papers have opened my eyes towards a new direction of research, a very interesting one, and their ideas are very nice. It would be an extraordinary achievement if they could be realized, flawless to the end...

Your page is very, very useful, and what you are doing deserves all my support and admiration, much more taking into account your financial conditions. If I may do anything about that, at some point, I'll let you know."

This website is also referenced in H. Rosu's fascinating survey article "Quantum Hamiltonians and prime numbers", Mod. Phys. Lett. A 18 (2003):

"See the excellent number theory & physics archive of M. Watkins at http://www.maths.ex.ac.uk/~mwatkins"

In their paper "The golden mean as clock cycle of brain waves" (Chaos, Solitons and Fractals 18 No. 4 (2003) 643-652, Harald and Volkmar Weiss acknowledge the site as one of several "...without which our work would be impossible", and in a subsequent email, Volkmar Weiss wrote "Your site was very helpful to us in an extraordinary way."

My page on the Riemann Hypothesis was recommended by Alan Boyle in his Cosmic Log, part of the MSNBC news website:

"To learn more about the Riemann Hypothesis, click through this Web portal on the problem at the University of Exeter."

Miscellaneous feedback from USA, France, India, Russia, Serbia, England, Wales, Columbia, Italy, Canada, Australia, Poland, Sweden, Israel, Germany, Japan, Mexico, Brazil, the Netherlands, Chile, Slovakia, Spain, Switzerland and New Zealand:

Prof. Michel Lapidus, Department of Mathematics, University of California Riverside, USA

"I wish to take advantage of this brief messge to tell you how valuable I find your archive...You are providing a real service to the research community and I hope that you will eventually be justly rewarded for all your hard work and passion for this subject. I myself have found new references which I had not heard about until I found them in your archives: for example, the papers of Spector related to but independent of the work of the physicist Bernard Julia on the free Riemann gas. I have discovered it in your archives a few weeks ago.

In fact, in my current essay, "In search of the Riemann zeros", I have added a reference to your archive where interested readers can find additional relevant references and interesting quotes."

Michel Planat, Laboratoire de Physique et Metrologie des Oscillateurs du CNRS, France

"First I would like to congratulate you for the very interesting website you are developing day after day. I already used it many times when it was recommended to me by Michel Waldschmidt.

I have also mentioned your website in my recently published book: Noise, Oscillators and Algebraic Randomness: From Telecommunication Systems to Number Theory, Lecture Notes in Physics 550 (Springer-Verlag, 2000)."

The website is also mentioned in Planat's article "1/f noise, the measurement of time and number theory" (Fluctuation and Noise Letters 0 (2001).

R. Padma, Ramanajun Institute, University of Madras, India

"You are doing an extremely useful service to the scientific community by putting together the links between physics and number theory. We have written a paper "Ramanujan-Fourier series, the Wiener-Khintchine formula and the distribution of prime pairs" by H. Gopalkrishna Gadiyar and R. Padma, Physica A 269 (1999), 503-510. As is obvious from the title, it is an article connecting statistical physics to number theory. I would urge you to look at the references given in that paper as they would interest you. By the way are you a physicist or a number theorist? Thanking you for your kind interest in our work."

Branko Dragovich, Mathematics Department, University of Belgrade and Department of Mathematical Physics, Steklov Mathematical Institute, Moscow

"Your activity in creating an archive of papers related to the employment of p-adic numbers in physics is very important and will stimulate further progress in this field. Please do not hesitate to ask me anything which might be useful in this direction."

David Broadhurst, Mathematics Department, Open University, UK

"Since writing I visited your site and really appreciated all the linking that you had done. It is a good web asset. Thanks for it."

V. S. Varadarajan, Department of Mathematics, UCLA, USA

"Thank you very much. I shall look at the website and see if I can give additional information. This is something nice you have done. This will be very helpful to researchers in this area."

Chris Hughes, Mathematics Department, Bristol University, UK

"Thank you very much for adding my papers to your site. I feel quite honoured - yours is by far the most comprehensive zeta site around."

Martin Huxley, Mathematics Department, Cardiff University, UK

"We're trying to enlarge the Research website for Cardiff, with new Number Theory pages and one about the zeta function. I would like to put in a link to your website..."

Michael Waldschmidt, Institut de Mathematiques de Jussieu, France
vice-president of the Societe Mathematique de France and organiser of the conferences "Number Theory and Physics" (Winter School, Les Houches, France, 03/89) and "Theorie de Nombres, Bruit des Frequences et Telecommunications" (Institut Henri Poincaré, Paris, 12/99)

"I have included a link to your home page in mine (under the words "Hypothese de Riemann") and during the meeting at IHP I shall certainly mention your home page which I feel is already an important contribution to the topic."

Jorge Mahecha, Physics Department, Universidad de Antioquia, Medellin, Columbia

"I thank you for your message. I felt honoured at finding my paper in your collection of works related to number theory. I looked at your site and found it very useful for anyone interested in this field."

Pierluigi Contucci, Mathematics Department, Universita di Bologna, Italy

"I had only a quick look at your web page but I enjoyed it very much, especially the animated plots. I am only an outsider in number theory and did some work with Knauf, but I share with you and others this interest which is even beyond science. All the best and keep me updated with your work."

Paolo Ribenboim, Department of Mathematics and Statistics, Queens University,Canada
author of The Book of Prime Number Records

"Thanks very much for your email. Your attempt - and the others you mentioned - should deserve careful attention. Unfortunately, I will never understand the ideas from physics which are required - I'll try to follow as a sideliner. These matters will interest my friends and colleagues, Pierre Cartier, Michel Lapidus, Michel Waldschmidt, Oleg Bogoyavlenskij."

Brian Conrey, Mathematics Department, Oklahoma State University, USA
executive director of American Institute of Mathematics

"Thanks for the information about your web-site. I found it very interesting. Dan Bump has a Riemann Hypothesis web site that you might want to link to: http://match.stanford.edu/rh/"

Keith Matthews, Mathematics Department, University of Queensland, Australia
coordinator of Number Theory Web

"Your site is very interesting and I have inserted links to it and your more philosophical site. I didn't know about the links to Riemann's paper."

Marek Wolf, Physics Department, Wroclaw University, Poland
author of "1/f noise in the distribution of prime numbers", Physica A 241 (1997), 493-499.

"It is a very interesting website!! Congratulations!!"

J.-F. Burnol, Mathematics Department, University of Nice, France

"Congratulations on your site. It is quite big now, and I was wondering if you have thought about making it searchable, for keywords, titles or authors."

Andreas Juhl, Maths Department, University of Uppsalla, Sweden
author of Cohomological Theory of Dynamical Zeta Function (Progress in Mathematics, Vol. 194, Birkhauser, 2001)

"Thank you for the information on the number theory web site. It's great and I will come back with comments a bit later."

"Since I consider your home-page project as an important means to popularise the subject I would like to support it by supplying some information..."


"It's now some time ago we had the last conversation. I have just taken a rough look at your rapidly developing home page. It is really very helpful in many directions!!"

Donald Spector, Physics Department, Hobart and William Smith Colleges, New York, USA

"I was pleased to see your site on prime numbers and physics. I do need to alert you to one item, which is that my paper "Supersymmetry and the M bius Inversion Function", Commun. Math. Phys. 127 (1990) 239 should be cited together with Bernard Julia's work. Both of us independently and simultaneously recognized the connection with partition functions, the Hagedorn temperature, etc. I offer my thanks in advance for your updating this information on your web site.

This whole area of number theory and physics is an interesting one, and I'm glad at your efforts in compiling links to all this information."

[a couple of years later:]

"Your collection of information and links on number theory and physics remains a valuable resource, and I'm glad to see how it's grown...Thanks for keeping this web site up and running. Collecting and tracking all this information and keeping it organized on the web pages takes a lot of time, I'm sure!"

Jeff Lagarias, ATT Research Labs, USA
author of "Number theory and dynamical systems" from The Unreasonable Effectiveness of Number Theory conference proceedings (1992)

"Thanks for the pointer to your archive/website. I hadn't looked at it before. It contains an impressive amount of interesting material."

Wentian Li, Lab of Statistical Genetics, Rockefeller University, New York City, USA
creator of the "1/f Noise Archive"

"Your site looks wonderful! I set up a link to yours from http://linkage.rockefeller.edu/wli/1fnoise/1fnoise_num.html"

Frances Amoroso, Mathematics Department, University of Caen, France

"Thanks for your message and for presenting your website. Can you put inside the following short list of references about the Riemann Hypothesis and Farey's sequence?"

Kryzystof Maslanka, Astronomy Department, Jagiellonian University, Poland

"Currently I am reading through your www page concerning the zeta function. It is excellent! Many interesting facts I have not been aware of. In particular, thank you for pointing attention to my www page."

G. Mussardo, International School for Advanced Studies in Trieste, Italy

"Thank you for your kind mail. It is indeed a very nice idea to prepare a web page where one can look at the surprising links between prime numbers and physics. I have in fact looked at your web page and I have enjoyed very much passing through the links there. To answer your question, I have recently explored the possibility to design a physical experiment that provides not only a test of primality (as done in my previous paper) but also the factorization in prime numbers when the number is composite. This is indeed possible. I have had no time though to write anything about it. If in the future I will decide to do it, I will keep in mind your initiative and I will contact you. Thanks for your interest."

Doron Cohen, Physics Department, Harvard University, USA

"You have a beautiful site! And I like your illustrations."

Omri Sarig, Mathematics Department, University of Tel-Aviv, Israel

"Thank you. Your site is very interesting."

Cheng-Hung Chang, Technische Universität Clausthal, Germany

"Hello, thank you very much for your e-mail and your new website. It really contains many interesting informations. We will collect some of our works and send to you later. By the way, you can visit the following new website: http://www.math-phys-zeta.de."

Rajat Bhaduri, Department of Physics and Astronomy, McMaster University, Canada

"I want to thank you for your effort in bringing so much interesting stuff all together in your website


I wanted to thank you for the splendid job you are doing."

Martin Holthaus, Condensed Matter Theory group, Fachbereich Physik, Carl von Ossietzky Universität, Oldenburg, Germany

"Thank you very much for your e-mail, and for informing me about your archive. I agree that the interface between statistical mechanics and number theory is a most fascinating subject.

. . .

I will use your web page to maintain contact with the field. If you know of other significant new developments in that area, please let me know."

Jyoichi Kaneko, Department of Mathematics, University of the Ryukyus, Japan

"I find your web site 'Number Theory and Physics Archive' exceedingly interesting."

Haret Rosu, Instituto Potosino de Investigación Científica y Tecnolégica, Mexico

"Thanks for your wonderful archive."

Wellington da Cruz, Departamento de Física, Universidade Estadual de Londrina, Brazil

"Your site for me was a great discovery, so try to maintain it."

Sergio Joffily, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil

"Thank you very much for your message concerning my paper "Jost function, prime numbers and Riemann zeta function". I was already aware of your very fine website, and I am greatly indebted to you for the aid your site has given my work. I will keep you informed as to any progress I make along these lines."

Daniel Grunberg, Faculty of Natural Sciences, Mathematics and Information Technology, Korteweg-De Vries Institute, University of Amsterdam, Netherlands

"Very nice site! I didn't know about all these connections – have myself had a passing interest in p-adic numbers and hope to use them some day in string theory, like others have done before."

Jim Phillips, Department of Physics and Astronomy, Rutgers University, New Jersey, USA

"Wunderbar! Wonderful! I have a lot of reading to do.

The note "Microscopic origin of collective exponentially small resistance states"

is now in press, and you will not be surprised to hear that the predictions about the prime number theorem and log p that it made have already been verified experimentally. (Computer time is very fast.)

I attach some new material that you may find helpful."

Barry Ninham, Department of Chemistry and CSGI, University of Florence, Italy

"I've just got into your website.

Your compendium is simply marvellous! CONGRATULATIONS. How you have managed to put so much stuff together in such a succinct, clear way evokes my utmost admiration. As G.K Chesterton said in a different connection, 'I don't have time to be brief.' You have obviously taken time."


"Please don't give up your enthusiasm. What you are doing is important. If people don't respond as you would hope, remember that most are busy with their own little worlds and don't have your vision."

Ilan Vardi, Laboratoire d'Informatique, l'École Polytechnique, CNRS, France

"Cool! I like your website [and] I have a couple of other preprints that might fit..."

Igor Volovich, Department of Mathematical Physics, Steklov Mathematical Institute, Moscow, Russia

"[p-adic physics] is an exciting topic indeed! You did a great job with your web-site!"

Kannan Nambiar, Rutgers University, USA and former Dean and Professor, School of Computer Science, Jawaharlal Nehru University, New Delhi, India

"Thanks again for archiving my papers in your site. I am grateful to you for keeping a site which can be so useful to those interested in serious research."

Saul Ares and Mario Castro, Department of Mathematics, Carlos III University, Madrid, Spain and Nonlinear Dynamics Group, Potificia Comillas University, Madrid, Spain

"It will be a pleasure and a privilege for us to have our work in your web-archive. We already knew about it and it has been our most useful tool during the work previous to writing our paper."

Gilberto Corso, International Center for Complex Systems and Department of Biophysics, Universidade Federal do Rio Grande do Norte, Brazil

"...congratulation for the wonderful site you are doing. I have felt very at home in your site, there is a mixing of organization and disorganization that is ideal for research. I mean, we are in the middle of the history of science and we do not know the right organization of the contents."

Claudio Bonanno, Department of Mathematics, University of Pisa, Italy

"Hello. Thank you very much for your interest in my paper. I already knew your website, so it was for me a great pleasure to know that my paper had been included."

Andy Sinton, Department of Mathematics, UC Berkeley, USA

"Thank you for your very helpful assemblage of information on zeta functions."

P. Babinec, Department of Biophysics and Chemical Physics, Comenius University, Bratislava, Slovakia

"I was about 10 years ago very interested in the connections between physics and Riemann zeta function, therefore I was very pleased when I have found your web page fully devoted to this field which is really excellent."

Christoph Weiss, Institute of Physics, Universität Oldenburg, Germany

"Congratulations on your home page on number theory and physics."

Thomas Sauvaget, Department of Mathematics, University of Nottingham, UK

"Thank you for your very informative site."

Srinivas Sridhar, Director, Electronic Materials Research Institute and CAS Distinguished Professor of Physics, Northeastern University, Boston, USA

"I have made numerous very enjoyable visits to your website. They have all been very illuminating."

Dhruv Bansal, Columbia University, New York.

"I've been reading through most everything on your website for the past couple of weeks. I'm fascinated. You've managed to collect together a great number of topics which interest me and which I seldom find concatenated in a single webpage. Thank you so much for taking the time and effort to put it together."

Gonzalo Gutierrez, Department of Physics, University of Chile

"Just to say thank you very much for your homepage!! Nice to find such interesting things in the web, like the relation between number theory with physics...

By the way, I am completely agree with your opinion about the Academia."

Bob Marcus, associate professor of computer science and mathematics, City University of New York (1973-1984) and st century mathematics. It is a great tribute to you that you created it without much outside funding."

Kevin Knuth, Physics Department, University of Albany (SUNY), New York (formely of NASA)

"I stumbled upon your web pages containing a compilation of many exciting links related to zeta functions and entropy.

I am looking forward to delving into your web pages...it seems to be a gold mine. Thanks for taking the time to put it together...it's a lot of work."

Germán Sierra Rodero, Instituto de Física Teórica, CSIC, Madrid

"I would like first of all to congratulate you for the interesting and useful web page on number theory and physics... I have learnt quite a lot from it!!"

Alexey Kuznetsov, McMaster University, Canada

"I enjoy reading the articles and other information on your number theory and physics archive, I like what you are doing with it. I wonder if it is possible to add my two recent articles about the Riemann zeta functions to this archive?"

Dániel Schumayer, Department of Physics, University of Otago, Dunedin, New Zealand

"...I will add a reference to your magnificent website. It is indeed nicely organised and a great source for someone who is interested in number theory and its applications in physics.

I hope you keep this website online and up-to-date. It is an invaluable starting point."

Dhruv Bansal, University of Texas

"When I started graduate school I was a big fan of the Number Theory and Physics archive you maintain. I considered it an invaluable resource for ideas on possible research directions. Life intervened, however, and I now find myself (happily) studying...[complex] networks... But now I've rediscovered your website and I think I'd like to start making some connections to my present work."

Hans Sauren, Zuyd University, Netherlands

"Great homepage with valuable information regarding physics & number theory. Please keep your homepage up to date and continue working on it. It's a great read."

Raghunath Acharya, Arizona State University

"I am taking the liberty of requesting you to list my preprint, entitled "REALIZATION OF THE RIEMANN HYPOTHESIS VIA COUPLING CONSTANT SPECTRUM", on your wonderfully useful website."

Tushar Das, University of North Texas

"I take this oppourtunity to thank you for putting up such a wonderful website - I am a beginning grad student and it is a real pleasure to read such passionately written mathematical writing."

Massoud Raji, Director of Iranshahr Institute (IT and Mathematics), Neyshabur, Iran

"In search of meaningful and understandable papers on Euler/Riemann Zeta Function I finally hit a very useful source in your http://www.secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/zetafn.htm

Thank you very much."

Lucian Miti Ionescu, Associate Professor of Mathematics, Illinois State University

"Just wanting to say that I find your site very helpful :)

Such "self-motivated and un-funded" work should be rewarded somehow..."

Matthew Burley, Wolverhampton University, UK

"I've just been reading your introduction p-adic numbers and adeles which, as someone with a limited background in the relevant mathematics, I've found to be the only accessible such article in existence. I thought I'd point out though that the link to it is broken..."

Bernhard Schiekel, University of Ulm, Germany

"I would like to thank you for your inspiring home page, especially for the 'number theory and physics archive'. In thinking about spectral functions in physics I've found in your archive very interesting references for my studies."

Wayne Kendal, University of Ottawa, Canada

"Your archive on number theory and physics has been a source of enlightenment for me. It has served as an introduction to a fascinating area of research that has helped direct my own research."

Gordon Chalmers

"I enjoyed very much your webpage. I will go through the details. Please keep up the work."

Andreas Martin Lisewski

"I hope that your web-archive on number theory and physics will continue its positive and fruitful evolution."

Serge Perrine

"Your site is a marvellous one, a source of inspiration that I appreciate very much. You must continue and be helped to progress."

Mike Oakes

"...it's flattering indeed to receive an email from the originator of such a splendid site as yours on zeta()!"

Julian Havil, Winchester College, UK

"I have been looking at your excellent website for some time. The Prime Number Theorem and Riemann Hypothesis stuff is very nice, if I may say so. I have nearly completed a book for Princeton University Press, part of which relates to these problems. May I ask you to consider agreeing to me including some of your work in it?

I am not a number theorist, in fact I am a schoolteacher, but I reckon I can puzzle stuff out and I need to get a feel for what I want to say about the RH and then learn it! I have tentative but quite rough chapters on them, partly based on your site.

I hope your financial situation sorts out. Wish I could help, but schoolteachers are not too flush!"

Craig Feinstein

"I very much like your website about the Riemann Hypothesis, as I learned a lot from it. I wrote a paper, that you may enjoy reading at http://arxiv.org/abs/math.NT/0312309 which argues that it is likely that the RH is unprovable. I am curious as to what you think."

Steve Dennis

"I discovered your wonderful website a few weeks ago as I was working through some ideas on the Goldbach Conjecture...please accept my appreciation for your excellent site. You have a gift for clarifying difficult concepts."

Matthew D. Heaven

"You have a marvellous site, and I have spent many hours browsing... As someone with some math background but none in number theory, I was amazed to discover that there is an exact expression for π(x)... The Manzoni animations are amazing also. I hope the university is paying you by now!"

Michael Smith

"I've been browsing your website for many many months now. I have found it an invaluable aid in broadening my understanding of the application of (prime) number theory to the physical world. It's a subject I've thought about much in my spare time over the last 3 years...

I'm basically a frustrated mathematician who ended up working in the City. I studied maths at Cambridge before switching to law in 1990 and latterly gravitating to banking...

... your website ... has been a constant source of inspiration for me... I have found the breadth of ideas you cover enchanting and a prime motivation for me to... return to the subject of my heart. It gladdens me to know that many other people are fascinated by the esoteric questions that captivate me. I wonder how many visitors your site receives and whether it has spurred any offers of research funding? As to the technical content I am probably not the right man to comment, but what it says and conveys about the Prime World is excellent. I haven't found anything else like it and you should be very proud of it."

Mike Scirocco

"I read through your introduction to Prime Numbers


and I was really impressed by how much information and references you included. It made for some very interesting reading.

Nice Job!"

Phil Caligiuri

"Thanks for a truly amazing website!!!

Please continue, if you are able."

Marcio F. Cerqueira

"I'm delighted by your fascinating page on primes and physics.

In sight of your 'message about the future of this site', I feel myself sad. I hope you have overcome your troubles."

Leo Aiello, Alberta, Canada

"Thank you for your wonderful website."

Patricia Hoyt, Jacksonville, Florida, USA

"I have been browsing your web site, and I have been very impressed by the site's organization, the quality of information, and the clarity and simplicity with which the information is presented. It is extremely well-written. The imagery is outstanding: I especially appreciated the animated prime counting function.

This is one of the best web sites I have seen in a long time. (I build large, complicated web sites for corporations and I tend to be critical.) A person could spend ages reading this fascinating web site. Congratulations on your excellence!"

Don Frisby, Winona State University Winona, Minnesota, USA

"A big 'THANK YOU' for your wonderful and inspiring website. Such a wealth of info I never expected to find at one site."

Arthur Denburg

"I am a non-mathematician, but I have recently become very interested in prime numbers. I found your website today, and I look forward to revisiting it often - if it continues to exist."

Jayne Boots

"Hello, I am an interested student who enjoys studying mathematical curiosities such as the Riemann hypothesis. When I found this site I was ecstatic. It provided me with vast amount of current information on modern physics and number theory...I appreciate any help you can give me and hope you keep up with this website because it is a great idea. After looking through your site I really do believe mathematics is beautiful...

Thank you."

Clay Turtle, Green Cove Springs, Florida, USA

"Just a line to show appreciation for your efforts and support of this work. Helping others to better understand the nature of the world in which they exist is a goal worthy of praise."

Sascha Richter, Frankfurt, Germany

"Your website is the most complete and interesting about the Riemann Hypothesis and the primes I know, congratulations!"

C.E. Nichols


I really like this site (especially the films part...wow!) ...thank you for a wonderful site!"

N. Sharma

"That's really a great site you've made. And Google has done a good job too to rank you number one :)

I was looking for some resources to study something about the distribution of primes when I landed at your site. This is a great section you've made. Its been a great start for me.

Do keep maintaining and adding more stuff."

Pablo Orellana

"I would like to congratulate for your superb web page!

Thank you very much!

I have the highest conviction that the cold and thin air of Number Theory reserves for us a very deep and new vision on Physics... I'm amazed other people share the same deep hopes. Thank you!"

Joe Cooper

"Thank you for your website!"

Tony Smith

"Your web site is fascinating to me, and I have linked to it from my web site. I was very unhappy to read on it about your financial situation. (It may not help much, but I just ordered a copy of your book from Amazon.com.) I also like your music, and your idea of anti-copyright freedom for music... I wish that the government were sufficiently enlightened to see that your web-site-work is important for maintaining a high culture, and that they would pay you a living wage to do what you enjoy."

Pravin Madhavan

"I checked out your website, personally I think this website is the most complete on Riemann's Hypothesis and prime numbers."

Sajid Umerji

"I found your website...and would like to commend you for the service you are providing to the mathematical community - your site is a truly valuable resource and a pleasure to read."

Philip Vermiglio, Michigan, USA

"It was quite heartening to find your math website. It's a passionate work of art


You should get paid for doing such a high-impact website."

Xiaoyue Guan

"I like your website and it is very informative."

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"I am astounded at your website and the elegance and precision with which you express yourself...Good luck with all your projects.


Your work is just incredible!!!"

Tom Messenger

"Just found your page thanks to the announcement about a possible proof of the Riemann hypothesis.

I come to this from purely a rank, amateur, standing but nonetheless, your explanations were very easy to follow.

If you should ever feel so inclined as to explain the theory of relativity likewise, especially as related to the speed of light, etc., I, for one, would enjoy reading it. Every time I see a layman's description of same, I come up with far more questions than answers.

Thanks again, it's been an enjoyable evening reading your webpage."

Clayton Bauman, Hillsboro, Oregon, USA

" I am writing to thank you for your web tutorial on the distribution of the primes and the Riemann Hypothesis. Even though I have a minor in mathematics and I understand complex numbers, the numerous articles and books I've read to try to really understand the Riemann Hypothesis have been no help to me, being clogged with empty symbol manipulations. Your tutorial is a breath of fresh air as you logically and patiently follow the historical path of human thought about the primes from Euler's zeta function to its analytic continuation...There is one more person in the world who really grasps the Riemann Hypothesis now!"

Reg Brooks

"First of all, thank you for your great site(s)!


Thanks for looking and keeping our minds alive!"

Albert Worley

"I'm considering doing my senior thesis on quantum chaology and have read much of the material from your site...Thanks for all the amazing work that went into your site."

Peter Bantowski

A brief note to express my appreciation and admiration for what you've been doing. Came across your URL while digging around for info on the perennial Mystery of the Primes and the pivotal role played by the zeta function in the investigations of Riemann et al."

Russell Johnston

"...thank you very much for taking the great trouble of organizing and establishing your website; and not least the courage to do so: it's been of real use to me, above and beyond other resources on the net, which a less competent site would not have been."

Paul Okolo

"First, I must commend your efforts at bringing such tremendous understanding to a single location. Your hunch is absolutely correct that there is something very fundamental about the positive integers that has been inaccessible for a long time. It has been inaccessible not because of its difficulty but rather for its absolute beauty and simplicity.

Clearly, the solution and explanation appears to be the most beautiful thing that I'm sure a mind can possibly contemplate of which the explanation to Riemanns Hypothesis and the behavior of the whole class of L-functions is simply an integral but small part of the puzzle!

Sadly, how does one share such when one is not a publishing mathematician nor is one a recognized academic? The hype around this certainly makes it almost impossible to reveal. However, the implications are breath-taking."

Paco García

"I just wanted to tell you I love your site http://www.secamlocal.ex.ac.uk/people/staff/mrwatkin. There is a lot to learn there...

Greetings from a computer engineer from Spain."

Rohit Gupta

"Namaste from Jaipur, India. I have been trolling your website for the past couple of days and I think I will be stuck here awhile. I still have to see all the sections, there are so many!"

Kieran Larkin (Australia)

"Over the last half dozen years or so I have found your zeta webpage to be a regular source of insight, amusement and very useful references. Interestingly your site does not seem to contain the following recent paper..."

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