Tuesday, January 20, 2015

André Weil on Gauss

I'm not trying to revoke the history of the 20th century by Bourbaki before the late Grothendieck. I'm not a historian and not a nostalgic mathematician. Rather, I would like to reminisce the phrase by one of the greatest mathematicians of the 20th century, André Weil, who was admired by Japanese mathematicians including Prof. Kunihiko Kodaira of complex algebraic geometry.

Other words by A. Weil (not his sister Simone Weil) were usually cited in French or in English translations like Wikiquote, but I found out that the very famous phrase is not well-known to non-Japanese mathematicians when I googled on the web. The followings are my quotation of his words from Japanese reference.

(night of 10-Oct-1955, when Weil came to Japan, Fuji hotel.)
"Well, start with your own idea.
Gauss did like that.
You start like Gauss as well.
Then, soon you will realize you are not Gauss.
It is OK.
Anyhow, start like Gauss."
(by Weil, a feeble translation by Makoto Sakurai)

Some mathematical physicists misunderstood these words were by Atiyah or Serre, but it is not true. In the original bibliography of the complete posthumous works of Yutaka Taniyama (1927-1958), it is written at the first page of the article "In touch with A. Weil" (page 199-208 of the second edition, 1994).

The words were so famous that they were cited elsewhere in different Japanese expressions, but the original precise Japanese did not appear at the Sugaku seminar or Japanese popular literature.

In the above, I did not mean to reflect the past mathematics, but I meant young mathematicians and mathematical physicists were extremely inclined to copy-and-paste the works of (Fields / Nobel or any other kinds) medalists. The grant agency is very crucial in the career of young scientists, so that the competition is harsh.

However, it is a sad situation that some wrong translations of physics works by "pure" mathematicians are prevalently overwhelming the original works by either pure mathematicians or (let me say) native physicists. I do not accuse any individual case that I regret in this post, but let me recall this episode of Weil as a warning against such prize-winners.

As I wrote above, I do not like to cite eminent people's articles (including Weil). Nevertheless, the copy-and-paste machines on the web are so harmful that their plagiarism will eradicate the sincere efforts of young talented mathematicians and physicists.

It is like Japanese classic musicians; the music students are said to learn the music score very well, but there is no joy of discovery. As I'm not a musician, let me say about mathematics that the abroad conferences or symposiums are in any case very rejoicing.

On the other hand, the Japanese people are not so involved with the speakers when it comes to the cases of Japanese symposiums or international conferences in English. The organizers are trying to ask questions, but the communications among participants and speakers are not so active. Well, there are language problems as well, but I said to the Chicago people, "my English is not so good, but it is better than ordinary Japanese." (The Chicago person said that my English was very good.) A French mathematician said language was not the problem, the problem was always mathematics.

Saturday, September 27, 2014

Weighted Arithmetic-Geometric means and logarithm

This was what I wrote yesterday after the April visit for the University of Chicago. This short article is written as a test of MathJax and the complement of the freshman math lecture at the year 2011. There is an extraction of my 9 page PDF file. \begin{eqnarray} \sum_{k=1}^N w_k a_k & = & w_1 a_1 + w_2 a_2 + \cdots + w_N a_N \nonumber\\ & \ge & a_1^{w_1} a_2^{w_2} \cdots a_N^{w_N} \\ & = & \prod_{k=1}^N a_k^{w_k} \nonumber\\ & := & \prod_{k=1}^N \exp \left[ w_k \ln a_k \right]. \end{eqnarray} The auxiliary conditions of antilogarithm and weight are as follows. \begin{eqnarray} 0 < a_1, a_2, \cdots, a_N \\ \Longleftrightarrow & a_k \in \mathbb{R}_{>0}, \\ 0 < w_1, w_1, \cdots, w_N (< 1)\ s.t.\\ w_1 + w_2 + \cdots + w_N = & \sum_{k=1}^N w_k = 1,\end{eqnarray}, where the equality holds if and only if a1 = a2 = ... = aN.

For the plan to avoid the misuse of ill-definition of general logarithmic function (of complex variables or matrix elements, or even some other completion of non-Archimedean / quantum dilogarithm ), I showed the inequality without using Jensen's inequality (convex inequality). [I used the elementary calculus of polynomials in one variable for N->N+1. Or, I simplified the forward-backward induction by a one-step backward induction.]

See the PDF resume of mine, later.

Tuesday, January 01, 2013

Gauss Way

Japan has already leaped the end of year 2012, but California is still before the beginning of year 2013.

The MSRI (Mathematiical Sciences Research Institute) at the Gauss Way, California, is planning a series of workshops: Noncommutative Algebraic Geometry and Representation Theory including
, but I cannot visit California in January 2013 for the following reasons.

1.  I have to teach my students as the academic calendar of Japan is written.
2.  I cannot afford to visit California without the financial support of Japan and/or the USA, which is on the verge of serious budget cut (fiscal cliff (財政の崖) or fiscal wall (財政の壁)).

About the no.2, I have more things to append. Although European people are still thinking Japanese people are "economic animals," it is not the case. Since the so-called financial bubbles, IT-bubbles, and biotechnology bubbles are gone within this/these 2 decades, Japanese people have been struggling to overcome simultaneous crises in the tax rate, the employment rate,  the welfare, and some civilian control of nuclear plants after the aftershocks of Tohoku earthquakes and Tsunami at 14:46, 11-March-2011 (JST).

On the contrary, before the Diet (Japanese Parliament or the Lower House) campaign at the December of 2012, I have done some electric annual ballot for the AMS (American Mathematical Society) vice-president, Boards, and Councils. The financial circumstance of AMS is not optimistic; as an AMS member of 8 years, I was asked for signature against the budget cut:

Tell Congress to Avoid January 2013 Sequestration

Although I am not a resident of the U.S.A., I am affiliated with the American Mathematical Society for a long term, including some eminent immigrant mathematicians from the overseas to American universities, but I do not cite individual researchers' names in this post.

OK. Let me go back to my personal financial problem. Even though I registered in the participants' list of the MSRI, they say they cannot afford to financially support my visit for the travel and living expenses while the vice deputy sent me an encouragement message about attending one or more workshops of the MSRI at the last year. I really interpreted this letter in the literal sense, but the U.S. mathematicians are now planning the January (9-12) 2013's San Diego, CA, Joint Meetings with the SIAM, the MAA(Mathematical Association of America) and so on, which encourage graduate students' NSF grant proposals with a little chance of travel expenses.

Needless to say, I am not a graduate student any more, but Japanese policy on the science development is not promising for post-doctoral members or part-time lecturers. Thus I was much interested in the events of January-2013, but neither Japanese researchers nor American institutes let me join in such important meetings since I have not obtained the (three or more) strong recommendation letters from eminent mathematicians in the world-wide. All I can do is write my original preprint from my original motivation, but the number of papers is not large.

As Carl Friedrich Gauss -- the prince of mathematics in the 19th century -- said, a genuine mathematician does not always have plenty numbers of recommendation letters; whereas he said "Few, but ripe" for his remarkable achievements in pure mathematics and mathematical physics by himself while writing his diaries.

Tuesday, October 09, 2012

Higgs Hunter

Last month, I visited Kyushu University, which lies in one of the southern islands of Japan, for the oral presentation at the Mathematical Society of Japan. Before the presentation at the morning session (at 21-Sep-2012) of algebraic geometry, I submitted my update of Ph.D. thesis with the elimination of some of my typos and obsolete references. I also noticed my change of permanent receivable e-mail address of the University of Tokyo. See Mixed anomalies of chiral algebras compactified to smooth quasi-projective surfaces and the slides uploaded at the researchmap database. The conference hall was at the "2nd Centre Zone" of the university, which was a little far from the Fukuoka (福岡) airport; we need to connect two railways of subway and local trains, and the transportation of school (semi-shuttle) bus was necessary from the nearby train station to the "Big Orange Station" at the entrance of Ito Campus.

My presentation was about the "Geometric Quantization of Wess-Zumino-Witten model" and not "Geometric Quantization of Chern-Simons theory". In addition, my presentation was a revisit of Spontaneous Symmetry Breaking by Nambu-Goldstone bosons and soliton's micro-local calculus (Dynamical Symmetry Breaking) of co-tangent bundle of beta-gamma conformal field theory without explicitly assuming the motivic integration of Kontsevich-Soibelman or Feynman's oscillator integrals. See the English abstract for the conference at the MSJ official website. The latter half of my presentation title was on the "virtual localization formula", but it is not the WKB (semi-classical) approximation of pre-quantization and polarization after the Oxford's school of differential geometers. My trial was to formulate the (topologically half-twisted) Super-Conformal Field Theories as an extension of Wess-Zumino-Witten term of level 1, which was claimed by N.Nerasov[2005] but not uploaded to the arXiv unlike proposed.

Last but not least, let me mention my travel airline briefly. The Skymark airline, which is a recently hot topic of an LCC (Low-Cost-Carrier) airline agency, was used from 06:20am to 08:15am (Japan's Standard Time) at 20-Sep-2012, from Haneda (羽田) airport in Tokyo to Fukuoka in order to attend the domestic meeting of the Algebra Session.

However, the returning way back from Fukuoka to Haneda was terribly delayed. I first waited more than half an hour at the Big Orange Station, which made me thirsty and sunburnt. I arrived at the Fukuoka airport one hour before the schedule while I left the conference hall at 14:00. I had to wait for the boarding at the gate 2 since the aircraft of LCC was delayed to arrive for the schedule of departure time 17:55, which was postponed to be after 18:15 and I had patiently awaited since otherwise I would have to wait for the next LCC flight of more than 2 hours later at night.

Unlike supposed, my oral presentation was not performed regularly because of the irregularly worked projector from my EEEPC901 net-book with Fedora 17, which I used for several times and demonstrated twice within the conference dates. The Algebra Session was tight in schedule, so that I used my OHP backup for the optical camera with the use of my green laser pointer. I hope my above-mentioned slide file will be useful for someone who is interested in the relation between the Higgs mechanism (of physicist's sense) and the chiral algebra (Hamiltonian method on the worldsheet Riemann surface) theory with the base change of target space Kaehler manifolds (Lagrangian method of factorization algebra).

The chairperson's question was about my next research plan and I said "I have worked more than 5 years on this topic. From the beginning around the AMS talk of Okounkov, an extension to non-toric cases is a long-standing problem. I also would like to apply the DGA method to quantum invariants." It was because Japanese mathematics is under a serious view from the outside society and Japanese mathematicians have to explain the value to the general public; since Japanese economy faces 20 years of serious decline and the universities are under severe budget cuts.

In the good-old-days of Greek geometry, mathematicians can naively and Platonically quote "Evidently Euclid did not stress the practical aspects of his subject, for there is a tale told of him that when one of his students asked of what use was the study of geometry, Euclid asked his slave to give the student threepence, "since he must make gain of what he learns.""

Nevertheless, nowadays world economics suggests a serious reconsideration of our position of academics in the real-world of general public. So I just started my oral explanation of presentation by saying "If you have to talk to a person in an area other than mathematics, you can appeal algebraic geometry has useful applications (such as blow-ups) to natural science, and not just calculus alone".

I hope I can keep my trial on the recovery of academic value in the calculation-based financial society.

Sunday, January 01, 2012

Earth Top and Spin Rotation


Today I prepared some academic documents to submit, so that I did not have time to take a sufficient rest.

Indeed, we had another earthquake (fortunately far southern to Japanese islands and Tokyo) with Magnitude M=7.0. As the Energy Magnitude is (in a conventional definition) defined as a logarithmic scale of effective Joule energy, we had 1/1000 times Energy if compared to that of the Tohoku earthquake (M=9.0).


The image above "The Earth Top" (taken by me) is what I am preparing for the last two lectures of dynamics and electro-magnetics at the year 2012 (Winter semester of 2011) at Tokyo. We will compute the inertia momentum "I", diagonalization by diag(I1, I2, I3) for non-symmetric gyro top, and the introduction of the coordinate transformation.

Galileo's episode (made up by historians?) is quoted as "Yes, that's right" (Answer to "Isn't the earth moving?") This saying has several variations, such as "Yet the earth does move." However, at the era of Galileo Galilei, it was still possible to study mechanics as a mathematical hypothesis like the heliocentric model by Nicolaus Copernicus in the 15C's and 16C's. Galileo's accused point [1564-1642] was to study his relativity principle (coordinate changes between two inertia frames) as a guiding principle of real-world problem.

I wish a happy new year and good documents for (special) relativity.

Wednesday, December 21, 2011

Newton's Festival at the University of Tokyo

Dear friends;

My homepage is temporarily closed for some reasons (, but I preserve its files and information). For almost one year, I worked for my mathematics lecture [brush-up and undergraduate mathematics at the summer semester] as well as my physics lecture [brush-up and introduction to dynamics / analytical mechanics (including some classical integrable systems of tops with inertia momentum tensor), and electro-magnetic special relativity at the winter semester].

Here is some mini-blogs (I'm sorry it is written in Japanese) for this year; I have a Facebook account for more English posts (or sometimes in French, German, or Japanese [from Twitter or Android cell phone]).


My old diary described my trip to a university of Japan, which had an "apple tree of Newton". Today was the "Newton Festival 2011" of Department of Physics, the University of Tokyo. However, as I explained above, I could not leave the lecture until 18:15, so that I could not attend the party at the Sanjo-Kaikan (山上会館) inside the Hongo Campus of the University of Tokyo.

As all of you must know, Japan is under the revival from the Tohoku earthquake at 11-March-2011, 14:46, and the nuclear crisis afterwards. (I explained some of the radioactivity information and radioactivity protection to my colleagues and students.) Therefore, I could not travel much for conferences or workshops far from Tokyo, so that it was very difficult to keep my research activity.

I wish you would have happy holidays and a "better" new year!

Best wishes,

Makoto Sakurai

Saturday, January 01, 2011

Japanese Rising Sun 2011


The sun is rising. I had observed before the dawn to the sunrise of New Year's Day 2011. The photos are listed anti-chronologically.

Have happy holidays and a good new year.

Makoto Sakurai