Dears,

There will be no real report this month, at least not in the form represented by reports one and two. The reason for that situation is very serious: I lost my digital camera. Everything because of Martin who was visiting Jerusalem... but blaming him does not help - the camera is lost. I must have left it in a taxi or in a bank or at some other place. I tried but I could not find it. The memory card in the camera was filled with very nice pictures (since they are lost anyway, I may safely claim that those were the best pictures ever taken). There were pictures of Martin, there were pictures of Julia and Henryk Michalewski who also visited me, and there were pics of Jerusalem. And all those photos are lost, and there will be no new photos at least not until I figure out how to utilize the analog camera I have here. Among other things, taking digital pictures is easy - one takes 100 pics, chooses the ones that are OK, deletes the other pics, repeats the process. With analog camera I cannot apply this algorithm... Well, the pictures I took were not that good, so there is no reason to cry.

Maybe I would decide to buy a digital camera and take some pictures and make a regular report, but I got these doubts: is there any point in taking any pictures anymore? Isn't it the case that all pictures were already taken? Interested in pictures from Israel? Check out this place or that site, or these pictures or that album. You may even study the other political end or even the other side.

So tell me, is there any point in taking more pics here????

What I wanted to show you...

I wanted to show you the Wall / Fence that is under construction here. There is a lot of opposition to it, and the arguments range from humanitarian ones to opposing the fact that the Fence / Wall is constructed outside the Green Line (pre-1967 border of Israel). I have to admit that I see good reasons for having this barrier, though I believe it should be built more along the internationally recognized border. The reasons for having the Wall are included among those presented on the following (very explicit and drastic and only for people with strong nerves) pictures: one, two and three. An analysis and description of the topic is also provided by JVL

Opposition to the Wall/Fence is presented in many sites, for instance here, or here or here. But I think that (as usual) the English Wikipedia gives the most balanced, complete and the fullest description of the topic (again, it is here).

More pictures of the wall/fence and specifically of that not far from Jerusalem.

What's on my mind...

Many people have heard and thought about the cartoon row. I have to admit I make no sense of it whatsoever. I tried to read various rationally looking explanations, I spent lots of time thinking and the conclusions I am arriving to are scary: whatever I say or write may and thus will offend somebody and therefore I should shut up or even better just die. In all that turmoil I am somewhat touched by this letter. I am still trying to understand the problem, reading various opinions etc, and you meanwhile may consider this:

     

I have to admit that the events around that crazy man added to my confusion. Should there be limits on Freedom of Speech and if yes how should they be decided and defined?

What's on my mind...

In December 2005, a colleague told me ... because you are against Applied Mathematics.... This sentence repeatedly returns to my mind since then and I feel I got to address the question: Am I against Applied Mathematics?

I could dismiss this question with a simple note that both my Mom and my Wife are applied mathematicians, so if I were against applied math in any degree, I would not be able to write the present page. I would be plain dead.

But, of course, this is not a proper way to answer a serious (after all) accusation. It also does not say a bit about my opinions on Mathematics etc. So let me try to elaborate somewhat on this topic, hoping that at some moment in future I will further expand this note. Maybe after getting some feedback from you?

First of all, Mathematics, or as I would prefer to say Mathematical Sciences, is a huge area of intellectual activity of human beings. I mean HUGE. Very much like Earth Sciences, Social Sciences or Life Sciences, Mathematical Sciences include many subareas with different cultures, traditions, methodology and goals. If you look at 2000 Mathematics Subject Classification you will notice that the applied part of mathematical sciences is somewhat underrepresented there and is put more towards the end of the list. Or maybe I should rather say that applied areas of mathematical sciences are crowded at the end of the list. Well, there is a good reason for this: while Statistics, CS, OR and/or Mathematics Education all originated in Mathematics and they do belong to Mathematical Sciences, they are not Mathematics anymore. I believe that almost all of modern Applied Mathematics is not (my) Mathematics. These branches evolved into totally different areas of human activity, with their own cultures, traditions and gurus. When a statistician talks to a mathematics education person, they may be a good example of an interdisciplinary research, but they better be aware that they are using different languages and disjoint references. Let me give an example of a situation like that (though not fitting exactly the context here). Some time ago I talked to a Polish life scientist working in the US about our needs related to our research etc. After some time I realized we are using the same language (Polish, BTW) but we do not understand each other. The most extreme example of differences is:

We talked about our work, but the work styles are totally incomparable. While you may say that I am slow and not so clever, you should not even dream about saying this about Saharon Shelah. And look at the ends of my reports to see how long it takes us to read/revise his papers.

What I am trying to say is that the concepts of research papers in Sciences and in (my) Mathematics are different. Applied scientists tend to write more papers, they have more publications, they also read more papers. In (my) Mathematics we do not write so many papers, and we do read less (in sense of numbers of papers read) - it is because our research involves activities of different kind and our papers impose different requirements on the reader. It is not possible to read (my) Mathematical Journals like novels or even textbooks. Reading a research article requires a lot of brain activity in addition to the actual reading process, typically one reads a paper from the very beginning to the very end without omitting a line. Martin stresses that

Reading a mathematical research article is a bit like reading the score of a symphony (only more so): The music is not on the paper, but we have to recreate it in our minds.

(He says this description should not be attributed to him, he heard or read this comparison somewhere.)

Actually the best proof that Applied Math is not Math is provided by applied mathematicians themselves: they managed (as a group) to arrange for themselves much higher salaries than those of regular mathematicians.

Thus in my mind Applied Mathematics is separated from (my) Mathematics and I know that it is just not my cup of tea. I do not read their results, but I also do not expect them to be interested in mine. I am just busy with (my) Mathematics and maybe sometimes I try to promote its values. But this does not mean that I am against everything else. I am not against Physics, Chemistry or Applied Math.

Have you noticed that my restriction above? Yes? So what is this my Mathematics ? Well, this is what many people call Pure Mathematics and what I prefer to call rather Theoretical Mathematics. It is very difficult to say where Theoretical Mathematics starts/ends but if you meet it you will surely know that this is She. One of Her characteristics is that statements are followed by PROOFS. The proofs are the essence/core of Mathematics. But we do not carry out the proofs for mere knowledge of the truth. Of course, the concept of the Truth is dear to my heart, but this is the beauty of the argument that is always the main reason for me to get interested in the result. A good negative example here is Four Color Theorem. The statement/result is somewhat interesting, but when the computer aided/generated proof was given, then I and many of my colleagues simple lost interest in the subject. The mathematical beauty of the argument got buried in the beauty of a computer code. Different kind of beauty, different kind of taste - for sure not mine.

To some extend the position of a mathematical proof can be compared to mountaineering. In that sport, getting to the top of the mountain is only somewhat important - most important is your route to the goal. If you are just interested in getting to the top, take a helicopter and fly there directly. Many (if not all) mathematicians declare that the main motivation for them is the search for beauty. I pointed to that both in the description of my research interests and in my letter on the YellowCake. And the proof/argument is one of the main sources of that beauty. As soon as you decrease the role of a proof replacing it by (for instance) computer simulations, you are not talking mathematics anymore. I do not say that the value of your activity is smaller by the fact that you do not prove (in mathematical sense) your claims, I just say that your activity is not mathematics anymore. In particular, I do believe that so called Experimental Mathematics is not Mathematics. It is an important work, but it is not the same kind of work that I am doing.

But I have to admit that I am very against some things, activities and types of behavior. I believe that we all should be against bad science, bad mathematics, all forms of pseudomathematics and all forms of charlatanry. Especially the latter one makes me mad.

I do respect all mathematicians and scientists working at different levels and in various areas, applied or theoretical, great and small. They all are needed. But I really cannot tolerate charlatans. I am generally a polite person so I do not fight them - mostly I avoid them, and whenever asked for an opinion I offer an honest one. Sometimes it is difficult to say that a person is a charlatan, as verifying the truth may require a specialized and/or advanced knowledge. But when you meet somebody claiming to be a mathematician who is about to solve the Riemann Hypothesis and this person is not a well known analyst - then you know who you are talking to. This reminds me that one day X told me that Y is a very good mathematician since he was working on Fermat's theorem. Since then I know what to think about Y.

What's on my mind...

This is the time of the year when we write reports and also when we are evaluated. I guess my evaluations are OK and essentially accurate (the full text of the evaluation is here). But one paragraph made me think:

Andrzej is a prolific researcher in the area of set theory and logic. However, his research is so esoteric that he has no real mathematical interaction with anyone at UNO, either with students or with other faculty. This tends to isolate him from the rest of the department. This intellectual isolation is unfortunate and creates an unpleasant atmosphere between Andrzej and other faculty. I would like to alleviate this situation so that Andrzej can feel more comfortable about his role in the department.

Esoteric is relative. Einstein in the Swiss Patent Office was conducting esoteric research (which, BTW, led to Annus Mirabilis Papers). Einstein in IAS was simply involved in the frontier of research. Same person, Same research. Of course, I do not dare to compare myself to Einstein, but as my friend put it

I would dispute the use of the word esoteric. The more appropriate would be plain advanced or even better highly advanced.

I really do not want to be pushy or over self-confident, but I do not feel esoteric when I visit HU, RU, KU and many other places. I do not feel esoteric when I present my research at conferences. And you know, there is a way to measure how esoteric your research is: go to MathSciNet. They have a new service there, MR Citation Database. Just use it (but unfortunately it is available only if you are a subscriber to MathSciNet). This is a new tool and it is not really fully functional, but it does give a feeling of how often people use your results. Of course I am not Shelah, but I think the results that are displayed there for my name DO NOT justify calling my research esoteric.

I was also given some suggestions for the next year (full text of that part is here). In the relation to alleviating my isolation the following suggestion/request were passed to me:

One specific suggestion is for Andrzej to encourage Math majors to give talks at the annual spring meeting of the Nebraska/South Dakota section of the MAA, and then to help them prepare these talks.

A friend of mine read both parts (III and IV) and his comment was

As they admit, you work a lot on things not related to your research and to help you they request more work of that kind?

Another friend wrote this:

The easiest solution to the problem, as they perceive it, would be to add a set theorist or general topologist to the faculty. It is unreasonable to expect from your undergraduate students to master set theory and other areas of mathematics on the level appropriate to work with you on any non-trivial topic.

Well, the suggestion of hiring somebody with me in mind goes too far, perhaps. I would be happy already if my wishes for some library additions were granted, but... I think I will not think about all this anymore.

Notes to myself - what I achieved in February:

To keep track of what I accomplished each month, let me note that in February:

A Polish report, somewhat disjoint from this one, is available here. The next report may be (but does not have to be) posted on Sunday, April 2th, 2006. I promise it will have some pictures from the Negev...

Yours,
Andrzej


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Last modified: Sat Mar 4 21:04:45 IST 2006