The American Scene; Job Hor: Math

I again in the 50s. Temperature is right now 31 degrees at midway, 30 at the American scene, a series of pre -recorded programs providing a closer look at those things which form our contemporary society, produced by the Illinois Institute of Technology and Cooperations at WMAQ. The discussion today will consider job horizons in mathematics. Now here is our host, Don Anderson. Good morning and welcome to the American scene. My name is Don Anderson. Today we're going to consider the job horizon in mathematics, one of the oldest and most basic fields of science. It is also one of the most dynamic and rapidly growing professions in the American scene. Mathematics has always been a fundamental importance in science and engineering, but its horizon as a field of employment has become greatly expanded with the advent of the electronic computer. A wide range of job opportunities has

appeared with the need to translate business and scientific problems into mathematical terms for computer solutions. As in the other sciences we have discussed in this series so far, mathematics may be divided into two broad areas, pure or theoretical mathematics and applied mathematics. The distinction is one of approach. The theoretical mathematician seeks to increase basic knowledge without necessarily considering its use. The applied mathematician seeks to solve practical problems. Private industry is the largest employer of mathematicians, primarily in the aircraft, missile, space, and electrical equipment industries. Education and government are the other major employers. The outlook for the future is for continued rapid growth in employment of mathematicians in all areas. To be successful in the field of mathematics requires a well -rounded and extensive education. The advanced degree is a necessity for an increasing number of jobs, but the rewards can be high for

the imaginative, curious, logical individual in this field which is so basic to the developments of the future. To help us better understand the job horizons in the field of mathematics, I am pleased to welcome this morning, Dr. Heim Reingold, Chairman of the Department of Mathematics at IIT, and Mr. Benjamin Mitman, Manager of Computer Applications at the IIT Research Institute. Good morning gentlemen, thank you for coming. And I think perhaps we might best start by defining what a mathematician is. Most of us have an idea of a man who sits down with a sheet of paper and works on long figures of columns of figures all day long. Is this really what a mathematician is? Well, actually a mathematician is one who tries to avoid adding numbers. He may try to devise methods which will make it unnecessary for him to add. But in order to answer what a mathematician is, perhaps it'll be better to try to define what mathematics is.

And even though there's no time or place here to give a lengthy, exact definition of mathematics, perhaps the simplest way to convey the idea of mathematics is to say that mathematics is the language. Now, whereas in everyday life, in commerce or writing letters, the English language is enough to convey one's ideas in a field of science, our language of English or French or whatever one may be using is simply not enough. And it is the language and the symbols of mathematics which have been developed to represent scientific ideas and then pass them on to other scientists who understand the language and has to explain the things that they are talking about. So that perhaps the simplest and shortest definition of mathematics would be that of a language of science. And a mathematician basically would be a person who

is schooled and expert in that field. In fact, the mathematician is notoriously very poor in calculating and in using and working on long -term computer. The advent of the computer, I think, has helped the mathematician in this vein. He can now use a calculator, an electronic computer, to get the right answer when he's adding up a comma figures. Well, there is a little story told in the history of mathematics about a certain famous mathematician whose name was Goss. And Goss, who was a little boy, was a genius of prodigy. And the story is that he was in school and the teacher tried to keep him busy. And one day, they each turned in order to keep him busy, asked him to add up the numbers from one to one hundred, hoping that little Goss would be busy for an hour perhaps. Whereas he came up with an answer in a few seconds. Well, if I had a black foot, I would show you what he did. The tricks he used in order not to add. He simply used that as a mathematical progression and had the answer in a second. In other words, he

showed the true spirit of mathematics in trying not to add numbers from one to one hundred and get the answer. And developing relationships between numbers and working with that. Right. There seems to be then several levels of using this language. In the introduction, we mentioned the theoretical mathematician and the applied mathematician. They evidently used the language in a different way for different reasons. Is this correct? Well, the applied mathematician has in his repertoire the same tools that the theoretical mathematician has. They have essentially the same background. Their orientation perhaps is somewhat different. The applied mathematician will use the tools of mathematics to help solve physical problems. Mathematics has been called the Queen of the Sciences. It's sometimes called a handmaiden of the sciences. In the case of the applied mathematician, he is employing mathematics in the handmaiden sense

as a means of solving problems that are of interest to the physical sciences, for example. Let me make this comment. In the past, we used to talk about applied mathematics and pure mathematics. There are many branches of mathematics. There's geometry, there's algebra, there's topology, there's two of numbers, there's analysis, and so forth. And we usually referred to that branch of mathematics, which was most commonly used in theoretical physics and engineering as being applied, and certain branches of algebra or geometry or number theory, which were not used by these people as being pure. But this is no longer true. There's hardly a branch of mathematics, which has not found its use, whether it be algebra or geometry or analysis. And so that the terminology now is to speak about the usage of the material rather than material itself, and we speak about the pure mathematician or the applied mathematician. The distinction being

not in the kind of material he deals with, but how he uses the material. Whether if his interest is largely the body of knowledge and its properties, for its own sake, for its own beauty, then we call him a pure mathematician. If his major interest, although he may be just as scholarly as the pure mathematician, but if his major interest is that of using that in conjunction to apply problems to interpret results to structure things, then we refer to him as an applied mathematician. An example of this is the field of what's known as Boolean algebra. This was a field of logic, theoretical mathematics, that was a very, that is a very important area of pure mathematics. The Boolean algebra has become the tool of computer designers today. It's a tool which allows a designer of a computer to describe in very succinct concise terms the structure, the internal

structure of the computer. And as a result, he by means of using symbology, the symbols of Boolean algebra, he can describe the problems that he would like to solve with the computer and as a result, and even produce a description of the computer in symbolic terms by using Boolean algebra. I would like to only add this since Ben here mentioned Boolean algebra. Boo was a British mathematician over about a last century, and I'm sure had he come back to life today, who would have been the most surprised man to find out that his material is being used by so many applied scientists, like engineers and physicists, because this was, well, I don't know what was heard from his mind. Do you think he'd be delighted with this trend? Well, it's probably he would be, but I mean, certainly his major interest was not in any application. He would be completely

astonished to find out that Boolean algebra is now such an important part of the, well, of the backfill of tricks that the electron engineer or computer man has. I think you may find that even today, there's a desire among computer people, I know, to have the quote pure mathematician become more interested in the computer from a theoretical point of view. Well, I was wondering whether the applied mathematician might not be expanding the body of theoretical knowledge when he works toward the solution of particular knowledge. Well, I wouldn't say he would be necessarily expanding the body of theoretical knowledge. And he's employing the theoretical knowledge that does exist. I think the emphasis in attempting to define the real structure of computers and the structure of programming is a mathematical problem that hasn't been yet considered by pure mathematicians. And I know there are many people in the computing field that would like to see some tell of

the pure mathematicians look at this problem. Well, let's talk about this business of the computer and automation. Is this not assuming the function, role, and job of the mathematician? I don't think you can say that. As a matter of fact, the computer has given many more jobs to mathematicians than it has taken away. As a matter of fact, the same question came up at a high school careers conference that I once participated in, and a young lady asked whether the computer will replace mathematicians. And I indicated to her that the computer has been giving many, many jobs to mathematicians. The only time that I could remember of anything coming close to a computer replacing a mathematician was something that happened when we installed the Univac 1105 at IIT Research Institute, or the Army Research Foundation at that time. The installation of this computer required that we remove many walls from existing office areas. And while this building was going on, one of our mathematicians came to me and he said,

I'm being displaced by a computer. So here was a case of displacement, but not replacement. And I don't think we will see many mathematicians being replaced. This question of whether or not people are still needed that is mathematician because of the emergence of the computer is a question that youngsters, young people as way frequently. And of course, one answer that we can give is that there is no computer that you can whisper in his ear, so to speak, and tell himself, this problem for me, or you, there is no computer that you can take a textbook of problems or no book of problems, put it on top of it and expect the answer to come out of the end. The computer understands only a certain type of language. It does not understand the ordinary language in which we, for example, discourse rise in here. And this translation of the mathematical problem into the language of computer understand is rather intricate and complex and it takes a mathematician, or at least someone who is

acquainted with computers and the theory behind it to speak to the computer. That's right. Certainly the development of more sophisticated languages would have to come out. Well, actually, the important thing is that we now work on problems that 10, 15, and 20 years ago, we would have completely not even touched because we would have acquired thousands of years of a man's labor in order to come about to some solution. And so obviously such problems in astronomy or some in physics were simply of a theoretical interest, but not of any practical interest. Well, for example, the space research work could not have been done without the computer because of a tremendous number of calculations that would be required. That is, we could never have put an object into space and when you consider the amount of calculations, the exactness with which we have to be able to calculate these things, it's a tremendous thing. Without a computer, this thing would have been completely

impossible, even though theoretically possible. But in practice, completely. Well, with all of these areas opening up, the emergence of the computer and the growing importance of the mathematician, how many mathematicians do we have in the country today? Well, it's somewhat difficult to give an exact number because there is, I suppose, there is a lack of an exact definition of what mathematician is, an engineer or physicist or any scientist who uses mathematics to large extent, sometimes becomes a mathematician. I would say that the total number of people that consider mathematicians in a sense that they paid used, at least one mathematical organization, and these mathematical organizations to pull out a directory, is about 12 to 15 ,000. That seems like a very small amount. That's a small amount. The interesting thing, as you

mentioned before, the number of people getting into this field via the computer route, there are estimates that in the computing business, there are the order of 50 to 100 ,000 people involved in programming and associated activities with the digital computer. Obviously, not all of these people are mathematicians in whatever definition you would want to give for the mathematician. But the opportunities certainly are now available to young people in this field, girls in particular, who, before, if they were interested in mathematics, they would generally be the schoolteacher in the Red School House. Today, many, many women are making important contributions in the computing field. One of the leading and earliest programmers in the field is a Dr. Grace Murray Hopper, who has done a considerable amount of

important work. There are opportunities, but the need for mathematically trained people has also been reflected then in a need for improved and increased education. Here is a problem, then, that we find in the educational domain, how do you train the number of people that you need in these fields, not only in computers, but in applied problems, the use of mathematics in a number of physical areas. Well, Dr. Rangold is the head of the department at IIT. How do we train them? Has there been a big change in that? Well, in training with mathematics, you have to consider different levels, so there's the bachelor's level, the master's level, and on the doctoral level. Now we have in this country 2 ,000 colleges. Those are the 1200 degree grantings, and only about 75 or 80 give the PhD degree

mathematics, and the number of PhDs given in this country has somewhat fluctuated between 3 to 400. Which is another amazing thing. When you consider that every college tries to get at least one person with a PhD degree, you arrive at such an accuracy that it is very, very serious. Now, it is also statistically a statistical fact that all the 3 to 400 PhDs that are put out in mathematics have got to non -academic jobs, government, industry, and software. So only about 150 to 200 are available for the universities, and this number is indeed insufficient to cover the needs of the country and the shoulders. It's barely enough to resupply the needs as people retire. I'm sure the number of people retiring perhaps exceeds the number that are getting PhD degrees. Of course, there is a considerable amount of benefit to be derived from people

who have less than the PhD degree. I don't know what the number of master's degrees in mathematics every year, but there are opportunities for people with bachelor's and master's degrees also as particularly in industry. In the university, of course, the PhD is pretty much a requirement. Well, I think another way in which this particular shortage is being alleviated is the fact that many non -mathematicians who are originally trained as engineers, businesses, chemists, biologists find themselves working in mathematical problems. Then they take courses in mathematics and then go to university or study their own. In a sense, and in practice, they become mathematicians. They function as mathematicians. In a sense, many people from other areas enter the profession and enter the field. In some of our earlier programs in the series on careers, we brought out the emergence of so many new fields in traditional areas of science and the interdisciplinary growth of fields within the area of science. Is this true in

mathematics as well? Yes, this is absolutely the case. There are a number of fields. For example, there is a field called mathematical biology in which a person studies biology and mathematics and then studies biology by means of mathematics. Another area would be the mathematical linguistics, the combination of linguistic studies and mathematics. MIT, for example, is offering a graduate program in mathematical linguistics. Interest in this area has grown since efforts to produce automatic translations of one language to another. There is the area of econometrics when this is a study of economics, a means of mathematics. And this, of course, is a field that has been active for one number of years. And there are other areas in which interdiscipline nature. Probably one area where one would least expect to find the mathematician is in business.

The use of mathematics during the war in an area known as Operation Research, this is an area that was developed during the war to attempt to solve certain military problems such as to optimize the possibility of finding a submarine in a given geographic area. These techniques that have been developed are now being applied to business problems, to attempt to maximize profit or minimize loss within a business organization. So you find that the mathematician in the executive offices of business people sometimes not very well understood, but they're there and they're making a contribution. As you pointed out at the beginning, Dr. Rangel, you really can't define a mathematician anymore today. It's not a compartmentalized man who has a particular training and is labeled mathematician. As a matter of fact, in many industries, a person trained in

mathematics works as a member of a team and they may even have the type of engineer. And there may be a few people working together or the engineer, the physicist, the sets off the problem. The mathematician may help in solving it, perhaps program it, and then the problem is of interpreting the results. But the mathematician over this type cannot be completely ignorant of the setting up of the problem or interpretation of which results. It has to be able to talk. The ivory tower disappears when you're around the table with engineers and physicists trying to solve a specific problem. As a matter of fact, I don't think you would ever have heard of a mathematician as being the president of a company, but yet today there are a number of small companies which are becoming larger companies, which have been organized, developed by mathematicians, to provide specific services that are necessary. Services, while you mentioned the actuarial field, there's one actuarial consulting. Another is

programming, computer programming, service organizations. Their organization is with the names like Computer Sciences Corporation, Computer Usage Corporation, Informatics. Organizations that were formed by people in computing and in mathematics and many of which have grown to quite large organizations, two to three hundred people. Well, the range of opportunities then is almost limitless, it seems, that if you don't want to work for someone else, you can start your own business. Very many people do that. The need for this exists today, and it will continue to grow. Let's talk a little bit more about this, the effect of the computer on the mathematician. It has created, the computer has created jobs for more mathematicians. Is it also used by the pure or theoretical mathematician to help expand the body of knowledge? Well, yes, definitely it is being used. There are many

theoretical problems, particularly in the number theory, that has been, have been unsolved for many years. And they still are unsolved. And attempts are being made to find information or approach the solution. Well, it's not the solution at least to get some information about these problems, true to use of modern computers. Well, I don't want to get too technical, but there is a theorem called Famous Life's Theorem, which is 700 years old. The Goldbach injector, which is unsolved. And much more information about these properties of the numbers that are going to those theorems have been found on computers. And it certainly is very helpful. And there are areas that would not at all seem to be applicable to computers, such as proving theorems of the conductor Rangel has been discussing. There are some research efforts now underway to attempt to use the computer in

a way that these theorems can be solved. Methods of the use of computers, the methods of defining problems, which would be then applicable to computer solution. Of course, the most important part of the computer is the fact that it can give numerical solutions to some very, very complicated problems. Problems that could take years to get a solution and numerical answer, the computer is now unable us to do that in sometimes in a few minutes. Now, most of the problems connected with space, the theories well known. These are old theories, Newtonian mechanics, Kepler laws. But the solution of these problems was simply fantastic in terms of labor. That's right. Well, just the problem of trying to put a ranger on the moon would be an inconceivable problem to try to solve without the capabilities they're provided

by. The mathematician through the computer is also moving into other fields and they've indicated that the business world is now making a greater use of mathematicians. He's also moving into the field of social science as well, isn't he? Yes. I might say this thing speaking about the business world. Or we, Illinois Tech, had a very interesting experience a few years ago where one of the leading banks in this area has encouraged one of its employees, a math major, to get his PhD degree on our campus in order to set up the computer and other problems. And he is now a very prominent member of the administration of the banks. What kind of rewards can a person expect to get from the field of mathematics financial rewards? Well, I would say it would be very similar to engineering and the sciences. It simply means that the beginning person with a bachelor's degree just going out into the field would probably start out with somewhere between $550 to $600 a month. And a person with a master's degree would probably start with perhaps $750

a month. And a person without experience in the PhD degree usually starts with at least $1 ,000 a month. I would roughly estimate depending. And the upper limit, well, they are. I know many universities now that are paying their top professors $25 ,000 a year. And of course, in industry or arts corporations, if he reaches management levels, I suppose this could be much larger. There have even been cases of high school mathematics teachers, women in particular, that have made piles on the stock market. An added use of your knowledge. I would not. No, you should make that. Briefly, what would you say to a young person who wondered whether he should go into the field of mathematics? Is it a good area for people to consider getting into today? If a young man or a young woman is talented in mathematics, the opportunities are there. I would say one thing they should do is

plan on getting a very, very solid mathematical education, education in physical sciences. And I guess the keyword would be the well -rounded education because as Dr. Angle indicated before, the mathematician deals with different kinds of problems, different types of disciplines, so the well -rounded education is great. I just want to make one comment is that the educational mathematician, or does that matter? The education of any individual mathematics begins not in college, but in kindergarten. The early start has made it. Well, thank you very much, gentlemen. This has been a most interesting discussion. And as is true in so many programs, we have hardly time to even begin talking about it. But you've shown that the field of mathematics is a broad -ranging field, and it requires inventive, curious people, and there are job opportunities for interested people in this field. Thank you, Dr. Rhine Gold and Mr. Mittman, and this is Don Anderson, saying good morning for the American scene.

This has been the American scene. Today's discussion, job horizons and mathematics. Add his guests, Dr. Hyme Rhine Gold, Chairman of the Department of Mathematics at IIT, and Mr. Benjamin Mittman, Manager of Computer Applications at IITRI. Host on the series is Don Anderson, Director of Public Service Broadcasting for IIT. The American scene is pre -recorded and produced by the Illinois Institute of Technology and Cooperation with WMAQ. Next week's topic, job horizons and nuclear science will be discussed by Mr. Charles Terrell and Dr. William Lowe, as we continue our investigation of the American scene. What do your dollars do? The dollars you give to Chicago Easter Seals? In general, your dollars help crippled children and adults lead happy, productive lives. More specifically, one dollar helps pay for orthopedic equipment. Five dollars provides a physical, occupational, or speech therapy treatment at one of the two Chicago Easter Sealed Treatment Centers. Any amount you can give is vitally needed. Please be generous. Help those who look to you for aid.