John von Neumann: biography and bibliography

Who is von Neumann? With his name are familiar to the broad masses of the population, the scientist is known to not even be addicted to higher mathematics. The thing is that he developed the exhaustive logic of the functioning of the computer. To date, it is implemented in millions of home and office computers.

The greatest achievements of Neumann

He was called a human-mathematical machine, a man of irreproachable logic. He was sincerely happy when he encountered a difficult conceptual task, requiring not just permission, but also the preliminary creation of a unique tool for this. The scholar himself, with his inherent modesty, in recent years, in extremely brief, three-point terms, announced his contribution to mathematics:

- justification of quantum mechanics;

- creation of the theory of unbounded operators;

- The theory is ergodic.

He did not even mention his contribution to the theory of games, the formation of electronic computers, the theory of automata. And this is understandable, because he talked about academic mathematics, where his achievements look as impressive peaks of human intellect as the work of Henri Poincare, David Hilbert, Herman Weil.

Sociable sanguine type

At the same time, with all his friends recalled that along with inhuman working capacity von Neumann had a tremendous sense of humor, was a brilliant storyteller, and his house in Princeton (after moving to the US) was known most hospitable and hospitable. Friends of the soul in him did not count and even for the eyes were called simply by the name: Johnny.

He was a highly atypical mathematician. Hungarian was interested in people, he was unusually amused by gossip. However, he was more than tolerant of human weaknesses. The only thing he was irreconcilable with was scientific dishonesty.

The scientist seemed to collect human weaknesses and quirks for a set of statistics of deviations of systems. He loved history, literature, encyclopedically memorizing facts and dates. Von Neumann spoke fluent English, German, French, in addition to his native language. He also communicated, however, not without flaws, in Spanish. I read Latin and Greek.

What did this genius look like? A full man of medium height in a gray suit with a leisurely, but uneven, but somehow spontaneously accelerated and retarded gait. A keen eye. A good conversationalist. He could talk for hours on topics of interest.

Childhood and Youth

Von Neumann's biography begins on December 23, On that day in Budapest, the family of banker Max Von Neumann was born Janos, the eldest of three sons. It is for him to become the John in the future for the Atlantic. How much in a person's life is proper education, developing natural abilities! Even before the school, Jan was trained by his father's hired teachers. He received a secondary education in an elite Lutheran gymnasium. By the way, with him at the same time studied E. Wigner, the future Nobel Prize winner.

Then the young man graduated in Budapest University. To his happiness, even in high school time Janosu met the teacher of higher mathematics Laszlo Rats. It was this teacher with a capital letter that was given to open in the boy a future mathematical genius. He introduced Janos into the circle of the Hungarian mathematical elite, in which Lipot Fejer played the first violin. Thanks to the patronage of M. Fekete and I. Kurshak, von Neumann, already at the time of obtaining the certificate of maturity, earned a reputation in the scientific community for a young talent. His start was really early. Janos wrote his first scientific paper "On the arrangement of zeros of minimal polynomials" at the age of 17 years.

Romantic and classic in one person

Neumann stands out among his venerable mathematicians for his versatility. With the exception, perhaps, only of number theory, all other branches of mathematics were, to varying degrees, subject to the influence of Hungarian mathematical ideas. Scientists (according to V. Oswald's classification) are either romantics (idea generators) or classics (they can learn the consequences of ideas and formulate a complete theory.) It could be attributed to both types. For clarity, let's present the main works of Neumann's background, while indicating the branches of mathematics to which they relate.

1. Set theory :

- "On the axiomatics of set theory" (1923).

- "On the theory of Hilbert's proofs" (1927).

2. Game theory:

- "The theory of strategic games" (1928).

- Fundamental work "Economic behavior and game theory" (1944).

3. Quantum mechanics:

- "On the foundations of quantum mechanics" (1927).

- Monograph "Mathematical Foundations of Quantum Mechanics" (1932).

4. Ergodic theory:

- "On the algebra of functional operators .." (1929).

- A series of works "On the rings of operators" (1936 - 1938).

5. Applied tasks of creating a computer:

- "Numerical inversion of high-order matrices" (1938).

- "Logical and general theory of automata" (1948).

- "Synthesis of reliable systems from unreliable elements" (1952).

Originally John von Neumann assessed the ability of a person to engage in his favorite science. In his opinion, the right hand of God's people is given to develop mathematical abilities up to 26 years. It is the early start, in the opinion of the scientist, is fundamentally important. Then the adepts of the "queen of sciences" have a period of professional sophistication.

Growing thanks to decades of studies, qualification, according to Neiman, compensates for the decline in natural abilities. However, even after many years, the scientist was distinguished for his giftedness and tremendous efficiency, which becomes unlimited in resolving important tasks. For example, the mathematical justification of quantum theory took him only two years. And in the depth of work it was equivalent to tens of years of work of the entire scientific community.

On the principles of von Neumann

Where did the young Neiman usually start his studies, about whose works the venerable professors said that "the lion will be recognized by claws"? He, beginning to solve the problem, first formulated a system of axioms.

We take a special case. What are the von Neumann principles that are relevant in formulating the mathematical philosophy of computer construction? In their primary rational axiomatics. Is not it true that these promises are imbued with brilliant scientific intuition!

They are integral and subject, although written by a theorist, when the computer was not even in sight:

1. Computers must work with numbers represented in binary form. The latter correlates with the properties of semiconductors.

2. The computer process produced by the machine is controlled by a control program, which is a formalized sequence of executable instructions.

3. The memory of the computer performs a dual function: storage of both data and programs. And both are coded in binary form. Access to programs is similar to accessing data. By the type of data, they are the same, but they are different ways of processing and accessing the memory cell.

4. The computer memory cells are addressable. At a specific address, you can access the data stored in the cell at any time. Thus, variables function in programming.

5. Providing a unique order for executing commands by applying conditional statements. At the same time, they will be executed not in the natural order of their recording, but following the specified programmer's addressability of the transition.

Impressed physicists

Neumann's horizon allowed us to find mathematical ideas in the broadest world of physical phenomena. The principles of John von Neumann were formed in creative joint work on the creation of the EDWAC computer with physicists.

One of them, named S. Ulam, recalled that John instantly grasped their thought, then already in his brain translated it into the language of mathematics. Having solved the expressions and schemes formulated by himself (the scientist made calculations almost instantly in his mind), he thus understood the very essence of the problem. And at the final stage of the done deductive work the Hungarian back transformed his conclusions into the "language of physics" and gave out this most relevant information to his dumbfounded colleagues.

Such deductiveness made a strong impression on colleagues who participated in the development of the project.

Analytical substantiation of computer work

The principles of functioning of von Neumann's computer assumed a separate machine and software parts. When changing programs, the unlimited functionality of the system is achieved. The scientist managed to determine the main functional elements of the future system in an extremely rational analytical way. As an element of control, he assumed feedback in it. The scientist also gave the name to the functional nodes of the device, which in the future became the key to the information revolution. So, von Neumann's imaginary computer consisted of:

- computer memory, or memory (abbreviated - memory);

- Logical-arithmetic device (ALU);

- control device (CU);

- input-output devices.

Even in the other century, we can perceive the brilliant logic that has been achieved by him as insight, as a revelation. But was it really so? After all, the above-mentioned structure, in its essence, became the fruit of the work of a unique logical machine in the human form, whose name is Neiman.

Mathematics has become his main tool. Excellent, about this phenomenon wrote, unfortunately, already the late classic Umberto Eco. "Genius always plays on one element. But it plays so brilliant that all other elements are included in this game! "

Functional diagram of a computer

By the way, the scientist explained his understanding of this science in the article "Mathematician". The progress of any science he considered in her ability to be in the sphere of the mathematical method. It was his mathematical modeling that became an essential part of the above invention. In general, the classical von Neumann architecture looked like this, as shown in the diagram.

This scheme works as follows: the source data, as well as the programs enter the system through the input device. Later they undergo processing in an arithmetic logic unit (ALU). It executes commands. Each of them contains the requisites: from which cells it is necessary to take data, what transactions on them to perform, where to save the result (the latter is realized in the memory device - memory). Output data can also be output directly through the output device. In this case (unlike storage in the memory), they are adapted to human perception.

General administration and coordination of the above-mentioned structural blocks of the circuit is performed by the control device (CU). In it, the control function is assigned to the team counter, which strictly controls the order of their execution.

On the historical incident

If to be fundamental, it is important to note that the work on creating a computer was still a collective one. Von Neumann's computers were designed by order and for the money of the Ballistic Laboratory of the US Armed Forces. Historical incident, as a result of which all the work done by a group of scientists was attributed to John Neumann, was born accidentally. The fact is that the general description of architecture (which was sent to the scientific community for review) on the first page contained a single signature. And it was Neumann's signature. Thus, due to the rules of registration of the results of the research, the scientists got the impression that the author of this whole global work was the famous Hungarian.

Instead of concluding

To be fair, it should be noted that even today the scale of the ideas of the great mathematician for computer development has exceeded the civilizational capabilities of the present day. In particular, the work of von Neumann was supposed to make information systems possible for self-reproduction. And the last, unfinished work was called super-actual even today: "Computer and the brain."