Who is von Neumann? The broad masses of the population are familiar with his name, even those who are not fond of higher mathematics know the scientist.
The thing is that he developed a comprehensive logic of the functioning of the computer. To date, it has been implemented in millions of home and office computers.
Neumann's Greatest Achievements
He was called a man-mathematical machine, a man of impeccable logic. He sincerely rejoiced when he faced a difficult conceptual task that required not only a solution, but also the preliminary creation of this unique toolkit. The scientist himself, with his usual modesty, in recent years, extremely briefly - in three points - announced his contribution to mathematics:
- justification of quantum mechanics;
- creation of the theory of unbounded operators;
- ergodic theory.
He did not even mention his contribution to game theory, to the formation of electronic computers, to the theory of automata. And this is understandable, because he talked about academic mathematics, where his achievements look as impressive peaks of human intelligence as the works of Henri Poincaré, David Hilbert, Hermann Weyl.
Sociable sanguine type
At the same timeall his friends recalled that, along with inhuman capacity for work, von Neumann had an amazing sense of humor, was a brilliant storyteller, and his house in Princeton (after moving to the USA) was reputed to be the most hospitable and cordial. Friends of the soul doted on him and even called him by his first name: Johnny.
He was a highly atypical mathematician. The 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 uncompromising about was scientific dishonesty.
The scientist seemed to be collecting human weaknesses and quirks to collect statistics on system deviations. He loved history, literature, remembering facts and dates encyclopedically. Von Neumann, in addition to his native language, was fluent in English, German, and French. He also spoke, though not without flaws, in Spanish. Read in Latin and Greek.
What did this genius look like? A stout man of average height in a gray suit with a leisurely, but uneven, but somehow spontaneously accelerating and decelerating gait. Insightful look. A good conversationalist. He could talk for hours on topics of interest to him.
Childhood and adolescence
Von Neumann's biography begins on 1903-23-12. On that day in Budapest, Janos, the eldest of three sons, was born into the family of the banker Max von Neumann. It is he who will become John in the future across the Atlantic. How much means in a person's life the right upbringing, which develops natural abilities! Even before school, Jan was trained by teachers hired by his father. The boy received his secondary education inelite Lutheran gymnasium. By the way, E. Wigner, the future Nobel Prize winner, studied with him at the same time.
Then the young man graduated from the University of Budapest. Fortunately for him, while still at university, Janos met a teacher of higher mathematics, Laszlo Ratz. It was this teacher with a capital letter who was given to discover in the young man the future mathematical genius. He introduced Janos to 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 had earned a reputation as a young talent in scientific circles by the time he received his matriculation certificate. His start was really early. Janosz wrote his first scientific work "On the Location of Zeros of Minimal Polynomials" at the age of 17.
Romantic and classic rolled into one
Neumann stands out among venerable mathematicians for his versatility. With the possible exception of only number theory, all other branches of mathematics were influenced to one degree or another by the mathematical ideas of the Hungarian. Scientists (according to the classification of W. Oswald) are either romantics (generators of ideas) or classics (they are able to extract consequences from ideas and formulate a complete theory.) He could be attributed to both types. For clarity, we present the main works of von Neumann, while denoting the sections of mathematics to which they relate.
1. Set Theory:
- "On the axiomatics of set theory" (1923).
- “On the theoryHilbert's evidence (1927).
2. Game theory:
- "On 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).
- Series of works "On operator rings" (1936 - 1938).
5. Applied tasks of creating a computer:
- "Numerical Inversion of Matrices of High Order" (1938).
- "The logical and general theory of automata" (1948).
- "Synthesis of reliable systems from unreliable elements" (1952).
Originally, John von Neumann assessed a person's ability to engage in his favorite science. In his opinion, by the right hand of God it is given to people to develop mathematical abilities up to 26 years. It is the early start, according to the scientist, that is fundamentally important. Then the adherents of the "queen of sciences" have a period of professional sophistication.
Qualification, growing thanks to decades of practice, according to Neumann, compensates for the decrease in natural abilities. However, even after many years, the scientist himself was distinguished by both talent and amazing performance, which becomes limitless when solving important problems. For example, the mathematical foundation of quantum theory took him only two years. And in terms of depth of study, it was equivalent to dozens of years of work by the entire scientific community.
Ohvon Neumann principles
How did the young Neumann usually start his research, about whose work venerable professors said that “you recognize a lion by its claws”? He, starting to solve the problem, first formulated a system of axioms.
Take a special case. What are von Neumann's principles that are relevant in his formulation of the mathematical philosophy of computer construction? In their primary rational axiomatics. Isn't it true that these messages are imbued with brilliant scientific intuition!
They are solid and objective, although they were written by a theorist when there was no computer yet:
1. Computing machines must work with numbers represented in binary form. The latter correlates with the properties of semiconductors.
2. The computational process produced by the machine is controlled by a control program, which is a formalized sequence of executable commands.
3. The memory of a computer performs a dual function: storing both data and programs. Moreover, both those and others are encoded in binary form. Access to programs is similar to access to data. By data type they are the same, but they differ in the way they are processed and accessed to the memory cell.
4. Computer memory cells are addressable. At a certain address, you can access the data stored in the cell at any time. This is how variables function in programming.
5. Providing a unique order of execution of commands by using conditional statements. At the same time, they will be executed not in the natural order of their recording, but following the specifiedjump targeting programmer.
Impressed physicists
Neumann's outlook allowed him to find mathematical ideas in the widest world of physical phenomena. The principles of John von Neumann were formed in creative joint work on the creation of the EDVAK computer with physicists.
One of them, named S. Ulam, recalled that John instantly grasped their thought, then translated it into the language of mathematics in his brain. Having resolved the expressions and schemes formulated by himself (the scientist almost instantly made rough calculations in his mind), he thus understood the very essence of the problem.
And at the final stage of the deductive work done, the Hungarian transformed his conclusions back into the "language of physics" and gave this most up-to-date information to his dumbfounded colleagues.
Such deductivity made a strong impression on the colleagues involved in the development of the project.
Analytical substantiation of the computer operation
Principles of functioning of the von Neumann computer assumed separate machine and software parts. When changing programs, the unlimited functionality of the system is achieved. The scientist managed to extremely rationally analytically determine the main functional elements of the future system. As an element of control, he assumed feedback in it. The scientist also gave the name to the functional units of the device, which in the future became the key to the information revolution. So, von Neumann's imaginary computer consisted of:
- machine memory, or storage device (abbreviated memory);
- logic-arithmetic unit (ALU);
- control unit (CU);
- I/O devices.
Even if we are in another century, we can perceive the brilliant logic he achieved as an insight, as a revelation. However, was it really so? After all, the entire above-mentioned structure, in its essence, became the fruit of the work of a unique logical machine in human form, whose name is Neumann.
Mathematics has become his main tool. Magnificently, unfortunately, the late classic Umberto Eco wrote about such a phenomenon. “Genius always plays on one element. But he plays so brilliantly that all other elements are included in this game!”
Functional diagram of a computer
By the way, the scientist outlined his understanding of this science in the article "Mathematician". He considered the progress of any science in its ability to be within the scope 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 it is shown in the diagram.
This scheme works as follows: initial data, as well as programs, enter the system through an input device. In the future, they are processed in the arithmetic logic unit (ALU). It executes commands. Each of them contains details: from which cells data should be taken, what transactions should be performed on them, where to save the result (the latter is implemented instorage device). Output data can also be output directly through an output device. In this case (as opposed to storage in memory), they are adapted to human perception.
General administration and coordination of the above structural blocks of the circuit is performed by the control unit (CU). In it, the control function is entrusted to the command counter, which keeps a strict record of the order in which they are executed.
About a historical incident
To be fundamental, it is important to note that the work on the creation of computers was still collective. Von Neumann computers were developed by order and at the expense of the US Armed Forces Ballistics Laboratory.
The historical incident, as a result of which all the work carried out by a group of scientists was attributed to John Neumann, was born by accident. The fact is that the general description of the 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 for reporting the results of the study, scientists had the impression that the famous Hungarian was the author of all this global work.
Instead of a conclusion
To be fair, it should be noted that even today the scale of the ideas of the great mathematician on the development of computers has exceeded the civilizational possibilities of our time. In particular, the work of von Neumann suggested giving information systems the ability to reproduce themselves. And his last, unfinished work was called super relevant even today:"Computer and brain".
