Who is von Neumann? The broad masses of the population are familiar with his name, the scientist is even known not to be fond of higher mathematics.
The thing is that he developed a comprehensive logic of the functioning of a computer. Today it is 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 resolution, 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:
- substantiation of quantum mechanics;
- creation of the theory of unlimited 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 work of Henri Poincare, David Hilbert, Hermann Weil.
Sociable sanguine character
At the same time, his friends recalled that, along with the inhuman ability to work, von Neumann had an amazing sense of humor, was a brilliant storyteller, and his house in Princeton (after moving to the USA) was known as the most hospitable and welcoming. Friends of the soul did not cherish it and even called for their eyes simply by 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 in was scientific dishonesty.
The scientist seemed to collect human weaknesses and quirks to compile statistics on system deviations. He loved history, literature, encyclopedically remembering facts and dates. Von Neumann, besides his native language, spoke fluent English, German, and French. He also spoke, though not without flaws, in Spanish. I read in Latin and Greek.
What did this genius look like? A full man of medium height in a gray suit with a leisurely, but uneven, and somehow spontaneously accelerated and decelerated gait. Insightful look. A good conversationalist. He could talk for hours on topics of interest to him.
Childhood and youth
Von Neumann's biography begins on December 23, 1903. 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 in the future beyond the Atlantic will become John. How much correct education means developing natural abilities in a person’s life! Even before the school, Yan was prepared by teachers hired by his father. The boy received secondary education in an elite Lutheran gymnasium. By the way, E. Wigner, the future Nobel Prize winner, studied with him at the same time.
Then the young man graduated at the University of Budapest. Fortunately for him, back in university time, Janos met a teacher of higher mathematics Laszlo Rat. It was to this teacher with a capital letter that he was given the opportunity to discover the future mathematical genius in a young man. He introduced Janos into the circle of the Hungarian mathematical elite, in which Lipot Feyer played the first violin.
Thanks to the patronage of M. Fekete and I. KĂĽrschak, von Neumann already by the time he received the certificate of maturity had earned a reputation in scientific circles as a young talent. His start was really early. Janos wrote his first scientific work, On the Location of Zeros of Minimum Polynomials, at the age of 17 years.
Romantic and classic all rolled into one
Neumann stands out among the venerable mathematicians for its versatility. With the possible exception, perhaps, of number theory, all other branches of mathematics were, to one degree or another, influenced by the mathematical ideas of the Hungarian. Scientists (according to the classification of V. Oswald) are either romantics (generators of ideas) or classics (they can extract consequences from ideas and formulate a complete theory.) It could be attributed to both types. Let us present for illustrative purposes the main works of von Neumann, while identifying the sections of mathematics to which they relate.
1. Theory of sets :
- “On the axiomatics of set theory” (1923).
- “To the theory of evidence of Hilbert” (1927).
2. Game Theory:
- “To 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 rings of operators” (1936 - 1938).
5. Applied tasks of creating a computer:
- “Numerical Inversion of High Order Matrices” (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 practice his beloved science. In his opinion, the right hand of God is given to people to develop mathematical abilities up to 26 years. It is an early start, according to the scientist, is fundamentally important. Then the followers of the “Queen of Sciences” begin a period of professional sophistication.
According to Neumann, the growing qualifications that have been growing over decades of training compensate for the decline in natural abilities. However, even after many years, the scientist himself was distinguished by both giftedness and tremendous working capacity, which becomes unlimited in solving important problems. For example, the mathematical foundation of quantum theory took him only two years. And in terms of depth, it was equivalent to tens of years of work of the entire scientific community.
About von Neumann's principles
How did the young Neumann usually begin his research, about whose work the venerable professors said that “they recognize the lion by the claws”? He, starting to solve the problem, first formulated a system of axioms.
Take a special case. What are the principles of von Neumann, relevant to the 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 substantive, although written by a theorist, when the computer was not yet in sight:
1. Computers should 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 using a control program, which is a formalized sequence of executable commands.
3. The memory of a computer performs a twofold function: storing both data and programs. Moreover, both of them are encoded in binary form. Access to programs is similar to access to data. By the type of data they are the same, but they are distinguished by the methods of processing and accessing the memory cell.
4. Computer memory cells are addressable. At a specific address, you can at any time access the data stored in the cell. In this way, variables work in programming.
5. Providing a unique order of execution of commands by applying conditional statements. At the same time, they will be executed not in the natural order of their recording, but following the transition targeting indicated by the programmer.
Impressive physicists
Neumann's horizons made it possible to find mathematical ideas in the widest world of physical phenomena. The principles of John von Neumann were formed in a creative joint work on the creation of an EDWAC computer with physicists.
One of them, named S. Ulam, recalled that John instantly grasped their thought, then he translated it into the language of mathematics in his brain. By resolving expressions and schemes formulated by himself (the scientist made approximate calculations almost instantly in his mind), he thus understood the essence of the problem.
And at the final stage of the deductive work done, the Hungarian inversely transformed his findings into the “language of physics” and gave this relevant information to dumbfounded colleagues.
Such deductivity made a strong impression on the colleagues involved in the development of the project.
Analytical substantiation of computer operation
The principles of functioning of the von Neumann computer assumed separate machine and software parts. When changing programs, unlimited system functionality is achieved. The scientist was able 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, the von Neumann imaginary computer consisted of:
- machine memory, or storage device (for short - memory);
- logical arithmetic device (ALU);
- control device (UE);
- input-output devices.
Even while in another century, we can perceive the brilliant logic he achieved as insight, as a revelation. However, was it really so? Indeed, the whole of the above structure, in essence, has become the result of the work of a unique logical machine in human form, whose name is Neumann.
Mathematics has become his main tool. Unfortunately, the late classic Umberto Eco, unfortunately, wrote about this phenomenon. “A genius always plays on one element. But he plays so brilliantly that all the 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 aforementioned invention. On the whole, von Neumann's classical architecture looked as it is shown in the diagram.
This scheme works as follows: the initial data, as well as programs, enter the system through the input device. They are subsequently processed in an arithmetic logic unit (ALU). It executes commands. Any of them contains details: from which cells data should be taken, which transactions to perform on them, where to save the result (the latter is implemented in the storage device - memory). The output can also be output directly through the output device. In this case (as opposed to storage in memory) they are adapted to human perception.
General administration and coordination of the work of the aforementioned structural blocks of the circuit is performed by a control device (CU). In it, the control function is assigned to the command counter, which keeps a strict record of the order in which they are executed.
About the 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 for the money of the Ballistic laboratory of the US armed forces.
A 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 chance. 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 that was Neumann's signature. Thus, due to the rules for processing the results of the study, scientists got the impression that the author of all this global work was the famous Hungarian.
Instead of a conclusion
In fairness, 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 capabilities of modern times. In particular, von Neumann's work suggested giving information systems the ability to reproduce themselves. And his last, incomplete work was called over-relevant even today: “The computer and the brain.”