The development of computing, as we understand it today, has been possible thanks to the contributions of some of the most important mathematicians of the 20th century, including Alan Turing and John von Neuman. The latter proposed a way to build computers capable of performing various types of functions; like ours, where we just have to install a different program for them to perform new tasks.
Von Neumann was born in Budapest in 1903 and He stood out from his youth for his mathematical abilities and for his remarkable photographic memory: he was able to recite books that he had read years before. He received his doctorate in mathematics at the age of 23 and was one of the first professors at the prestigious Princeton Institute for Advanced Study in the United States. He is known for his advances in many fields of science, such as computing, quantum physics, analysis, or game theory. During World War II, he collaborated on the Manhattan project.
His contribution to computing is based on the ideas of Alan Turing. In 1936 Turing had devised a mathematical object, known as the Turing machine, which formalized the concept of an algorithm or, in other words, a computer program. Turing introduced the concept of a universal Turing machine, capable of reproducing any algorithm, as long as the instructions were entered properly. The actual construction of it was called a “general purpose” computer. This concept refers to what we now understand as a programmable computer.
The first general purpose computer —ENIAC (Electronic Numerical Integrator and Computer)—was built by engineers John Prepert Eckert and John William Mauchly in 1945. This computer could, in practice, reproduce any algorithm as long as the instructions were configured by reconnecting wires appropriately. This was a long and tedious process, very limited by the number of cables and therefore the size of the computer itself.
Von Neumann was the one who managed to design a computer to which instructions could be entered electronically. In his prototype it was enough to insert the instructions through a magnetic tape reader-recorder. The architecture of the proposed computer is known today as Von Neumann architecture. In 1945 Von Neumann circulated a draft where he detailed how to build computers using this architecture, which were called general purpose computers with “program storage capacity”. Today, all modern computers are of this type.
The key to the Von Neumann architecture was inspired by the universal Turing machine: storing instructions in the computer’s own memory. Von Neumann designed his computer with a structure divided into three large parts, the CPU (central processing unit), memory, and input and output devices (such as a keyboard and a screen).
The CPU was in charge of reading and modifying the contents of the electronic memory and it did so following the instructions contained in part of the computer’s memory. In addition, it was possible to modify the memory, for example, by entering data using the keyboard, and thus modify the operating instructions of the CPU and, therefore, the function that the computer executed. Von Neumann, along with Prepert Eckert and Mauchly, built the first general-purpose computer capable of storing programs —EDVAC (initials of Variable Automatic Electronic Discrete Calculator)— at the University of Pennsylvania (USA).
An SUV of science, economics and psychology
Von Neumann’s contributions to computing did not end here. He also invented a mathematical object called a cellular automaton. These dynamical systems also bore some resemblance to Turing machines, and were well suited for modeling natural systems where many objects interact with each other. Von Neumann not only introduced them, but also designed the first examples of self-replicating automata, capable of duplicating an initial object indefinitely following simple evolution rules. These ideas were further developed by the mathematician John Conway, and inspired the famous game of life, an example of a cellular automaton.
Von Neumann is also one of the founders of the field known as game theory, which mathematically studies the rational behavior of individuals in the face of a conflict with various possible strategies. This theory has applications in many other fields of knowledge, notably in economics and psychology. Unfortunately, this math genius died prematurely at the age of 53, diagnosed with cancer, probably due to radiation received during the nuclear tests on the Manhattan Project.
robert cardona is a postdoctoral researcher at the ICMAT and in the Universitat Politècnica de Catalunya.
Coffee and Theorems is a section dedicated to mathematics and the environment in which they are created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share meeting points between the mathematics and other social and cultural expressions and remember those who marked their development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: “A mathematician is a machine that transforms coffee into theorems.”
Edition and coordination: Ágata A. Timón G Longoria (ICMAT).
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