|If we wish to forsee the future of mathematics our proper course is to study the history and present condition of the science.|
This material is a speculation on the future exploitation of Logic and Mathematics in information systems.
The presentation begins with some preliminary material which connects mathematics and logic with aspects of IT systems development. This is intended to provide motivation for the sequel.
Then a small number of major historical developments in logic, mathematics and science are described.
These show how, over grand historical timescales, emphasis on rigour and formality has alternated with pragmatic but chaotic creativity.
Finally it is suggested that we are now in the latter stages of just such a creative explosion, when the power of logic and mathematics in IT are ill-perceived, but may soon be rediscovered.
Re-use is a key factor in the economics of information technologies which will get more important as the superhighway turns into an effective electronic global marketplace. Abstraction is the name we use for the process of replacing particulars by generalisations. This prime re-usability enabler is the business of mathematics, the science of abstraction.
Global digital networks will make it possible to supply as a commodity to every household and business in the world, not only ever increasing volumes of information but also information processing as a commodity. Realising this consumer convenience depends upon getting the protocols right, and logic and mathematics are part of what it takes to do that.
Digital computers have always been thought of as electronic brains, but have yet to demonstrate much intelligent capability. Logic and mathematics are among the areas where computers can be expected to show truly intelligent capabilities first, and this will contribute to another revolution in how we use computers.
Formality & Rigour
Creativity & Chaos
|The Mathematical Revolution|
|The Scientific Revolution|
|The Formal Revolution|
|The Digital Revolution|
|The Next Logical Revolution|
The Birth of Mathematics
600 B.C.-300 B.C.
During the period of classical Greek mathematics, mathematics is established as an abstract deductive science using logic systematically to derive within the framework of the axiomatic method a structured body of proven mathematical theory.
Mathematics and Science
The revival of intellectual vigour in the renaissance resulted in a new science based on mathematics. Necessity freed mathematics from the chains of Greek rigour, was the mother of important advances such as coordinate geometry and the calculus, and stimulated the rapid development of analysis throughout the 17th Century.
The Formalisation of Mathematics
From the time of classical Greek mathematics to the beginning of the 19th century, Greek standards of rigour remained preeminent. These standards were not sustained during the great expansion of mathematics which took place since the Renaissance.
During the 19th century a renewal of standards at last took place. Mathematics was rigourised, placed on a firm foundation and finally formalised.
The Digital Revolution
We are now witnessing the final stages of The Digital Revolution which began with the invention of the digital computer. Universal access to broadband global networks connecting powerful digital processors embedded in ubiquitous consumer products, digitisation of broadcast media, growth of interactive media, and the information economy transform society. Information representation formats evolve rapidly to permit higher levels of delivered functionality.
The Next Logical Revolution
|Logic Through History||a chronology||A Chronology of Digital Computing Machines (to 1952)|
(agricultural, industrial, computer)
|Threads in the Web of Mathematics|