Maths, Logic, Computing

Past, Present and Future

Logic Through History A Chronology of Digital Computing Machines (to 1952)

Past Present Future

Mathematics
as Deductive Science
The Greeks transform mathematics from a body of technique to a deductive science. Aristotle invents logic.

Characteristica Universalis
Leibniz dreams of a universal logical language in which all disputes can be settled by computation.

The Rigorisation of Analysis
The theory of real numbers and the foundations of the calculus get straightened out.

The Formalisation of Mathematics
In the hands of Frege logic at last becomes adequate for mathematics. Russell & Whitehead's Principia Mathematica shows that mathematics can be formalised.

The Universal Turing Machine
Alan Turing casts light on the limits of computation and breaths life into the idea of intelligent computers.

The Explosion of Formalism
As digital computers get off the ground formal notations proliferate. Formal expression is a prereqisite of getting a computer to solve a problem.

The Digital Revolution
As computing power gets ever cheaper mass media migrate from analogue to digital representation and global broadband networking ushers in the information megaload.

Evolving Representations
Digital isn't the whole story. Evolution of delivered functionality depends upon evolution of the logical structure information representation.

Proliferating Protocols
Where the network is king, its how you communicate that counts. Representation is just a part of the communication problem, protocol is another part. Network as Mathematician
The network gets good at formalised mathematics, surpassing in rigour and problem solving capability the majority of todays professional mathematicians.

Design Deskilled
Computer Aided Design software based on mathematical modelling techniques enables ordinary people to design almost anything.

Models for
Work, Learn and Play
In the future many people will do creative work using mathematically based CAD tools. Those same tools (with some simpler models) will be used in education. Good games software demands realistic computer modelling techniques than CAD tools and turns out to be the best way to train in engineering design.

Integration and Solutions
The search for ways of making diverse software interwork and integrate in delivering solutions to business needs leads to the emergence of a de-facto standard Characteristica Universalis.

Past	Present	Future
Mathematics as Deductive Science The Greeks transform mathematics from a body of technique to a deductive science. Aristotle invents logic. Characteristica Universalis Leibniz dreams of a universal logical language in which all disputes can be settled by computation. The Rigorisation of Analysis The theory of real numbers and the foundations of the calculus get straightened out. The Formalisation of Mathematics In the hands of Frege logic at last becomes adequate for mathematics. Russell & Whitehead's Principia Mathematica shows that mathematics can be formalised. The Universal Turing Machine Alan Turing casts light on the limits of computation and breaths life into the idea of intelligent computers.	The Explosion of Formalism As digital computers get off the ground formal notations proliferate. Formal expression is a prereqisite of getting a computer to solve a problem. The Digital Revolution As computing power gets ever cheaper mass media migrate from analogue to digital representation and global broadband networking ushers in the information megaload. Evolving Representations Digital isn't the whole story. Evolution of delivered functionality depends upon evolution of the logical structure information representation. Proliferating Protocols Where the network is king, its how you communicate that counts. Representation is just a part of the communication problem, protocol is another part.	Network as Mathematician The network gets good at formalised mathematics, surpassing in rigour and problem solving capability the majority of todays professional mathematicians. Design Deskilled Computer Aided Design software based on mathematical modelling techniques enables ordinary people to design almost anything. Models for Work, Learn and Play In the future many people will do creative work using mathematically based CAD tools. Those same tools (with some simpler models) will be used in education. Good games software demands realistic computer modelling techniques than CAD tools and turns out to be the best way to train in engineering design. Integration and Solutions The search for ways of making diverse software interwork and integrate in delivering solutions to business needs leads to the emergence of a de-facto standard Characteristica Universalis.

Threads in the Web of Mathematics

created 1996/8/12 modified 1997/6/29