Set theory developed with surprising suddenness in the late nineteenth century. The theory was not preceded by the kind of long, evolutionary period that is generally associated with big mathematical breakthroughs. To mention two familiar examples, the calculus and non-Euclidean geometry developed over a period of many years and had contributions from a large number of people. The early development of set theory, by contrast, was very largely due to one man, Georg Cantor (1845-1918).
This 1999 talk at UMass-Lowell was my last major lecture of the previous century, and it summarizes that century's work on the foundations of mathematics, discusses connections with physics, and proposes a program of research for the next century. Not to be confused with another talk with the same title, my Distinguished Lecture given at Carnegie-Mellon University in 2000.
In 1614, John Napier discovered the logarithm which made it possible to perform multiplications and divisions by addition and subtraction. (ie: a*b = 10^(log(a)+log(b)) and a/b = 10^(log(a)-log(b)).)
This was a great time saver but there was still quite a lot of work required. The mathematician had to look up two logs, add them together and then look for the number whose log was the sum. Edmund Gunter soon reduced the effort by drawing a number line in which the positions of numbers were proportional to their logs.
In the period very roughly from the beginnings of modern physics (1905) up to Alan Turing's description of the Turing machine in 1938, one of the focal points of dispute in the theory of knowledge was the foundations of mathematics.
The main players in this struggle are:
Gottlob Frege: the founder of Logicism, the position that the whole of mathematics can be reduced to a set of relations derived one from the other solely by means of logic, without reference to specifically mathematical concepts such as number. Wittgenstein attempted to carry Frege's concepts of mathematics over to the natural language, with predictably inane results. Frege was also the inspiration for Rudolph Carnap and the various schools of Logical Positivism which continued to wrestle with the problems generated by the new physics. Frege took no part in the struggle after 1903, and died in bitterness and isolation in 1925 having failed to complete a system based on his concept without the appearance of contradictions or logical flaws. His project was later continued by Bertrand Russell and Alan Whitehead.
The purpose of this forum is to provide a virtual environment for scholarly discussion of the History of Mathematics (in a broad sense), amongst professionals, and non-professionals with a serious interest in the field. All scholarly aspects of the history may be discussed, and in addition such issues as:
History/Philosophy of History of Mathematics
Current trends in the History of Mathematics
Ethnomathematics
History of mathematics in teaching mathematics
Origin of mathematical terms/symbols
Biographies and obituaries
Bibliographical references
Announcements of conferences, meetings, jobs, ...
The main ideas which underpin the calculus developed over a very long period of time indeed. The first steps were taken by Greek mathematicians.
To the Greeks numbers were ratios of integers so the number line had "holes" in it. They got round this difficulty by using lengths, areas and volumes in addition to numbers for, to the Greeks, not all lengths were numbers.
Leucippus, Democritus and Antiphon all made contributions to the Greek method of exhaustion which was put on a scientific basis by Eudoxus about 370 BC. The method of exhaustion is so called because
one thinks of the areas measured expanding so that they account for more and more of the required area.
The word abacus comes from the Greek word "ABAX" meaning a calculating board or calculating table. It was invented by the Chinese, the first known record of the abacus was from an ancient sketch in a book from the Yuan Dynasty which was in the fourteenth century. It has a Mandarin name which is"Suan Pan" which means calculating plate. It's inventor is unknown. The Abacus is mostly referred to as the first computer
My current research interests include logic, game theory, and cosmology and gravitation.
On-line material on these topics will be posted under texts and graphics.
Also material deriving from earlier studies may be included if appropriate for one reason
or another.
General Information
If you are looking for a fast, very good overview of the history of mathematics, then select Overview . Perhaps the most extensive archive for the history of mathematics is MacTutor at Saint Andrew's University in Scotland. This is the work of John O'Connor and Edmund F. Robertson of the School of Mathematical and Computational Sciences. The archive contains information on more than 1000 mathematicians, in two groups: long biographies (alphabetical index or chronological index) and short biographies index. There is a Chronology showing the overlapping lives of mathematicians in the long biographies. Further, there is a birthplace map, a mathematicians of the day page, and a list of anniversaries for the year. Finally (but not exhausting everything in MacTutor) is a list of other good sources of information available on the web concerning the history of mathematics. On the other hand, the most extensive as well as spectacular resource may be at Clark University. David E. has amassed a massive (ptp) amount of information. Just consider his Regions or Web Resources, to identify only two of his contributions. Further, by going to his Home Page page, you can access such things as regional mathematics, subjects, chronology, timelines (these are particularly fascinating), and books and other resources. Other web resources worthy of note are at the University of Utah.
