Excerpts:
Al'Biruni's contributions to science are of major importance. He believed that the Earth rotated on its
axis and made accurate calculations of latitude and longitude. In 1000 he wrote on calendars and in
1030 he wrote al Qanun al-Mas'udi which contains a collection of 23 observations of equinoxes
beginning with observations by Hipparchus and Ptolemy and ending with two observations which he
made himself.
He also wrote a treatise on timekeeping, wrote on the astrolabe and a mechanical calendar. He makes interesting observations on the velocity of light, stating that its velocity is immense compared with that of sound.
Comments:
By pure luck, I found another mathemetician who contributed to the body of work that existed before the Age of Exploration that proved that the world was not flat. I still don't believe that teachers actually taught (or at least implied) that Colombus proved that the world was round. That much was already known. The only pieces missing were reliable maps of where land masses were. By-the-way, Where did Columbus get his data on the circumference of the world? Others had already calculated a much more accurate number.
Excerpts:
Nina Bari's father was a doctor. She attended L O Vyazemska's School for Girls and showed great potential in mathematics. In
1918 she entered the Faculty of Mathematics and Physics at Moscow State University.
In the Moscow School of Mathematics she came under the influence of Luzin. Also in this strong mathematical group were
Stepanov, Aleksandrov and Urysohn. She graduated in 1921 and began teaching. However soon after this the Research Institute
of Mathematics opened at Moscow State University and Bari became began research there in addition to her teaching posts.
Bari worked under Luzin for her doctorate on the theory of trigonometrical series. This was awarded in 1926 and after this Bari
became a research assistant at the Institute of Mathematics and Mechanics in Moscow.
During 1927 - 29 she spent time in Paris, attending lectures by Hadamard, and also visited Lvov and Bologna. In 1932 she became a full professor at Moscow State University.
The year Bari graduated from Moscow State University, V V Nemytski entered there to read mathematics. They became close friends sharing not only mathematical interests but also a love of hiking in the mountains. They were eventually married. Bari was an outstanding research mathematician who wrote over fifty research articles. In [1] her final publication, a research monograph on trigonometric series, is described as follows: The range and depth of topics covered is quite extensive, and most of her work in the field is included. But even within so long a monograph, the subject could not be completely exhausted. ... It has become a standard reference for mathematicians specializing in the theory of functions and the theory of trigonometric series.
Bari also wrote textbooks, Higher Algebra (1932) and The Theory of Series (1936). She edited the complete works of Luzin and was the editor of two important mathematics journals. She also translated Lebesgue's famous book on integration into Russian. She died by falling in front of a train on the Moscow Metro. It has been claimed that this was suicide due to depression caused by Luzin's death eleven years earlier. One of her students wrote after her death:- The untimely death of N K Bari is a great loss for soviet mathematics and a great misfortune for all who knew her. The image of Bari as a lively, straightforward person with an inexhaustible reserve of cheerfulness will remain forever in the hearths of all who knew her.
Comments:
The reason I chose this biography was that it was the first one I came to that
seemed interesting and wasn't in the book. Not much was said about this woman's
mathematics. However, I found her depression and subsequent suicide somewhat
noteable.
Excerpts:
Pierre de Carcavi received no university education.
Carcavi is best known for his correspondence with other mathematicians rather than for his own mathematics. He
was friends with Huygens, Fermat (as mentioned above) and Pascal and corresponded with them.
Fermat sent many of his works to Carcavi after he moved to Paris in 1636. In 1650 Fermat sent Carcavi a treatise entitled Novus secundarum et ulterioris radicum in analyticis usus . This work contained the first known method of elimination and Fermat wanted it published. Both Pascal and Carcavi were asked to find a publisher for the work. Carcavi approached Huygens, trying to publish not only this paper of Fermat's but also other papers which Fermat had sent him. Unfortunately neither Carcavi nor Pascal succeeded and Fermat's papers were never published.
Carcavi's friendship with Pascal, like his friendship with Fermat, lasted over many years. In 1658 Pascal solved the problem of the area of any segment of the cycloid and the centre of gravity of any segment. He also solved the problems of the volume and surface area of the solid of revolution formed by rotating the cycloid about the x-axis.
Pascal published a challenge under the name of Dettonville offering two prizes for solutions to these problems. He lodged the prizes and his own solutions with Carcavi. Carcavi and Roberval were asked to judge the solutions submitted. Pascal gave his calculating machine, the Pascaline, to Carcavi. Carcavi also corresponded with Galileo, Mersenne, Torricelli and Descartes and he is important in transferring information from one to the other. He made many suggestions during his correspondence with other mathematicians which were later developed and incorporated in the papers of these other mathematicians. Carcavi was elected to the Académie des Sciences in 1666. In 1668 Carcavi was appointed to a committee, along with Huygens, Roberval, Auzout, Jean Picard and Gallois, to test whether the method of determining longitude, which had been submitted to the Académie des Sciences by a German, was practical.
Comments:
I found it interesting that Carcavi had no education at the university
level, yet he was friends with well known mathematicians and scientists.
The text about him even said that he wasn't known for his math, but for
his work with others.
Excerpts:
Chrystal is best remembered today for Algebra a two volume
work which was completed by 1889. He was also involved in
educational reform throughout his career and was a major figure
in setting up the educational system in Scotland.
In 1867 Chrystal attended Aberdeen University, graduating (1871) in mathematics and physics. He obtained a scholarship to Cambridge and went to Peterhouse in 1872. While an undergraduate at Cambridge he was influenced by Adams, Stokes and Maxwell. He graduated in 1875 with Stokes as one of his examiners and became a lecturer at Corpus Christi College in Cambridge. He was bracketed first with Burnside in the final examination. Chrystal was considered the most widely read among the young mathematicians.
Chrystal worked with Maxwell on the experimental verification of Ohm's Law in the newly opened Cavendish Laboratory in Cambridge.
In 1877 Chrystal applied for the chair of mathematics in St Andrews. With outstanding references from Maxwell, Thomson, Stokes and others he was appointed.
In 1879 he was appointed to the chair of mathematics in Edinburgh where he was to remain for the rest of his career.
Chrystal is famed for his contributions to Encyclopaedia Britannica, Electricity, Magnetism, Mathematics, Parallels and many others such as biographies of mathematicians.
Chrystal is best remembered for his two volume Algebra (1889). He wrote several papers on differential equations which were published between 1891 and 1896.
Chrystal was involved in educational reform throughout his career and was a major figure in setting up the Scottish Higher Leaving Certificate which has lasted, with modifications, to the present day.
His last major piece of work was a study of seiches, a form of wave observed on the Scottish lochs. He undertook both experimental and theoretical work on sceiches, as part of the Scottish Lake Survey.
Comments:
Chrystal was a lecturer and seemed to make his biggest contributions in the
area of mathematics education and educational reform. He is best remembered
for his Algebra textbook, and the Scottish Higher Learning Certificate on
which he worked is still in place. He knew and assisted well known
researchers, but is not credited with any great mathematical work himself.
Many of his well-known colleagues thought highly of him and recommended him
for the chair of mathematics at Edinburgh.
Chrystal gives a good example of what might be accomplished by a good teacher of mathematics. We shouldn't expect to make any great discoveries, but we can work on improving mathematics education and generating excitement among our students on the subject.
Excerpts:
John Collins's father died when John was 13 years of age and he had to earn a living from that time. His first job was as an apprentice bookseller in Oxford, a job which he did for around three years. In 1641 he became a clerk at Court and in this position began to learn mathematics.
His position as a clerk was a short one and in 1642 he became a seaman. For seven years he served, and during this time he continued to study mathematics while at sea. In 1649 he became a mathematics teacher in London, a post he held until 1660.
For 1660 onwards Collins worked at a number of jobs but most often as an accountant for various different organisations. From 1667 he worked as librarian for the Royal Society in London, in addition to his other jobs.
Collins' importance is, as Barrow said, being the English Mersenne . He corresponded with Barrow, David Gregory, James Gregory, Newton, Wallis, Borelli, Huygens, Leibniz, Tschirnhaus and Sluze.
Collins published books by Barrow and Wallis and left a collection of 2000 books and an uncounted number of manuscripts.
He did publish works of his own, however. For instance he published works on sundials, trigonometry for navigation and the use of the quadrant. He had a paper on cartography published and also wrote on accounting, compound interest and annuities. In 1664 he published Doctrine of Decimal Arithmetick.
A canal was proposed to join the river Isis (the name given to the upper part of the river Thames in Oxford) and the river Avon (which flows west). Collins went to Oxford in 1683 to survey the proposed route of the canal. On this trip, however, he became ill and although he returned to London, he never recovered from the illness.
Comments:
I choose this mathematician because it is interesting that Mr. Collins
learned
mathematics on his own and he held many odd jobs. Most mathematicians
were fortunate enough to receive a University education yet John was motivated enough
on his own accord to learn for learnings safe. It is also interesting
that John had experience with boating.
Excerpts:
John Craig was a pupil of David Gregory in Edinburgh. He entered the University of Edinburgh
in 1684 and graduated in 1687. Two years later he went to England and became a curate. He
continued his career was in the church and was vicar at a number of places in Wiltshire. He also
tutored mathematics taking pupils at his home.
Craig became a friend of Newton. He also continued his contacts with David Gregory and corresponded with other Scottish mathematicians such Maclaurin.
Craig published 3 major works which contain the earliest example of the dy/dx notation of Leibniz in Britain and also contained the integration symbol . While he was still a student in Edinburgh, Craig published Methodus figurarum lineis rectis et curvis comprehensarum quadraturas determinandi which contains Leibniz's notation. This notation is also used in the work he published in 1693, Tractatus mathematicus de figurarum curvilinearum quadraturis et locis geometricis.
Craig was involved in a dispute with Jacob Bernoulli over the calculus. He also had a dispute with Tschirnhaus.
Craig published several more papers on the logarithmic curve, the curve of quickest descent and quadrature of figures.
In 1699 he published Theologiae Christianae Principia Mathematica which applies probability to show that the evidence of the truth of the gospels is diminished through time. He claimed that it reaches 0 in the year 3144, so "proves" that this is an upper bound for the second coming.
In 1718 he published a work on optics De optica analytica.
In the last part of his life Craig went to London in the hope that his mathematical abilities would be noticed. He was elected a Fellow of the Royal Society in 1711.
Comments:
The reason I chose John Craig was his different aproach to the second
coming. In my life, I have heard of many ways that people have arrived at this
calculation, but never using calculus. He reasoned that the truth of the gospel
is diminished through time. He claimed that the second coming will be in 3144
This is when the upper limit reaches zero, so this upper bound is proof.
Excerpts:
John Craig was a pupil of David Gregory in Edinburgh. He entered the University of Edinburgh
in 1684 and graduated in 1687. Two years later he went to England and became a curate. He
continued his career was in the church and was vicar at a number of places in Wiltshire. He also
tutored mathematics taking pupils at his home.
Craig became a friend of Newton. He also continued his contacts with David Gregory and corresponded with other Scottish mathematicians such Maclaurin.
Craig published 3 major works which contain the earliest example of the dy/dx notation of Leibniz in Britain and also contained the integration symbol . While he was still a student in Edinburgh, Craig published Methodus figurarum lineis rectis et curvis comprehensarum quadraturas determinandi which contains Leibniz's notation. This notation is also used in the work he published in 1693, Tractatus mathematicus de figurarum curvilinearum quadraturis et locis geometricis. Craig was involved in a dispute with Jacob Bernoulli over the calculus. He also had a dispute with Tschirnhaus. Craig published several more papers on the logarithmic curve, the curve of quickest descent and quadrature of figures.
Comments:
I thought that the fact that Craig supposedly calculated
the Second Coming of Christ was an interesting fact and feat.
Excerpts:
After graduating as Senior Wrangler in 1902 he worked for a Smith's prize.
Results similar to those he obtained
were, unfortunately, published in a French journal before he had submitted.
He started work on a new topic
submitting a winning entry on matrices for the Smith's prize of 1904.
While at Cambridge, he had
read Larmor's famous book Aether and Matter and then, in 1905, after
reading Einstein's paper on special
relativity, he began to work on that topic. Cunningham published The
Principle of Relativity in 1914, the first
English book on the topic. Many papers on relativity followed.
Comments:
I enjoyed the fact that even though he lost out on one Smith's prize, he
kept trying.
I also liked the fact that he was a pacifist.
He also went from analysis to relativity in his research.
Excerpts:
Grace Brewster Murray Hopper
Born: 9 Dec 1906 in New York, USA Died: 1 Jan 1992 in Arlington, Virginia, USA
Grace Hopper studied at Vassar College and Yale, then joined the Naval Reserve in 1943. From 1944 she worked with Aiken on the Harvard Mark I computer. It was while working on this project that she coined the term 'bug' for a computer fault. The original 'bug' was a moth which caused a hardware fault in the Mark I.
In 1949 Hopper joined the Eckert-Mauchly Computer Corporation where she designed an improved compiler. She was part of the team which developed Flow-Matic, the first English-language data-processing compiler.
Hopper was named the first computer science Man of the Year by the Data Processing Management Association in 1969. In 1991 she was awarded the National Medal of Technology.
Comments:
I chose Grace Hopper because I wanted to find someone who was known for
something most people had heard about but maybe did not know where it came
from. Hopper coined the term 'bug' for a computer fault.
Excerpts:
When Pierre returned to France in 1699 he came into a large inheritance from his father. He usedWhen Pierre returned to France in 1699 he came into a large inheritance from his father. He used
this wealth to purchase an estate at Montmort (and therefore became Pierre Rémond de Montmort).
He lived most of his life in Château de Montmort on his estate and often invited top mathematicians
to visit him. For instance Nicolaus(I) Bernoulli spent three months at Château de Montmort.
Montmort's reputation was made by his book on probability Essay d'analyse sur les jeux de hazard
which appeared in 1708. The book, which is a collection of combinatorial problems, is a
systematic study of games of chance and shows that there is important mathematics in this area.
Montmort was elected to be a Fellow of the Royal Society in 1715, when he was on a trip to England. The following year he was elected to the Académie Royal des Sciences.
Comments:
I find it interesting that a man devoted his life's work to the study of games. He ultimately proved that mathematics is fun not a chore.
Excerpts:
John F. Nash studied at the Carnegie Institute of
Technology (now Carnegie-Mellon University)
receiving a BA and an MA in mathematics in 1948. In
1950 he received his doctorate from
Princeton with a thesis Non-cooperative Games .
In 1949, while studying for his doctorate, he wrote a paper which 45 years later was to win a Nobel prize for economics. During this period Nash established the mathematical principles of game theory. P Ordeshook wrote: Milnor in [2] describes Nash during his years at Princeton: He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well. However, my most vivid memory of this time is of the many games which were played in the common room. I was introduced to Go and Kriegspiel, and also to an ingenious topological game which we called Nash in honor of the inventor.
From 1952 Nash taught at MIT. His work on the theory of real algebraic varieties, Riemannian geometry, parabolic and elliptic differential equations was extremely deep and significant in the development of all these topics. but resigned due to ill health.
Nash delivered a paper at the tenth World Congress of Psychiatry in 1996 describing his illness. It is reported in [4]. He was described in 1958 as most promising young mathematician in the world but he soon began to feel that the staff at my university, the Massachusetts Institute of Technology, and later all of Boston were behaving strangely towards me. ... I started to see crypto-communists everywhere ... I started to think I was a man of great religious importance, and to hear voices all the time. I began to hear something like telephone calls in my head, from people opposed to my ideas. ...The delirium was like a dream from which I seemed never to awake.
Despite spending many periods in hospital because of his mental condition, his mathematical work continued to have success after success. He said: I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia.
In 1974 Nash made a recovery from the schizophrenia from which he had suffered since 1959. However his ability to produce mathematics of the highest quality did not leave him. He said I would not treat myself as recovered if I could not produce good things in my work. Nash was awarded (jointly with Selten) the 1994 Nobel Prize in Economic Science for his work on game theory.
Comments:
I thought Nash was interesting because he was not only an
excellent mathematician, but also won the nobel prize in
economics. I also thought it was interesting about his
recovery for Schizophrenia...
"I would not treat myself as recovered if I could
not produce good things in my
work."
Excerpts:
Bieberbach was an inspiring, if unorganised, lecturer and Hanna almost became a
geometer. However after the Nazi's came to power in 1933 Hanna became unhappy. She
left Berlin University in 1934 to marry Bernhard Neumann. As Bernhard was a Jew, they
were forced to leave Germany in 1938. They settled in England.
Hanna Neumann's maiden name was Caemmerer. She attended Berlin University and there she was taught analytic and projective geometry by Bieberbach, differential and integral calculus by Schmidt and number theory by Schur.
A letter from two of her students, published after her death, shows her character: We will remember her not only as a mathematician, she was a friend who always had a sympathetic ear for any student, and was never too busy. We will always miss her tremendous dedication and sincerity, and the friendliness of her presence.
Comments:
I chose to review the biography about Hanna mainly because she is a woman. I also chose her because it was a more recent biography.
I found it interesting that she was devoted not only to her work, but also to her husband, and the lives of her students as shown by the letter they wrote. I admire her dedication and sincerity and hope to be remembered by my students as she was.
Excerpts:
She attended Berlin University and there she was taught
analytic and projective geometry by Bieberbach, differential and integral
calculus by Schmidt and number theory
by Schur.
However after the
Nazi's came to power in 1933 Hanna became unhappy. She left Berlin
University in 1934 to marry Bernhard
Neumann. As Bernhard was a Jew, they were forced to leave Germany in 1938.
They settled in England.
In 1963 Hanna and Bernard went to Australia where she was
to spend the rest of her career.
In 1971 she undertook a lecture tour of Canada. After lecturing in a number
of universities Hanna reached
Carleton University, Ottawa. There she took ill and died two days later.
Hanna worked in group theory
her book Varieties of Groups (1967) is a classic
Comments:
She was a determined young woman. She studied mathematics for years when
it wasn't popular for women to do that.
She devoted her entire life to mathematics.
Excerpts:
Pólya worked in probability, analysis, number theory, geometry, combinatorics
and mathematical physics.
While in Zürich his output of mathematics was very large and wide ranging. In 1918 he published
papers on series, number theory, combinatorics and voting systems. The following year in addition
to papers in these topics he published on astronomy, probability. While he was doing this wide
range of work he was working on some of his deepest results in the study of integral functions.
The political situation in Europe forced Pólya to move to the USA where after working at Brown University for two years he took up an appointment at Stanford. Before going to the USA Pólya had a draft of a book How to solve it written in German. Pólya had to try four publishers before finding one to publish the English version in the USA. It sold over one million copies over the years. Pólya gave wise advice
If you can't solve a problem, then there is an easier problem you can't solve: find it.
Comments:
I did A short essay on Polya for Discrete Math at Roane State. Dr. Polya
was interesting as an individual as well as being an original mathematician.
A significant part of his accomplishments is missing from the biographical
sketch--he was unsurpassed in teaching teachers to teach math.
Excerpts:
Proclus was brought up at Xanthus in Lycia. He later studied philosophy under
Olympiodorus the Elder at Alexandria. He then went to Athens where he studied
under the philosophers Plutarch and Syrianus.
Proclus became head of Plato's Academy in Athens and remained there until his death. He wrote Commentary on Euclid which is our principal source about the early history of Greek geometry.
Proclus had access to books which are now lost and others, already lost in Proclus's time, were reported on based on extracts in other books available to Proclus.
He wrote Hypotyposis, an introduction to the astronomical theories of Hipparchus and Ptolemy. He described how the water clock invented by Heron could be used to measure the apparent diameter of the Sun.
Comments:
Proclus' theories are very similar to Plato and yet he is not very
well known at all. He also gave a proof showing that the earth is
the center of a circle in which other circles rotate around the
circumference.
Excerpts:
Robinson's family emigrated to Palestine in 1933, forced out of Germany since they wereRobinson's family emigrated to Palestine in 1933, forced out of Germany since they wereRobinson's family emigrated to Palestine in 1933, forced out of Germany since they were
Jewish. There Robinson studied mathematics under Fraenkel and Levitzki. He went to the
Sorbonne in 1939 but was forced to flee when the Germans invaded. After reaching England on
one of the last small boats to evacuate refugees, he changed his name from Robinsohn and worked
on aerodynamics during World War II.
After the War he attended London University and received a Ph.D. in 1949 for pioneering work in model theory, the metamathematics of algebraic systems. He went to Toronto in 1951 to take up a chair of applied mathematics but left for Jerusalem in 1957 to fill Fraenkel's chair.
During a year visiting Princeton he made the discovery for which he is best remembered, non-standard analysis. In 1967 he was appointed to Yale where he died of cancer at the age of 55.
Comments:
I chose this mathematician because he was born on October 6. This date meant
nothing special to me until this morning when my sister called me to tell me she was
expecting a baby on October 6. His life was interesting to me for he managed
to flee Germany during World War II, escaping the Nazi concentration camps.
Excerpts:
The other main direction of his work was to study gambling as a
source to stimulate problems in probability and decision theory.
Another important work by Savage is How to gamble if you must :
Inequalities for stochastic processes in 1965, written jointly
with L Dubins.
Comments:
I thought it was interesting that he used his mathematic skills to help
in gambling. I guess that is the best way to figure something out.
Excerpts:
Thomas Simpson
Born: 20 Aug 1710 in Market Bosworth, Leicestershire, England Died: 14 May 1761 in Market Bosworth, Leicestershire, England
Simpson is best remembered for his work on interpolation and numerical methods of integration. His first job was as a weaver. At this time he taught mathematics privately and from 1737 he began to write texts on mathematics.
He also worked on probability theory and in 1740 published The Nature and Laws of Chance. Much of Simpson's work in this area was based on earlier work of De Moivre.
Simpson was the most distinguished of a group of itinerant lecturers who taught in the London coffee-houses. He worked on the Theory of Errors and aimed to prove that the arithmetic mean was better than a single observation.
Simpson published the two volume work The Doctrine and Application of Fluxions in 1750. It contains work of Cotes. In 1754 he became editor of the Ladies Diary .
The following description of Simpson by Charles Hutton (made 35 years after Simpson's death) is interesting
It has been said that Mr Simpson frequented low company, with whom he used to guzzle porter and gin: but it must be observed that the misconduct of his family put it out of his power to keep the company of gentlemen, as well as to procure better liquor.
It would be fair to note that others described Simpson's conduct as irreproachable .
Comments:
The name Simpson caught my attention since I am a fan of The
Simpson's cartoon on television. I learned that Thomas Simpson did work on
interpolation, which is a method my high school teacher confused many
students with in trigonometry. The other main reason I chose Thomas
Simpson is the fact he is known for having a bad reputation.
Excerpts:
HUGO STEINHAUS
Born: 1887 in Poland
Died: 25 Feb 1972
Steinhaus did important work on functional analysis. In particular he
worked on orthogonal series, probability theory, real
functions and their applications. In particular he is associated with the
theory of independent functions, arising from his work in
probability theory.
In 1944 Steinhaus proposed the problem of dividing a cake into n pieces so that it is proportional (each person is satisfied with their share) and envy free (each person is satisfied nobody is receiving more than a fair share). For n = 2 the problem is trivial, one person cuts the cake, the other chooses their piece. Steinhaus found a proportional but not envy free solution for n = 3. An envy free solution to Steinhaus's problem for n = 3 was found in 1962 by John H Conway and, independently, by John Selfridge. For general n the problem was solved by Steven Brams and Alan Taylor in 1995.
Steinhaus was the main figure in the Lvov School up till 1945 when he moved to Wroclaw. He spent the war years hiding from the Nazis, suffering great hardships, going hungary most of the time and thinking about mathematics. He is best known for his books Mathematical Snapshots and One Hundred Problems... .
Comments:
I thought it was interesting that someone would see the problem of dividing
a cake as a mathematical challenge. Wonder about choosing "envy free" as
part of the problem. How do you know if you divided a cake up into envy
free proportions? Maybe somebody really likes cake...
The years in hiding thinking about mathematics are intriguing, too. Think he would be an interesting person to listen to.
Excerpts:
Thom is known for his development of catastrophe theory, a mathematical
treatment of continuous action producing a discontinuous result.
He attended the Collège Cuvier at Montbéliard, then he attended the Lycée Saint-Louis in Paris. His university education was at the Ecole Normale Supérieure in Paris. Thom taught at Grenoble in 1953-54, then at Strasbourg from 1954 until 1963. He was appointed a professor in 1957. In 1964 he moved to the Institut des Hautes Etudes Scientifique at Bures-sur-Yvette.
Thom's theory is an attempt to describe, in a way that is impossible using differential calculus, those situations in which gradually changing forces lead to so-called catastrophes, or abrupt changes. The theory has widespread application in the physical and biological sciences and in the social sciences.
Presented by Thom in Structural Stability and Morphogenesis (1972), the theory has been developed by many mathematicians.
His earlier work had made him well known before he worked on catastrophe theory. His work on topology, in particular on characteristic classes, cobordism theory and the Thom transversality theorem led to his being awarded a Fields' medal in 1958.
Comments:
Catasrophe theory sounds interesting... gradual changes leading to larger ones.
Something I've never heard of before... at least not in the field of mathematics.
Excerpts:
Josef Hoëné de Wronski
Born: 23 Aug 1778 in Wolsztyn, Poland Died: 8 Aug 1853 in Neuilly (near Paris), France Hoëné Wronski wrote on the philosophy of mathematics.
He was born Josef Hoëné but he adopted the name Wronski around 1810 just after he married. He had moved to France and become a French citizen in 1800 and then, in 1810 he moved to Paris. His first memoir on the foundations of mathematics was published there in 1810 but, after it received less than good reviews from Lacroix and Lagrange, Wronski broke off relations with the Institute in Paris. Among other things he did was design caterpillar vehicles to compete with the railways. However they were never manufactured. His main work involved applying philosophy to mathematics, the philosophy taking precedence over rigorous mathematical proofs. He criticised Lagrange's use of infinite series and introduced his own ideas for series expansions of a function. The coefficients in this series are determinants now known as Wronskians (so named by Muir in 1882).
In 1812 he published a work claiming to show that every equation had an algebraic solution, contradicting Ruffini's results which were already published. Wronski's work here, although of course wrong, nevertheless still has important applications. Wronski spent the years 1819 to 1822 in London. He came to England to try to obtain an award from the Board of Longitude but his instruments were detained by the Customs as he entered the country. He found himself in severe financial difficulties but, after his instruments had been returned to him, he was able to address the Board of Longitude. His address On the Longitude only contained generalities and did not impress. His book Introduction to a course in mathematics was published in London in 1821.
For many years Wronski's work was dismissed as rubbish. However a closer examination of the work in more recent times shows that, although some is wrong and he has an incredibly high opinion of himself and his ideas, there is also some mathematical insights of great depth and brilliance hidden within the papers.
Comments:
I chose this mathematician due to the fact that I remember using the
Wronskian determinants in my work in differential equations. I found it
interesting that Wronski chose his name shortly after marrying and moving
to Paris. Whether he took his wife's name or not isn't mentioned, but it
was very interesting to me for him to possibly contemplate doing this.
Also, I found it quite interesting that he is known equally for his
failures and over-inflated ego. He seemed to be quite a character.
Excerpts:
Yunus is famed for his astronomical observations and as an astrologer. He also produced many
trigonometry tables, all designed for astronomical purposes.
His major work, an astronomical handbook, was al-Zij al-Hakimi al-kabir. al-kabir means 'large' which is apt and al-Hakimi means that the work is dedicated to Caliph al-Hakim. The book is certainly large, containing 81 chapters. There are lists of observations made by Yunus and his predecessors. He describes 40 planetary conjunctions accurately and 30 lunar eclipses used by Simon Newcomb in his lunar theory.
In addition there are planetary longitudes and calendar tables. Trigonometric functions are given as arcs rather than angles. Spherical trigonometry reaches a high level of sophistication in this work.
Yunus was described by his biographer as follows:-
He was an eccentric, careless and absent-minded man who dressed shabbily and had a comic appearance.
Yunus predicted the date of his own death to be in seven days time when he was in good health. He tidied up his business affairs, locked himself in his house and recited the Koran until he died on the day he predicted.
Comments:
I chose this biography because his appearance was described by his biographer as comic. I thought that it was very unusual that he was in good health when he predicted his death. The most unusual part was that he died on the day he predicted.
Excerpts:
Zorn received his doctorate from Hamburg in 1930, his doctoral work
being supervised by Artin.
He was appointed to Halle but, in 1933, he was forced to leave
Germany because of the Nazi
policies.
Zorn emigrated to the USA and worked at Yale from 1934 to 1936 where he established 'Zorn's Lemma'. Zorn then moved to the University of California where he remained until 1946 when he became professor at Indiana.
As well as his well known work in infinite set theory, Zorn worked on topology and algebra. One of his early results was to prove the uniqueness of the Cayley numbers, he showed that it was the only alternative, quadratic, real nonassociative algebra without zero divisors. Herstein was one of his students.
Comments:
I thought it was interesting that he fled to the U.S. because
of Nazi policies.