**GNST 301.14
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Euclid

Brief useful references about this ancient Greek mathematician can be found in the Oxford University of Science <http://www.xrefer.com/entry.jsp?xrefid=487989&secid=.-&hh=1 > and the Oxford English Reference Dictionary <http://www.xrefer.com/entry/487989>.

Euclid is famous for his great work

An excellent biography coupled with a useful overview of the early history of mathematics with links to other early Greek mathematicians can be found at St. Andrew's University, Scotland, U.K.: <http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html >.

Pythagoras

Pythagoras was interested in mathematical principles, the number concept, the concept of mathematical figures and the abstract idea of a proof. He made remarkable contributions to the mathematical theory of music and was a said to be a very good musician.

An excellent biography and overview of Pythagoras' contributions and works -- including his realization that irrational numbers exist -- from St. Andrew's University, Scotland, U.K.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Pythagoras.html>

Examine this extremely useful biography of Pythagoras from Eric Weinstein at Wolfram Research <http://scienceworld.wolfram.com/biography/Pythagoras.html>.

A brief biography of Pythagoras can be found at the Faculty of Sciences, Central University of Venezuela.

<http://euler.ciens.ucv.ve/English/mathematics/pitagora.html >

This site from Bellview Community College has a brief note of history on Pythagoras and a proof of the theorem.

<http://scidiv.bcc.ctc.edu/math/Pythagoras.html >

Click here to go to a number of theorum proof sites that can be of interest.

Aristotle believed that the Earth was the centre of the universe, with the sun and the planets orbiting around it. The stars, unchanging and eternal, were solidly attached to a crystal sphere beyond the planets. Aristotleís n atural philosophy saw Nature as orderly, hierarchical, and teleological.

An excellent biography and overview of Aristotle's contributions and works can be found at St. Andrew's University, Scotland, U.K. where the above quotation originates:

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Aristotle.html>

Another excellent biography and summary of Aristotle's accomplishments, including Life, Writings, Logic, Metaphysics, Philosophy of Nature, The Soul and Psychology, Ethics,Politics and Art is provided courtesy The University of Tennessee at Martin:

<http://www.utm.edu/research/iep/a/aristotl.htm>

A brief biography <http://userwww.sfsu.edu/~rsauzier/Aristotle.html> from San Francisco State University.

From

<http://www3.baylor.edu/~Scott_Moore/aristotle.html>

From

<http://www.epistemelinks.com/Main/Philosophers.aspx?PhilCode=Aris>

See also "The Ancient City of Athens" where Aristotle lived:

<http://www.indiana.edu/~kglowack/athens/>

Eratosthene

<http://www.chuckiii.com/Reports/Mathematics/Eratosthenes.shtml>

An excellent brief biography and explanation of Eratosthenes

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Eratosthenes.html>

A brief biographical overview and links to some of his discoveries can be found at Albertson College <http://www.albertson.edu/math/History/emacy/Classical/biography.htm>.

<http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Archimedes.html>

Another wonderful site about Archimedes with many links and references can be found at Drexel University.

Ptolemy

Following Aristotle, Ptolemy created an astronomical system where the sun, planets, and stars revolved round the Earth which was the foundation of the medieval world picture. The Ptolemaic view was accepted until Copernicus devised the heliocentric system. Ptolemyís work on astronomy and navigation remained a textbook until superseded by the discoveries of the 15th century.

An excellent brief biography and explanation of Ptolemy's contributions and major works can be found at St. Andrew's University, Scotland, U.K.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Ptolemy.html>

Brief bibliographic overview and summary of contributions, this time from The University of Arizona.

<http://seds.lpl.arizona.edu/billa/psc/theman.html>

By performing extensive dissections and vivisections on animals, Galen studied the muscles, spinal cord, heart, urinary system, and proved that the arteries are full of blood. A brief introduction to the knowledge context of Galen and his contributions to our understanding of the human circulatory system, thanks to TimeLineScience, can be found here:

<http://www.timelinescience.org/resource/students/blood/galen.htm>

Al-Khwarizmi was an Islamic scholar who influenced mathematical thought more than any other mediaeval writer. His book on algebra,

A high-quality overview of Al-Khwarizmi's contributions can be found at St. Andrew's University, Scotland, U.K.<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Al-Khwarizmi.html>

Another brief but high-quality biography can be found at <http://members.tripod.com/~wzzz/KHAWARIZ.html>.

An Islamic scholar, Al-Kindi was influenced most stro ngly by the writings of Aristotle but other philosophers such as Plato can also be seen in al-Kindi's ideas. An informative biography can be found at <http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Al-Kindi.html>, St. Andrew's University, Scotland, U.K.

An excellent overview of Bacon's life and his primary contributions can be found in The Internet Encyclopedia of Philosophy, University of Tennessee at Martin:

<http://www.utm.edu/research/iep/b/bacon.htm>

Another good biographical overview can be found, with the tull text of

<http://darkwing.uoregon.edu/~rbear/adv1.htm>

Biographical overview, dates of Bacon's major accomplishments from the Galileo project, Rice University.

<http://es.rice.edu/ES/humsoc/Galileo/Catalog/Files/bacon.html>

A good biographical overview with emphases on his advancement of the philosophy of science from the Radical Academy is located at:

<http://www.radicalacademy.com/philfrancisbacon.htm>

Copernicus provided the first impulse to question Aristotle's world view when he showed in 1543 that the movement of the planets were better explained if the sun was the center for the Earthís and the planetsí movements.

Copernicus' complete biographical time-line can be found at the Nicolas Copernicus Museum in Frombork, Poland:

<http://www.frombork.art.pl/Ang11.htm>

An excellent biography and overview of Copernicus' contributions and works can be found at St. Andrew's University, Scotland, U.K.:

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Copernicus.html>

See also, "The Copernican System," at Rice University.

<http://es.rice.edu/ES/humsoc/Galileo/Things/copernican_system.html>

Tycho Brahe was the first scientist to show that the sphere of stars was not at all unchanging, when he in 1572 observed the strong light from a supernova, and could prove that this was far beyond the planets. He went on to develop a number of new astronomical instruments, and together with his assistants on the island of Hven, he carried out a great number of astronomical observations with a precision that had never been achieved before.

Here is the extremely informative and complete official Tycho Brahe website: <http://www.tychobrahe.com/>.

Another excellent biography and summary of Brahe's contributions and works can be found at Rice University.

<http://es.rice.edu/ES/humsoc/Galileo/People/tycho_brahe.html>

Excellent biography and overview of Bruno's contributions and works. Remember he was burned at the stake in Rome in 1600! This is from Rice University:

<http://es.rice.edu/ES/humsoc/Galileo/People/bruno.html>

Kepler was a strong supporter of the heliocentric theory of Copernicus and the discoverer of the three laws of planetary movement. He worked for Tycho Brahe, and it was in part their relationship that allowed him to disvover these three laws. An excellent biography can be found at <http://euler.ciens.ucv.ve/english/mathematics/ > (click on "Kepler, Johannes") from the Faculty of Sciences, Central University of Venezuela.

Kepler was a man of firsts, some of which are listed here -- to correctly explain planetary motion; to explain the principles of

Another excellent biography and overview of Kepler's contributions and works is provided by St. Andrew's University, Scotland, U.K.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Kepler.html>

NASA's Kepler Mission page [1] contains an excellent biography and overview of Kepler's accomplishments: <http://www.kepler.arc.nasa.gov/johannes.html>.

Find out about the relationship between Kepler and Brahe, and how "the Mars problem" led him to discover elliptical planetary orbits here: <http://www.space.com/searchforlife/kepler_and_mars_010604-1.html>

Rice University provides another excellent biographical source on Kepler:

<http://es.rice.edu/ES/humsoc/Galileo/People/kepler.html>

Galilei was the first astronomer to use the telescope, and could with its help show new relationships in the universe, such as Jupiter having its own moons and that the solar activity was varied. Galilei also formulated the foundation for modern physics. His inventive and inquiring scientific mind can be seen in his invention of the air thermoscope.

Brief biography, good example of conformity enforcement. Good description of his life and excellent links to other related web links. St. Andrew's University, Scotland, U.K.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Galileo.html>

Institute and Museum of the History of Science of Florence, Italy. Describes his inventions using graphical content, demonstrates diversity of his ideas Strong multimedia emphasis on his mechanical inventions <http://galileo.imss.firenze.it/museo/4/index.html>

The Galileo Project, Rice University <http://es.rice.edu/ES/humsoc/Galileo/>. Excellent biographical overview, historical links, summaries of Galileo's conflicts with the church, his contributions and works <http://es.rice.edu/ES/humsoc/Galileo/Resources/galileo_links_tc.html>.

You can trace Galileo's entire life from beginning to end right here, also from Rice University:

<http://es.rice.edu/ES/humsoc/Galileo/galileo_timeline.html>.

Very brief biography, Internet Encyclopedia of Philosophy, University of Tennessee at Martin.

<http://www.utm.edu/research/iep/g/galileo.htm>

Descartes was a scientific philosopher who developed the theory of mechanical philosophy. This philosophy was highly influential until replaced by Newton's advances in explicit scientific methodology. Descartes believed that God created the universe as a perfect clockwork mechanism of vorteces that functioned deterministically without interventio and that that matter had no inherent qualities, but was simply the "brute stuff" which occupied space. Descartes was the first to make a graph permitting geometric interpretation of a mathematical function and gave his name to Cartesian coordinates . He is famed for the mind-body distinction, scepticism and "I think, therefore I am."

The Internet Encyclopedia of Philosophy provides a complete overview of Descartes' contributions in science, philosophy and religion <http://www.utm.edu/research/iep/d/descarte.htm>.

From St. Andrew's University, Scotland, U.K., an excellent biography and overview of Descarte's contributions and works.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Descartes.html>

A succinct and excellent biography with very useful links can be found at Eric Weisstein's Science World site at Wolfram Research <http://scienceworld.wolfram.com/biography/Descartes.html>.

Courtesy the On-line Literature Library, here is the full text of

Boyle is famed for Boyle's Law (

An excellent interactive web page illustrating Boyle's Law, from Davidson College, N.C.: <http://www.chm.davidson.edu/ChemistryApplets/GasLaws/BoylesLaw.html>.

Excellent biography and overview of Boyle's contributions and works. St. Andrew's University, Scotland, U.K.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Boyle.html>.

Also see

Sir Isaac Newton wrote in a letter to his colleague Robert Hooke dated 5 February 1676,

It is generally agreed that Newton contributed more to the development of science than any other individual in history and was the greatest single influence on theoretical physics until Einstein. He generated an overarching conceptual framework for understanding the universe which was more consistent, elegant, and intuitive than any developed before. His work far surpassed the achievements of the great scientific minds of antiquity. Newton developed improved methods of astronomical observation [1], [2] and stated explicit principles of scientific methods [1], [2], [3] which applied universally to all branches of science (

The basic principles of scientific investigation set down by Newton have persisted virtually without alteration until today.

Newton created the most important and influential works on physics of all times,

Newton formulated the classical theories of mechanics (see: Newton's universal law of gravitation [1 ], [2 ] and laws of motion ) and optics and invented calculus years before Leibniz (but Newton did not publish his own material until after Leibniz had published his).

A succinct and excellent biography with very useful links can be found at Eric Weisstein's Science World site at Wolfram Research <http://scienceworld.wolfram.com/biography/Newton.html>.

An encyclopaedic reference to Sir Issac Newton can be found at the Oxford Xrefer site:

<http://www.xrefer.com/entry/220746> which includes many useful cross-references.

Another excellent biography and overview of Newton's contributions and works can be found at St. Andrew's University, Scotland, U.K.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Newton.html>

Also see <http://euler.ciens.ucv.ve/english/mathematics/>, Faculty of Sciences, Central University of Venezuela -- go to "Newton, Sir Isaac" for an excellent biography.

Also see empiricism, skepticism,

Leibniz was self-taught in mathematics, but nonetheless developed calculus independently of Newton. His notation was by far superior (including the integral sign and derivative notation) and is still in use today.

Leibniz was a universal genius and has been called one of the primary founders of modern science. An excellent biography and overiview of Leibniz's contributions and works can be found at St. Andrew's University, Scotland, U.K.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Leibniz.html>.

An encyclopaediac reference on Leibniz can be found at the Oxford xrefer site: <http://www.xrefer.com/entry/494769> which includes many useful cross-references.

Also see <http://euler.ciens.ucv.ve/english/mathematics/>, Faculty of Sciences, Central University of Venezuela -- go to "Leibniz, Gottfried Wilhelm von" for an excellent biography

Although he pursued mathematics as an amateur, Fermat's work in number theory was of such great quality that he is generally regarded as one of the greatest mathematicians of all times.

An excellent biography and overview of Fermat's contributions and works can be found at St. Andrew's University, Scotland, U.K.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Fermat.html>

A highly-detailed description of Fermat's work, including some of his letters in French, can be found at University of Dublin, Trinity College, School of Mathematics

Also see Fermat's Last Theorum (1), (2), solved at last by Wiles in 1995, some 330 years after Fermat's death.

This page leads to other excellent biographies, stories and reviews of Lavoisier's contributions, including the following:

Lavoisier's Friends: an exceptionally complete and detailed resource:

<http://historyofscience.free.fr/Lavoisier-Friends/index.html>.

Sports Science History Maker: Lavoisier

<http://www.sportsci.org/news/history/lavoisier/lavoisier.html>

Chemical Revolutionary Executed!

<http://www.woodrow.org/teachers/ci/1992/Lavoisier.html>

Remember:

A more detailed biography can be found in the

Also see

Charles Babbage was a polymath and has been called -- most would say quite rightly -- the father of the modern computer. In many ways he was a man far ahead of his time. He created word-puzzle dictionaries, researched differential and integral calculus, invented the locomotive cow-catcher and the speedometer, totally despised the noise of street musicians, loved railroads and railway technology and did mathematical work to help set up the British postal system. For 11 years he was also Lucasian Professor of Mathematics at Cambridge University.

Human error and general public ignorance about science strongly frustrated Babbage. He is best known for his work in designing and attempting to build three mechanical computers to overcome human failings in calculation. Although he had minor success with his first simpler efforts, he never lived to see the more complex of his "analytical engines" completed. Based on Babbage's original designs, in 1991 the Science Museum in London built a full-sized version of one of Babbage's last mechanical computers which has worked ever since.

A brief biography can be found in the Oxford Dictionary of Scienctists at the Xrefer site: <http://www.xrefer.com/entry/493956>.

More comprehensive, high-quality bibliographies on Babbage can be found at the Charles Babbage Institute <http://www.cbi.umn.edu/exhibits/cb.html> and the Virginia Polytechnic's site: <http://ei.cs.vt.edu/~history/Babbage.html>.

Also see

Based on empirical evidence, Dalton developed the atomic theory of matter which was the basis of much of the chemistry done in the rest of the 19th and early 20th century.

From the Chemical Heritage Association 'Achievers' web site, a good introductory bibliography including a presentation of Dalton's 'Table of Elements and their Combinations':

<http://www.chemheritage.org/EducationalServices/chemach/ppt/jd.html>.

From the TimeLine of Science, a simple introductory bibliography: <http://www.timelinescience.org/resource/students/matter/dalton.htm>.

From WebQuest, a basic introduction to thinking about atomic theory, including a bit of history about Democritus (400 BCE) who speculated upon (but could derive no empirical evidence for) what he thought to be the indivisible constituent parts of matter, which he called "atomos," and the 2000-year hiatus in this type of thinking until John Dalton appeared: <http://www.chemheritage.org/EducationalServices/webquest/dalton.htm>.

Sir Charles Darwin is one of the most famous naturalists to have lived within the past 150 years, so it is no wonder that many biographies for him can be found on the web. Two are listed below.

<http://darwin.baruch.cuny.edu/biography/index.html>

<http://userwww.sfsu.edu/~rsauzier/Darwin.html>

The Natural History Museum, London, U.K., has a full centre devoted to Charles Darwin which is worth a visit. It can be found here: <http://www.nhm.ac.uk/darwincentre/>.

From the On-Line Literature Library, here are four full-text items, including Origin of Species [1], [2], The Voyage of the Beagle and The Descent of Man (still incomplete on-line). Here is another on-line version of The Voyage of the Beagle from the Zoologisk institutt in Bergen, Norway [in English].

Here is a fine site entitled "Charles Darwin and the Galapagos".

To provide a good context for the work of Darwin, the University of California, Berekely, has an excellent site on Evolution Theory and Science <http://www.ucmp.berkeley.edu/history/evotheory.html>, including a clickable 300-year time line of evolutionary thought.

You may wish to examine The Journal of Syms Covington, assistant to Charles Darwin on the second voyage of the HMS Beagle.

Questions are raised about Charles Darwin as a scientist and writer. What do you think?

Also see BBC's

Faraday was an inveterate experimenter and collector but was not a mathematician. He discovered that a magnet suspended over a wire conducting electricity would revolve, leading him to envision magnetic force as circular. He also discovered magnetic optical rotation, invented the dynamo for converting electricity to motion, discovered electromagnetic induction and developed the laws of electro-chemistry. Most importantly, Faraday's work led to others' mathematical theories of electricity and magnetism. In particular, Maxwell's theoretical work would not have been possible without Faraday's experimentation and discovery of various laws.

An excellent biography of Faraday can be found through the

<http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Faraday.html>

Another excellent brief biography can be found at Eric Weisstein's Science World site at Wolfram Research <http://scienceworld.wolfram.com/biography/Faraday.html>.

Maxwell extended and mathematically formulated Michael Faraday's theories of electricity and magnetic lines of force. Independent of Ludwig Boltzmann, Maxwell developed the Maxwell-Boltzmann kinetic theory of gases which demonstrated that only molecular movement was associated with temperatures and heat. He also developed the idea of "Maxwell's Demon" (1 ), (2 ), (3 ), (4 ). Maxwell's work created the foundation for Heinrich Rudolf Hertz's investigations . Maxwell also calculated that the propagation speed of an electromagnetic field is approximately that of the speed of light and proposed that the phenomenon of light is therefore an electromagnetic phenomenon.

An excellent biography can be found at St. Andrew's University, Scotland, U.K. <http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Maxwell.html>.

Another excellent brief biography can be found at Eric Weisstein's Science World site at Wolfram Research <http://scienceworld.wolfram.com/biography/Maxwell.html>.

Röntgen was a keen naturalist, dedicated scientist, inventor and experimenter. He did extensive work on cathode rays which led him to the discovery of X-rays. He won the Nobel prize in physics in 1901

<http://www.nobel.se/physics/laureates/1901/rontgen-bio.html>

Based on a scientific career investigating gases and the structure and characteristics of atoms, Sir John Thomson is famed for his discovery of the electron. He won the Nobel prize in physics in 1906

An excellent biography of his life and achievements can be found at the Nobel e-Museum at:

<http://www.nobel.se/physics/laureates/1906/thomson-bio.html>

An excellent exhibit on Thomson's discovery of the electron from the American Institute of Physics can be found here: <http://www.aip.org/history/electron/>.

Marie Curie was the first person ever to receive two Nobel Prizes

From the Chemical Heritage Association 'Achievers' web site, here is an excellent biograhpy with links to very good additional resources:

<http://www.chemheritage.org/EducationalServices/chemach/ans/msc.html>

Also see Curie's excellent Nobel e-Museum biography at:

<http://www.nobel.se/chemistry/laureates/1911/marie-curie-bio.html>

Here is an excellent exhibit on Marie Curie and radioactivity from the American Institute of Physics: <http://www.aip.org/history/curie/>.

Although he did much of his most famous theoretical work while merely a third class technician at the Bern patent office, there is probably no physicist whose name has become so widely known as that of Albert Einstein. It is no wonder that TIME Magazine named him "person of the century " (meaning the 20th Century, of course).

Einstein received the Nobel Prize in Physics 1921

A thorough bibliography of Einstein is provided by St. Andrew's University, Scotland, U.K.

<http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Einstein.html >.

An excellent biography of Albert Einstein can be found at the Nobel e-Museum at

<http://www.nobel.se/physics/laureates/1921/einstein-bio.html >.

A biography relating Einstein to the Manhatten Project can be found through

Another excellent biography at <http://euler.ciens.ucv.ve/english/mathematics/> (click on "Albert Einstein") is available from the Faculty of Sciences, Central University of Venezuela.

A comprehensive compendium of web-based resources about Albert Einstein can be found here <http://www.westegg.com/einstein/ >.

The NOVA website supporting the video "Einstein Revealed" contains excellent links to further resources.

This good overall biography is from -- where else? -- Biography.

Albert Einstein has been quoted very frequently.

Here is an excellent exhibit on Einstein from the American Institute of Physics <http://www.aip.org/history/einstein/> with many detailed links.

Rutherford received the Nobel Prize in Chemistry (1908)

Rutherford's investigations into the scattering of alpha rays and the nature of the inner structure of the atom which caused such scattering led to the postulation of his concept of the "nucleus", his greatest contribution to physics. Rutherford was the first person to deliberately transmute one element into another.

An excellent biography of Rutherford can be found at the Nobel e-Museum at

<http://www.nobel.se/chemistry/laureates/1908/rutherford-bio.html >

Niels Bohr received the Nobel Prize in Physics (1922)

Working from concepts in quantum theory and incorporating improvements from Heisenberg's ideas (1925), Bohr created a picture of atomic structure that still largely describes the physical and chemical properties of the elements.

An excellent biography of Bohr can be found at the Nobel e-Museum at

<http://www.nobel.se/physics/laureates/1922/bohr-bio.html >

Based on empirical telescopic evidence, Hubble observed many galaxies beyond our own receding at great speed in all directions and demonsrating galactic red shifts, thus confirming the idea of an expanding universe. He discovered a linear relationship between the velocity of receding galaxies and their distance from the Earth, developing Hubble's Law (also see: Hubble Parameter) and calculated the approximate size and age of the observable universe. Every current cosmological model now incorporates the concept of expansion of the universe.

Through xrefer, an excellent biography and summary of Hubble's achievements <http://www.xrefer.com/entry/494608 > is provided by the Dictionary of Scientists, Oxford University Press.

If you are intrigued with the idea of an expanding universe, you might wish to check this article from Scientific American, and this column on 'the big crunch' from the Stanford University

One of the founders of the quantum theory, he is best known for his uncertainty principle , or indeterminacy principle, which states that it is impossible to determine with arbitrarily high accuracy both the position and momentum (essentially the velocity) of a subatomic particle such as the electron. For this work he won the 1932 Nobel Prize in Physics

<http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Heisenberg.html>

An excellent exhibit on the uncertainty principle can be found here <http://www.aip.org/history/heisenberg/> at the American Institute for Physics.

Schrödinger is known for his mathematical development of wave mechanics (1926), a form of quantum mechanics (see quantum theory ), and his formulation of the wave equation that bears his name. The Schrödinger equation is the most widely used mathematical tool of the modern quantum theory. For this work he shared the 1933 Nobel Prize in Physics with P. A. M. Dirac

A full biography of Schrödinger can be found at the Nobel e-Musem at

<http://www.nobel.se/physics/laureates/1933/schrodinger-bio.html>.

Another excellent Schrödinger biography can be found in the Oxford Dictionary of Scientists through xrefer at <http://www.xrefer.com/entry.jsp?xrefid=495147&secid=.-> where useful cross-references are also located.

A brief biography from San Francisco Statue University also provides background: <http://userwww.sfsu.edu/~rsauzier/Schrodinger.html>.

Gödel was a brilliant mathematician / logician who is most famous for showing [1], [2] that in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of that system. This demonstrated for the first time that mathematics is not a complete and self-consistent system as had been believed. This also proved that a computer can never be programmed to answer all mathematical questions.

What is thought of as Gödel's first incompleteness theorem (1930) states that all consistent axiomatic formulations of number theory include undecidable propositions (Hofstadter , 1989).

Gödel's second incompleteness theorem states that if number theory is consistent, then a proof of this fact does not exist using the methods of first-order predicate calculus . Stated more colloquially, any formal system that is interesting enough to formulate its own consistency can prove its own consistency

An excellent and thorough biography can be found at St. Andrew's University in Scotland <http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Godel.html>.

A particularly fine and highly-recommended web resource appropriately entitled "Godel on the Net" can be found here.

Two other brief biographies with useful sidebar links can be found through Xrefer in

Also see

Fermi won the 1938 Nobel Prize in Physics

In 1926, Fermi discovered the statistical laws, now called Fermi-Dirac statistics, that govern the particles subject to Pauli's exclusion principle. Studying the atomic nucleus itself, in 1934, Fermi evolved the beta decay theory. Based on the work of Pauli and Curie, he demonstrated that nuclear transformation occurs in almost every element subjected to neutron bombardment.

Following the discovery of fission by Hahn and Strassman (1939), Fermi recognized that a chain reaction of secondary neutrons was possible. He then directed a classic series of experiments which ultimately led to the construction of an atomic pile which produced the first controlled nuclear chain reaction.

An excellent biography of Fermi with very useful links can be found at Eric Weisstein's Science World site at Wolfram Research <http://scienceworld.wolfram.com/biography/Fermi.html>.

A brief but useful biography of Fermi is provided by

The Nobel e-Museum provides another excellent biography of Fermi at <http://www.nobel.se/physics/laureates/1938/fermi-bio.html>.

Robert Oppenheimer was an outstanding physicist and excellent teacher. He successfully managed the Manhatten Project, comprised of the most brilliant minds in physics, which resulted in the development of the first American atomic weapons at the close of WW II. After the war Oppenheimer fell afoul of the U.S. anticommunist platform because he opposed development of the hydrogen bomb and was permanently removed from nuclear projects.

Through Xrefer, an excellent biography on Oppenheimer can be found in the

Often called the father of the hydrogen bomb, Teller was part of the Manhatten Project but is most famous for having worked very closely with Stanislaw Ulam to develop and create a successful working hydrogen weapon. Teller also played the most significant role in the removal of Robert Oppenheimer from his career as a nuclear scientist after the Manhatten Project.

Through Xrefer, a brief but very clear biographical sketch can be found in

Brief but useful and interesting biographies of Teller are provided by

Here is a revealing and highly-informative interview with Teller; his home page can be found here.

Gamow was a Russian-American physicist who worked out the theory of alpha decay and showed that, as a star burns hydrogen, the star heats up. Based on work with Ralph Alpher and Hans Bethe, he supported the "big bang" theory of Lemaître.

Alpher's major work was in cosmology. Working with Hans Bethe and George Gamow he generated the so-called "alpha-beta-gamma" [Alpher-Bethe-Gamow] theory of how elements were created, , which Gamow incorporated into the big-bang theory. Alpher predicted microwave background radiation would be a "signature" of the big bang. This radiation was first detected in 1965.

Based on work done by Maurice Wilkins <http://scienceworld.wolfram.com/biography/Wilkins.html> who had worked on the atomic bomb, Francis Crick <http://scienceworld.wolfram.com/biography/Crick.html> and James Watson <http://scienceworld.wolfram.com/biography/WatsonJames.html> worked together at the Cavendish Laboratory in Cambridge to develop the breakthrough double-helix model of DNA.

The three shared the The Nobel Prize in Physiology or Medicine in 1962

Here are further biographies for Crick, Watson and Wilkins through the Nobel e-Museum.

Dr. Gell-Man received the Nobel Prize (1969) in physics

Gell-Man's biography can be found at <http://www.santafe.edu/sfi/People/mgm/mgmbio.html> which comes from his home page at the

A brief biography with other useful links can be found at the Nobel e-Museum at

<http://www.nobel.se/physics/laureates/1969/gell-mann-bio.html>.

Stephen Hawking holds the Lucasian Chair of Mathematics at Cambridge University in the U.K. Click here to learn who in the history of mathematics has held this very important and prestigious research position (you will note that Sir Isaac Newton and Charles Babbage have been there!).

A great source of information about Hawking can be found through St. Andrew's University, Scotland, U.K.<http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hawking.html>.

Stephen Hawking is certainly not ignorant of the importance of the web -- here is his home page. See especially, "lectures" and "physics colloquiums" the latter of which you can access from the bottom of the "lectures" page (BTW, if you don't already have them mounted on your computer, you will need PDF viewer and perhaps Ghostview).

The following is another good-quality biography and brief description of Hawking's major contributions / works which contains a reflection back to Galileo and Newton.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Hawking.html>

For background information, see also The University of Cambridge Cavendish Laboratory.

Dawkins is a particularly thoughtful sociobiologist . He has argued in

A brief introduction to Dawkins can be found through Xrefer in

You may also wish to examine the work of Stuart Kauffman [1 ], [2 ], [3 ], late of the Santa fe Institute and now Chief Scientist of BiosGroup .

Eric Weinstein's World of Science <http://scienceworld.wolfram.com/> from Wolfram Research is an excellent starting point for investigating Scientific Biographies, Physics, Astronomy, Chemistry and Mathematics.

Johnson, George (2002)

=top>

Internet History of Science Sourcebook, Fordham University

Excellent beginning source of time-line and developments. Famous scientists'

biographies available. Good detail, good-quality links to other sources.

<http://www.fordham.edu/halsall/science/sciencesbook.html#Scientific%20Revolution>

Chronology from 30,000BC to 500BC. St. Andrew's University, Scotland, U.K.

<http://www-groups.dcs.st-andrews.ac.uk/~history/Chronology/30000BC_500BC.html#530BC>

Also see Full Mathematical Chronology, St. Andrew's University, Scotland, U.K. -- includes links to all major mathematicians

<http://www-groups.dcs.st-andrews.ac.uk/~history/Chronology/full.html>

Full index of Mathematical History Topics, St. Andrew's University, Scotland, U.K.

<http://www-gap.dcs.st-and.ac.uk/~history/Indexes/Hist_Topics_alph.html>

First-rate history of science site at Washington State University, Pullman. Great for library research.

<http://www.wsulibs.wsu.edu/hist-of-science/>

Here are MacTutor's 100 most popular bibliographies -- extremely useful! From St. Andrew's University, Scotland, U.K. <http://www-gap.dcs.st-and.ac.uk/~history/Miscellaneous/Popular.html>

The Museum of the History of Science, Oxford University <http://www.mhs.ox.ac.uk/> has on-line exhibits, an image library and many useful links. Parts of this site remain under construction, but the

overall quality is still very good

The University of Delaware Library <http://www2.lib.udel.edu/subj/hsci/internet.htm> provides a History of Science and Technology and A Guide to Internet Resources. This site is very comprehensive and somewhat useuful.

The Alan Turing homepage -- humanistic, good leads to other sources in this field of computing

<http://www.turing.org.uk/turing/>; also see [1], [2], [3], and Kurt G ödel [4], [5].

EpistemeLinks.com <http://www.epistemelinks.com/> includes thousands of sorted links to philosophy resources on the internet and has several additional features. See especially: GEMSArchive.

The History of the Royal Society of London. St. Andrew's University, Scotland, U.K. Exceptionally useful. <http://www-groups.dcs.st-andrews.ac.uk/~history/Societies/RShistory.html>

The Copernicus Frombork Musuem in Poland, "Nicolai Copernici Musaeum Fromborcense". Beyond the focus on Copernicus, the Museum is worth exploring.

<http://www.frombork.art.pl/>

The Inquisition. Excellent summary of this period in religious and scientific history. Rice University.

<http://es.rice.edu/ES/humsoc/Galileo/Things/inquisition.html>

Important Astronomers, their Instruments and Discoveries, from ~1500 BC to the early 1800s. University of Arizona <http://seds.lpl.arizona.edu/billa/psc/hist1.html>. Note this is the first of three sequential web pages.

Ten Definitions of Innovation, prepared by Debra M. Amidon, ENTOVATION® International, listed in

ScienceTimeLine.Org -- from 1000AD to 2000AD. Interesting details on milestones over a period of 1000 years; a reasonably good overview of highlights throughout this period.

Each part of the timeline covers a different period. Between 1000 and 1600 these periods span 100 years. The years 1600 to 1900 are broken into periods of 50 years, while the 20th century is covered in four blocks of 25 years each.

At the top of the page for each time period is some text which has the heading "Setting the scene" and which has a yellow background. This part of the page provides some general information about the ideas and event of the time.

Underneath the scene-setting text is a section with the heading "The science", which has a green background. This part of the page provides details of important scientific ideas, people, events and inventions of the period.

<http://www.timelinescience.org/index.php>

Go to the Faculty of Sciences, Central University of Venezuela <http://euler.ciens.ucv.ve/english/mathematics/> for a good selection of high-quality biographies of humankind's most famous mathematicians.

Here's a good website for physicists' biographies at the University of Cambridge in the UK, and another website entitled "Science Through the Centuries" with a clickable timeline for the major physicists who have done their life's work at Cambridge.

If you would like to find further information about nuclear weapons and many related issues, plus biographies of all the scientists involved in the Manhatten project, visit The Nuclear Files <http://www.nuclearfiles.org/>.

Bienvenidos a Galapagos! <http://www.terindell.com/asylum/jason/index.html> courtesy

The Glass Bead Game (Das Glasperlenspiel)

<http://userwww.sfsu.edu/~rsauzier/Biography.html#Biology>, a wonderful assortment of biographies in science.

Here is the official biography of Stuart Kauffman posted at the Santa fe Institute. Here's what he is up to now -- the application of compexity theory to business and finance.

We seek empirical evidence for cosmological events that are of interest -- and here's a great example that tends to confirm the theory of our ever-expanding universe: the most distant receding supernova ever seen <http://www.lbl.gov/Science-Articles/Research-Review/Magazine/2001/Fall/departments/frontline/supernova.html>

The Department of Chemistry and Biochemistry at the University of Guelph provides a very useful and very basic three-part overview of the Development of Mechanics. We start with the classic tour, from Descartes, through Newton, Leibniz and Faraday, to "the peak of classical physics". We then proceed to the tour of experimental observations that advanced the formation of quantum theory. The third part of the overview, "Quantum Theory Comes of Age," takes us from Neils Bohr through Werner Heisenberg to Paul Dirac. Lacking any great detail, this overview remains useful. The mathematical basics for quantum theory at this site is very clearly presented.

From the Chemical Heritage Association, the Chemical Achievers web site has exceptional value and deserves exploration.

<http://www.chemheritage.org/EducationalServices/chemach/home.html>

If you have introductory-level science questions, ScienceNet from the U.K. can be very helpful.

<http://www.sciencenet.org.uk/qpages/search.html>

If you have an interest in the future of science, technology and public policy, here's a useful page from the Organization for Economic Cooperation and Development (OECD). <http://www.oecd.org/EN/document/0,,EN-document-18-nodirectorate-no-13-35022-18,00.html>

The home page of the American Institute for Physics provides many useful background links.

Cosmic questions and controversy? Here is the Counterbalance Meta Library, a shared collection of topics, definitions, audio and video clips which cover the constructive interaction of science, ethics, philosophy and religion.

The National Library of Medicine Audiovisual Program Development Branch has an interesting site introducing AV techniques to examine such things as the

A useful page on some basic laws of chemistry <http://www.chm.davidson.edu/ChemistryApplets/GasLaws/> from Davidson College, N.C.

The impact of science on society: three famous folks' bios, speeches, questions and answers.

Looking for information about famous inventors and inventions? This excellent site provides great links, biographies and information for the invention-hungry!!

Xrefer, the web's reference engine.

Adobe Acrobat Viewer download page.

Ghostscript, Ghostview and GSview download page.

Shockwave info page and links to downloads.

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