William Rowan Hamilton

Wiliam Rowan Hamilton was the greatest mathematician of the English-speaking people after Isaak Newton. Hamilton was born in Dublin in 1805 and died in 1864. His great fame has had curious and regular changes. This scientist was celebrated but not understood during his lifetime. After his death his reputation declined and people began considering him the scientist of the second rank. In the 20th century he became the subject of an extraodinary revival of interest and appreciation.

In 1826, at the age of only 21, Hamilton submitted to the Royal Irish Academy a paper entitled "A Theory of Systems of Rays" which in effect made a new science of mathematical optics. In 1832 he announced to the Royal Irish Academy a remarkable discovery in optics which followed up his theory of systems of rays. In 1835 Hamilton received the honor of knighthood for his works, and two years after, in 1837, Hamilton was elected President of the Royal Irish Academy.

In 1837, six years after Gauss invented his treatment of complex numbers, Hamilton arrived at his own independent discovery of the same ideas which he applied to rotations and vectors in the plane, as other had done. In the second paper on this subject Hamilton generalized from ordered pairs to n-tuples with emphasis on quadruples (or "quaternions"), which extended the algebra of the vectors in the plane to vectors in space. Thus, the concept of a complex number a+bi was extended to the form a+bi+ci+dk (a,b,c,d real) where i?=j?=k?= -1=ijk. Thus, in 1843 Hamilton made his greatest discovery - the calculus of quaternions. He named the set of four numbers a quaternion, and found that he could multiply quaternions as if they were single numbers. But he also discovered that the algebra of quaternions differed from ordinary algebra in one crusial respect: it was noncommutative. The surrender of the commutative law was a tremendous break with tradition. It marked the beginning of a new era.

From 1843 until his death Hamilton's chief interest for 22 years was to develop the new calculus. Hamilton's discovery was quickly followed by other new algeras, such as the theory of matrices which is likewise noncommutative. Thus Sir William Hamilton started a new glorious school of mathematics, though it was not to come into full flower for another half century.

(В.В. Леонтьев, В.В. Булатов “Английский язык для математиков”, 2001)

6.5 Look through the list of words and phrases below. Tick (V) the word combinations you are confident about and cross (X) the ones you need to revise.

o phenomena of nature

o pull of gravity

o mechanics of the earth

o reflecting microscope

o theory of differencial equations

o number theory

o quadratic/cubic/quartic equations

o differential calculus

o n-tuples

o quadruples/quaternions

6.6 For further information on the biographies of famous scientists and their achievements use Famous Scientists WebQuest

http://www.kn.sbc.com/wired/fil/pages/webwebquestel.html

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