Mathematics
In mathematics, Smith's most notable achievement is the construction of what has been called the Smith generic cyclic polynomial. For any integer n not divisible by eight, this constructs a polynomial which, upon specializing the values, gives all of the cyclic extensions of any given base field with characteristic prime to n. This can then be extended to metacyclic extensions, such as dihedral groups.
Smith was also a member of the Amdahl Six group, which held the record for the largest known prime number from 1989-1992.
Read more about this topic: Gene Ward Smith
Famous quotes containing the word mathematics:
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)
“... though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.”
—Amelia E. Barr (1831–1919)
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)