Tuesday, March 18, 2008

Carl Gustav Jacob Jacobi 1804-1851 - Our Mystery Mathematician Revealed

A ∂ listing of his accomplishments...

  • Jacobi's Elliptic Functions (applying elliptic functions to number theory used to prove such results as the Fermat's 2-square and 4-square theorems)
  • One of the early founders of the theory of determinants; in fact, he invented the n x n functional determinant formed by the differential coefficients of n functions of n variables (think of the Jacobian in those multiple integrals when transforming variables)
  • Jacobian
  • Jacobi Symbol
  • Jacobi Identity
  • Jacobi Integral used for the sidereal coordinate system in astronomy
  • Jacobi Method for eigenvalues

Of course I always lean toward any mathematician of whom it is said:
"...widely considered to be the most inspiring teacher of his time" and, oh, by the way, "one of the greatest mathematicians of all time..."
Further, there is no documented evidence of any steroid use during his most prolific period!

And our winners are...


Hi Dave,

That is Carl Jacobi of the Jacobian fame. Interestingly, when my
daughter was first introduced to the Jacobian when dealing with
cylindrical coordinates, she was just told that she needed to include
a Jacobian when she changed variables in the integral, and for this
case the Jacobian was 'r'. It was only a few classes later that the
actual computation was introduced.

I guess one reason you picked him was by tracing back from Ito's
stochastic differential equations; you logically get to a pioneer in
partial differential equations.



I include just this insightful quote:

From a paper by François Ollivier:

It is said that Jacobi once told to a student who wanted to read all the mathematical
literature before starting his research: "Where would you be if your father
before marrying your mother had wanted to see all the girls of the world?"


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