Here is a position that arose in the final round of the 2002 U.S. Amateur Team East.
Then IM Hikaru Nakamura is playing Black for the "Weera Family" team against Senior Master Shelby Getz of "Ham Samisch on Rye". Black is a pawn ahead in a rook and pawn ending.
The winning technique requires applying "mathematical precision" to force the pawn through.
White, to move, forces the Black king away from the support of the pawn, then moves behind it again, with 1.Rf8+ Ke1 2.Rg8.
Black then forces the White king back with 2...Ra3+ 3.Ke4, and plays 3...Kf2, once more threatening to queen the pawn.
8  
 
 
 

7  
 
 
 

6  
 
 
 

5  
 
 
 

4  
 
 
 

3  
 
 
 

2  
 
 
 

1  
 
 
 
 
a  b 
c  d 
e  f 
g  h 

 
Play continues with
4.Rf8+ Ke2 5.Rg8 Ra4+ 6.Ke5 Kf3
8  
 
 
 

7  
 
 
 

6  
 
 
 

5  
 
 
 

4  
 
 
 

3  
 
 
 

2  
 
 
 

1  
 
 
 
 
a  b 
c  d 
e  f 
g  h 

 
Take a glance at the last three positions and review the move sequences that produced them.
Through repetition of the same procedure Black has moved his king up and White's king back.
Black could now continue the procedure and drive the White king back even further, or he could stop here, since
with his rook on the fourth rank and his king on the third rank Black can now "build a bridge"
to protect his pawn from attack. Thus, after
7.Rf8+ Kg3 8.Rg8+ Rg4 the pawn will queen.
Mathematical? Yes. There is a concept in mathematics and computer science called
recursion.
It is the successive repetition of a process, producing results that are fed into the next iteration of the process.
For example, the Fibonacci series 0,1,1,2,3,5,8,13,... is produced by starting with two numbers and successively
adding the previous two numbers to produce the next one. Note that the first few steps in the winning chess sequence above are recursive, illustrating a kinship between chess logic and mathematical logic.
More about recursion. If you want to learn more about recursion there is a wonderful popular book
that talks about recursion in mathematics, art, music and language, titled
Godel, Escher, Bach : An Eternal Golden Braid, by Douglas R. Hofstadter.
Ed Eusebi, content editor, www.nscfchess.org