When we think of design, we normally think of biology or perhaps physics, but usually not mathematics. How can we see design in something that could not be any different than it is? I don’t know if mathematics could have been different than it is, but as a mathematician, I still see design in mathematics, and plenty of it.
The non-mathematician, who may think of mathematics as consisting only of arithmetic and perhaps algebra and geometry, could never imagine the richness that is here, waiting to be discovered, in the many fields and subfields of mathematics. How could he imagine that there are enough interesting and challenging problems to keep thousands of mathematicians busy and entertained throughout their lifetimes?
Many imagine that those mathematicians are just so many thousands of clueless nerds, and think no more of the matter, unfortunately. But now for better things:
Number theory is the study of the positive integers: 1,2,3,4, …. One might think that at least in this field of mathematics the number of interesting problems would be soon exhausted, and that all of the most important problems would be quickly solved; but one would be quite wrong on both counts. Many simple-sounding problems in number theory remain unsolved to this day, for example, are there an infinite number of “twin primes” – primes which differ by 2 (the minimum possible), such as 881 and 883.
– Granville Sewell. In the Beginning, p. 40.
More twin prime news here.
Note: Yes, that Granville Sewell.