“What is the math question to which string theory is the only answer?” That question appears in an article about string theory which an esteemed correspondent sent to me.

You might wonder what string theory is. The article describes it thus:

String theory posits that the most basic building blocks of nature are not particles, but, rather, one-dimensional vibrating strings that move at different frequencies in determining the type of particle that emerges — akin to how vibrations of string instruments produce an array of musical notes.

My son found an entertaining video that puts string theory in perspective>

That is about the extent of my knowledge of string theory. I am, however, curious about the idea that a string (which is a kind of line) can be one-dimensional. A point is one-dimensional; a string (the abstract kind, not the one your kitten plays with) is two-dimensional. Ah, the mysteries of the universe.

In any event, I have no idea what kind of math question might produce “string theory” as the one and only answer. But I do know that it is possible in mathematics to get the same answer by using many different equations.

Consider 4,  which is a nice small, round number. There are infinitely many ways to get 4 as the answer to an equation by using arithmetic, algebra, differential calculus, integral calculus, and so on. Here are three of the many possible ways of writing an algebraic equation, where y stands for desired answer (4):

1. y = a + bx
2. y = a + b/x
3. y = a + x/b
4. y = ab/x + c

In each case, 4 is the desired answer, a and b are parameters with known values, and x is the number that produces 4 given the values of a and b . Given a = 1 , b = 2 , and c = 3 , x takes the following values in each equation:

1. 1.5
2. 2/3
3. 6
4. 2

There can be many more — and more complex — algebraic equations that the four in my example. There can be many more parameters than a , b , and c in each of the equations. Every parameter in every equation can take an infinite number of values. And, as noted above, the mathematical operations that produce the desired result might be expressed by many types of equation — from arithmetic and algebra to calculus and beyond.

In other words, it might be possible to produce an equation to which “string theory” is the answer. But it seems that it might be possible to produce an infinitude of equations to which “string theory” is the answer. Where does that get us?

Is there a cosmologist in the crowd?