I received a great question from my Formspring account that deserves its own post. Here is the question:

Can you tell me something interesting about your research? The answer I would really like to see would not be math related, but more how your research matters/makes a difference to someone outside of the math world. For example, why does my mother care?

The short answer: there is absolutely no reason why your grandmother should care about *my* research. I am not being falsely modest when I say that the chances of my research being useful to anyone outside of mathematics is pretty slim.

The long answer: your grandmother should care that mathematical research is being done, but probably won’t care about any individual’s particular research. Mathematics has changed the world with its applications, from sending people to the moon to making it possible to safely send your credit card number to amazon.com. So I will start by assuming that everyone can recognize that mathematics has tremendous applications to physics, chemistry, and engineering, which in turn have tremendous impacts on people’s lives (after all, you *are* reading this on some sort of a computer monitor, which would not have been possible without mathematics).

Why, then, should your grandma want me to do research when I only do pure (rather than applied) mathematics? There are two parts to this answer:

- Much of applied mathematics comes from pure mathematics. For instance, let’s say that the internet was developed in the 1950’s. In the 1990’s, people started wanting to make purchases using credit card numbers. One of the main ways of doing this is by using RSA encryption, which basically protects your credit card number from thieves. But this is based on work done by Pierre de Fermat (of “Fermat’s Last Theorem” fame, although “Fermat’s Little Theorem” is more relevant here), a French mathematician who died in 1665. He was clearly not intending on creating an application for computers, since he predated the internet by about 300 years. But his pure mathematics led to applied mathematics that your grandma cares about (depending on how computer literate she is).
- So pure mathematics can lead to applied mathematics, and applied mathematics can lead to something your grandma might care about. So why would you grandma want
*me*to do pure mathematics, given that I have already admitted that it is almost certain that she will never care about anything I do? Because I am not 100% certain. The chances of any one mathematician doing anything your grandma (eventually) cares about is slim; the chances of*some*mathematician doing something your grandma cares about is quite high.

Again, though, why should *I* do research? Why shouldn’t we just leave it to the mathematical “geniuses” of the world? Because it is nearly impossible to pick out who is going to do important research *until they have already done it*. Moreover, the people who end up doing “useful” mathematics sometimes depend on the people who do not do “useful” mathematics.

As much as I hate to use the analogy, this is similar to soldiers in World War II. It is with the greatest respect to our veterans that I say that if you removed any one soldier from the war—make is so he (this is WWII, recall, so he is not a she) never entered battle—we still would have won the war. You could probably make the case that you could erase thousands of our troops without affecting the outcome. But you could not remove *all* of the troops. And you could not say who was going to be considered a hero until after the war is done (which is why they hand out medals *after* the soldier does the heroic act). Also, the hero relied on his fellow troops to get to the point where he could do a heroic act.

Again, I do not want to compare mathematicians to soldiers, but mathematicians are fighting a war against—let’s be grandiose and call it—”ignorance.” If I am removed from this war, the outcome probably will not change. But we cannot remove everyone. Plus, we cannot know who to remove, since we cannot know who the “heroes” will be until after the fact. Plus, the heroes rely on the non-heroes, so we do not need to remove too many people.

So your grandma does not care about my research, but she should be glad that I am playing my role by doing it.

July 11, 2010 at 1:43 am |

Thanks for the answer Bret, I actually went out of my way the other day (two extra clicks on the computer) to see if you had answered this questions on Formspring yet. So my grandmother could care less about your research until she does care, but we won’t know when or if that will happen. Seems like an honest answer to me. When I first saw your Formspring post, and another post about group theory, I wondered, why? What is the significance of your work. I am rather removed from pure mathematics since I live in an applied environment, but I like the rsa comment. So, keep doing what your doing, and one day I might care;)

July 12, 2010 at 4:55 pm |

Thanks, Alex!

Bret

PS—Nice new cat!

July 12, 2010 at 10:43 pm |

Well said, Bret!

July 13, 2010 at 12:19 pm |

Thanks, Erica. How would you change the answer for philosophy? You probably would not use cryptography as an example—what would you use?