Tag Archives: Mathematics

Weekly Photo Challenge: Converge

By Vladimir Brezina

A convergent infinite series

Convergent series

wherein the sum of an infinite number of alternating positive and negative terms, progressively decreasing in absolute magnitude, is the unity. (Borges would be pleased.)

Converging reflections 1
Converging reflections 2

A contribution to this week’s Photo Challenge, Converge.

Two MacArthur Geniuses

By Johna Till Johnson

I don’t normally pay a lot of attention to the MacArthur Genius awards. The name alone annoys me, because it’s simultaneously elitist and undefined.  What makes artist X a “genius” while her peers are merely “talented”? And how can we be sure that out of all the talented people in the universe, the committee has miraculously selected the 12, or 20, that are talented enough to be considered geniuses?

But I do like the notion of awarding creative people a big chunk of change—this year, it was $625,000 over a period of five years—with no constraints. And I also think it’s cool that the awards are so broad-ranging. They go to poets, activists, artists, musicians… and even the occasional scientist, mathematician, or engineer.

Which brings me to this year’s awards. I was overjoyed to see the award given to two people in particular.  One was Craig Gentry, a cryptography researcher at IBM’s T. J. Watson research center, who’s done groundbreaking work in the area of homomorphic encryption.

Craig Gentry

Craig Gentry

Homomorphic encryption is, in some respects, the holy grail of encryption, because it enables machines to process encrypted data without ever decrypting it. That doesn’t sound like much, but consider: Today, if your email is stored on Google’s servers, it’s fully accessible to Google (which has been known to turn it over to the NSA).

It’s fully accessible because you need Google to do useful things for you (like sort the mail into folders). With homomorphic encryption, you could keep your mail entirely encrypted without giving up any of the functionality (such as folder-sorting). But Google would have no idea what you named your folders, or what was in your email—and the NSA couldn’t read it, either.

Now imagine that instead of ordinary email, we’re talking about medical or financial records—and you can see the benefit.

The issue at the moment is that the computational horsepower required to make homomorphic encryption is immense, so only starting to become practical in real-world applications. But Craig was among the first to show it was theoretically possible. And he did it incredibly elegantly, using a Zeno’s-paradox-like approach that started with “somewhat homomorphic” encryption that iteratively refined itself to become “fully homomorphic”.

And there’s one other thing I like about Craig: He writes really, really well. His Stanford University PhD thesis, which you can find here, is a joy to read. I don’t mind ploughing through dense scientific papers—but I really appreciate it when someone writes gracefully and well.

Yitang Zhang

Yitang Zhang

Another one of this year’s “geniuses” is Yitang Zhang, who is a number theorist at the University of New Hampshire in Durham. Yitang (who I’ve read goes by “Tom”) recently proved the “bounded gaps” conjecture about prime numbers.

Slate’s Jordan Ellenberg (who’s a mathematics professor at the University of Wisconsin) does a much better job explaining what this is and why it matters than I could do. I urge you to read his writeup here.

Suffice it to say that Tom cracked a really, really hard problem in one of the most demanding areas of mathematics. And he’s apparently a really nice, funny, down-to-earth guy, as described in this University of New Hampshire Magazine article.

But that’s not all: Tom is 57—and has done much of his most creative work in the past 10 years (ie from his late 40s onwards).

Mathematics is a field as notorious as gymnastics or ballet for having a youthful peak–the joke among mathematicians is that anyone over 30 is washed up. Gauss, one of the most famous mathematicians ever, did his most significant work by the age of 22—a fact pointed out by my overly gleeful number theory professor when I was 21 or so.

So it’s great to see someone not only doing great things, but doing them at the relatively “advanced” age of 57.

I’m sure the other 19 MacArthur Fellows have done equally great work in their fields. But seeing the awards go to these two made me happy—and I wanted to share my joy with you!