Last Friday, I attended an Emory Public Lecture titled "Adding and Counting" by Ken Ono. During this well attended lecture, Professor Ono beautifully revealed the new theory he and his colleagues have discovered: that partition functions behave like fractals and a closed formula to count the number of partitions for any number n. The results confirm an observation made by Ramanujan in 1919.
The partition function p(n) counts the number of ways a number n can be partitioned. For instance, over addition, n=4 may be partition in five distinct ways: 1+1+1+1=1+1+2=1+3=2+2=4. Thus, p(4)=5. For a better idea of what it means to "behave like fractals", watch the video above and notice the same structure appears repeatedly upon zooming in. A formula for p(n) has intrigued mathematicians for centuries.
Professor Ono joined the faculty of the Mathematics Department at Emory University last semester and I have had the pleasure of taking a Number Theory course with him last semester. For more information on this new theory, please see the Emory eScienceCommons and AMS press release. Congrats to Professor Ono and his team on this remarkable advancement of Mathematics!
The partition function p(n) counts the number of ways a number n can be partitioned. For instance, over addition, n=4 may be partition in five distinct ways: 1+1+1+1=1+1+2=1+3=2+2=4. Thus, p(4)=5. For a better idea of what it means to "behave like fractals", watch the video above and notice the same structure appears repeatedly upon zooming in. A formula for p(n) has intrigued mathematicians for centuries.
Professor Ono joined the faculty of the Mathematics Department at Emory University last semester and I have had the pleasure of taking a Number Theory course with him last semester. For more information on this new theory, please see the Emory eScienceCommons and AMS press release. Congrats to Professor Ono and his team on this remarkable advancement of Mathematics!
