As I blogged about earlier Ono and colleagues have developed a formula that spits out the partition number of any integer. This news thrills me. It motivates me to get faster to that edge of the field. Below you'll find a link to the paper by Ono et al. Like me, you may not be ready yet to fully understand such a paper. I will use it as a benchmark to measure my skills by and as a guide for selfstudy. Come to think of it I need to add more papers to the benchmark. One about the Riemann hypothesis and one about Fermat's Last Theorem.
Links:
 Article in NewScientist
 Paper "lAdic properties of the partition function." ( pdf )
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Wow it would take a lot of background to understand such a paper as you say it's a measure by which you can test your own skill. Looks like you are beginning to find your own research program.
ReplyDeleteExactly. A measure, a benchmark to test your skill. I use the great theorems and problems like Fermat's Last Theorem, The Prime Number Theorem and the Riemann Hypothesis as a compass.  What do I need to know to fully understand them? And work from there.  Browsing the Journal of Number Theory is an inspiration as well.
ReplyDeleteyes I have a similar attitude myself for understanding the key calculations in physics it's always good to map out some goals in my case as I've said before I want to understand Von Neumann's book on quantum mechanics and Hawking and Ellis's book on the large scale structure of space time. But it will be a while before I gain the necessary skills in pure maths. In the mean time there are some key calculations in cosmology and particle physics for which I have a lot of the background already but it's one thing to understand basic principles quite another to actually fill in all the details of a particular paper a very challenging crossword or sudoku puzzle. In that you know the answer but just as in the case of your paper there are far too many gaps for those who aren't already experts in the field to follow.
ReplyDeleteOn another topic I really hope we can meet up in Edinburgh as well. As I'm sure Neil will be as well. Best time is the summmer early autumn. At the minute it is still rather gloomy. Good luck with the TMA's I want to finish off both parts of TMA01 for M208 this weekend then start the Complex Analysis One.
That time period is fine with me. I haven't seen my tutorial schedule for M373 yet but I am sure that I have a lot of dates to choose from in that time frame.  I guess you inspired me, I am reading on and off in 'New Cosmic Onion' and 'Collider'.  You are going to be very busy with all these TMAs. Good luck!
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