The Abel Prize is the equivalent of a Nobel prize in mathematics. No I didn't win it, but I got the invitation codes to get into the party in Oslo next month.
I've been to two of these previously, one in Trømso and one in Trondheim. In both places I had roles in the children's day, giving math shows and organizing . After the prize award ceremony and lectures and party in Oslo, the winner goes to another city in Norway the next day where there is a math learning event for school children (usually somewhere around 8th grade), more lectures, and another party. Mind you the Abel prize winners are usually quite old, I think only one has been younger than 70. They are usually quite tired after day 2. The party in Trømso is one my top memories in Norway. Trømso is far north in the arctic circle. We were a small group of about 25 for dinner and drinks. The mayor of Trømso, in all of his mayoral bling, wrote and sang a song for the Abel prize winner. In Norwegian tradition, there were many speeches and funny stories during dinner, and because the winner was not Norwegian it was all in English, which I appreciated at the time. Here's a link to the cool thing we built a couple of years ago in Trondheim:
http://www.matematikksenteret.no/content/2212/Abelprisen-og-et-digert-tetraeder
OK don't be mad, but what sort of breakthroughs can still be made in Mathematics for someone to earn a Nobel prize equivalent? I mean, what are the frontiers of mathematics that are still being pushed forward? I honestly have never really considered it as I would another science-- then again I know a lot of modern algebra was just "recently" developed within the 20th century.
Breakthroughs are happening all the time in mathematics. Actually the Abel prize is usually not given for a breakthrough that happened this year, but for a lifetime of breakthroughs. Here's some info on this year's winners (two this year which is unusual). One of them is John Nash -- he was the subject of the movie "A Beautiful Mind". He didn't get the prize for the movie though. John F. Nash, Jr. and Louis Nirenberg share the Abel Prize
The Norwegian Academy of Sciences and Letters has decided to award the Abel Prize for 2015 to the American mathematicians John F. Nash, Jr. and Louis Nirenberg “for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.” The President of the Academy, Kirsti Strøm Bull, announced the new laureates today 25 March. They will receive the Abel Prize from His Majesty King Harald at a ceremony in Oslo on 19 May.
John F. Nash, Jr., aged 86, spent his career at Princeton University and the Massachusetts Institute of Technology. Louis Nirenberg, aged 90, worked at New York University’s Courant Institute of Mathematical Sciences. Even though they did not formally collaborate on any papers, they influenced each other greatly during the 1950s. The results of their work are felt more strongly today than ever before. Mathematical giants Nash and Nirenberg are two mathematical giants of the twentieth century. They are being recognized for their contributions to the field of partial differential equations (PDEs), which are equations involving rates of change that originally arose to describe physical phenomena but, as they showed, are also helpful in analyzing abstract geometrical objects. The Abel committee writes: “Their breakthroughs have developed into versatile and robust techniques that have become essential tools for the study of nonlinear partial differential equations. Their impact can be felt in all branches of the theory.”
In the 1950s Nash proved important theorems about PDEs, which are considered by his peers to be his deepest work. Outside mathematics, however, Nash is best known for a paper he wrote about game theory, the mathematics of decision-making, which ultimately won him the 1994 Nobel Prize for economics, and which features strongly in the 2001 film about him, A Beautiful Mind. Long career Nirenberg, who was born in Canada, has had one of the longest and most feted careers in mathematics, having produced important results right up until his 70s. Unlike Nash, who wrote papers alone, Nirenberg preferred to work in collaboration with others, with more than 90 per cent of his papers written jointly. Many results in the world of elliptic PDEs are named after him and his collaborators, such as the Gagliardo–Nirenberg inequalities, the John–Nirenberg inequality and the Kohn–Nirenberg theory of pseudo-differential operators.
“Far from being confined to the solutions of the problems for which they were devised, the results proven by Nash and Nirenberg have become very useful tools and have found tremendous applications in further contexts,” the Abel committee says. Many awards Both men have received many distinguished awards. As well as winning the prize in economic sciences in memory of Alfred Nobel, Nash has won the John von Neumann Theory Prize (1978) and the American Mathematical Society’s Steele Prize for a Seminal Contribution to Research (1999). Nirenberg has won the American Mathematical Society’s Bôcher Memorial Prize (1959) the inaugural Crafoord Prize awarded by the Royal Swedish Academy of Science (1982), the Steele Prize for Lifetime Achievement from the American Mathematical Society (1994) and the first Chern Medal for lifetime achievement from the International Mathematical Union and the Chern Medal Foundation (2010).
Awesome, thanks for your response. Its application to economics is one thing perhaps so obvious that I hadn't considered it. That's what I'm sort of asking about. It's not about just being the best mathematician, as it could arguably be in a field like Classical poetry writing where you've got a particular system of skills to use as best as possible to be the the best poet. Rather, it's as though all of a sudden you've discovered a new facet in poetry-writing that was previously unattainable to any writer.“Their breakthroughs have developed into versatile and robust techniques that have become essential tools for the study of nonlinear partial differential equations. Their impact can be felt in all branches of the theory.”
Most people name the Fields Medal as the math-equivalent of a Nobel prize. In recent history, there was a lot of work figuring out the math required to get string theory to work. There's also a bunch of big unsolved problems in a few different veins of mathematics. A famous one to computer people is P != NP, which would prove the complexity and consequent intractability of many problems. There's stuff related to predicting prime number which always makes cryptography nerds perk their ears up. In another vein, there's Gödel's incompleteness theorems which say that it is impossible to prove that system of logic underlying all of mathematics is consistent, using that same system of logic. So on the more philosophical end of the spectrum, there are people studying other systems of logic to extend the domain of what is provable and what we know for certain about what we have proven.OK don't be mad, but what sort of breakthroughs can still be made in Mathematics for someone to earn a Nobel prize equivalent?
A good friend of mine is doing research in mathematics, and from what I understand math research is focused on (logically) proving new ideas based upon other ideas. His research is about exploring a new theorem that might be provable (he hasn't cracked it yet). Here's a collection of math reserach papers, if you're interested in what that looks like.
I'm pretty sure if you solve any of these problems you might be in a good place. I was just reading about the Unabomber, who didn't win a Nobel for his work or anything, but was quite a talented mathematician before he went Luddite and hid in the woods and, well, you know, bombed people. In general though I'm under the impression there are several unsolved problems out there that people still work on trying to solve, for kicks, and to prove stuff. I think Erdos left behind several unsolved problems that people have been working on; IIRC one got solved relatively recently and it was a big to-do. But it's been a while since I took any math classes, even about Erdos. Pretty great idea of the Bible, tbh, if you ask me.He had his own idiosyncratic vocabulary: Although an agnostic atheist,[18][19] he spoke of "The Book", a visualization of a book in which God had written down the best and most elegant proofs for mathematical theorems.
I like the idea of "The Book". There's a lot of very elegant proofs in mathematics. One of my favorite is the proof that there is no greatest prime number. Assume there were a biggest prime, P. Now make the number 1 x 2 x 3 x 4 x 5 x .... x P plus 1. This number cannot be evenly divided by 2 or 3 or 4 or any number up to P because there will always be a remainder of 1 (that's the plus 1 on the end of the expression). That means the number must itself be prime or it must have a prime factor that is greater than P. Either way, we've shown that there must exist a prime greater than P, and we started by saying that P is the greatest prime. Therefore there is no greatest prime number. For example, if you suppose the greatest prime number is 5, make a new number 1 x 2 x 3 x 4 x 5 + 1 = 121. Try dividing 121 by 2, 3, 4, and 5. There will always be a remainder of 1. That means 121's prime factors must be greater that 5 (they are: 11 and 11). So 5 is not the greatest prime.
Have you heard about Britain's infinite coastline? I'm sure you have, if you're telling me about this. But that's one I like. Although your proof got messed up by the markup, I understand that there should be a plus at the beginning, and end, of your bolded section.