khaled Posted January 19, 2011 Posted January 19, 2011 I am average at simple Calculus, simple Probability & Statistics, simple Geometry & Linear Algebra ... and I'm very good at Mathematical Logic, Discrete Tomography & Graph Theory, Algorithm I have two questions --"i know they sound silly", Q1: Am I good enough to try solving one of the Seven Millennium Prize Problems ? Q2: If I propose a Paper using a simple proof using the simple principles in mathematics, do I have to know everything about the complex systems built over the simple principles of mathematics ?
timo Posted January 19, 2011 Posted January 19, 2011 Q1: Obviously, the more you know that other people don't, the higher the chance that no one has unsuccessfully tried your Ansatz before. Good at logic, discrete math, graph theory and algorithms (dunno what tomography is) applies to pretty much every computer science student, for example (not sure how many of them are interested in math, though). Q2: Depends. Generally: no. But if for example you make big claims about division by zero without knowing that division is commonly defined as the multiplication by the inverse, then you're possibly proving things in a mathematical structure that no one is interested in.
ajb Posted January 19, 2011 Posted January 19, 2011 Q1: The Millennium Prize Problems are well-known difficult problems that have alluded very talented mathematicians who work in or close to the areas in which the problems are formulated. So I would say it is unlikely, but not impossible that a relatively inexperienced mathematician could tackle them. Q2: I would say that even the most experienced expert in a field does not know everything in that field. You have to find something new and interesting. Doing so usually means you will have to have some general knowledge about the field, but by no means would you have to understand every paper written in the field.
khaled Posted January 19, 2011 Author Posted January 19, 2011 Thanks for your replies, and one of the problems is "N = NP" Problem, which is related to Algorithms & Computer Science ... So, That's the closest thing to me as a Computer Science student ... Q1: The Millennium Prize Problems are well-known difficult problems that have alluded very talented mathematicians who work in or close to the areas in which the problems are formulated. So I would say it is unlikely, but not impossible that a relatively inexperienced mathematician could tackle them. you said "but not impossible that a relatively inexperienced mathematician could tackle them." Well I tackled some things on 4 of the problems ...
ajb Posted January 19, 2011 Posted January 19, 2011 Well I tackled some things on 4 of the problems ... You have made progress on solving 4 of the problems?
khaled Posted January 19, 2011 Author Posted January 19, 2011 One more thing, I have made a drawing, related to Navier-Stokes Equation Problem The formal context about the problem was: Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. Although these equations were written down in the 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations. The drawing is related to Water and Boat Engines ... .. so can I post the drawing on here .. to help other scientists get more ideas about this problem ? You have made progress on solving 4 of the problems? yes, and not a real progress, but it was a progress well, after a time it might need alot of help from specialists and a life-time ... I wrote some papers, but they are based on basic ideas, not much in mathematics.
imatfaal Posted January 19, 2011 Posted January 19, 2011 Khaled - fyg the n v np problem has already been claimed, although the proof is hotly disputed as inadequate and too prose-based rather than mathematically-rigorous. you can read up about the proposed proof here at Dick Liptons Blog. Cedric Villani - who was awarded a Fields Medal last year in Hyderabad - admitted that he struggled to follow some of the presentations of the other medalists at the convention. I am not sure if it is possible to be a generalist in mathematics anymore - ie someone who can have a good understanding of the majority of cutting edge maths. Villani compared mathematical diversion to the spread of languages - no matter how well versed you are in one area it does not help you in other areas because even the basis of communications, the language, is different. My point is that mathematics has developed to such a state that it would be practically impossible for one human to be able to attempt more than one of the problems. It is great that you have the drive and ambition to learn - but perhaps a bit of generalised knowledge before specialising. G'luck
khaled Posted January 19, 2011 Author Posted January 19, 2011 Khaled - fyg the n v np problem has already been claimed, although the proof is hotly disputed as inadequate and too prose-based rather than mathematically-rigorous. you can read up about the proposed proof here at Dick Liptons Blog. Cedric Villani - who was awarded a Fields Medal last year in Hyderabad - admitted that he struggled to follow some of the presentations of the other medalists at the convention. I am not sure if it is possible to be a generalist in mathematics anymore - ie someone who can have a good understanding of the majority of cutting edge maths. Villani compared mathematical diversion to the spread of languages - no matter how well versed you are in one area it does not help you in other areas because even the basis of communications, the language, is different. My point is that mathematics has developed to such a state that it would be practically impossible for one human to be able to attempt more than one of the problems. It is great that you have the drive and ambition to learn - but perhaps a bit of generalised knowledge before specialising. G'luck I feel like listening to the explanation of the path I'm walking nowdays, besides that I've chosen to become a teacher, to teach Mathematical Logic, Mathematical Modelling and Programming on the Computer, and Algorithms ... But, since I'm still a Batchelor student, then I'm not late at this point.
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