<p>newyorker, you mean Maria is valedictorian?!</p>
<p>Ok wow how could you say Number Theory is bland. Number Theory is THE hardest and most open branch of mathematics. I didn't put math as either my primary or secondary field/subfield but I am in Number Theory right now and it is NOT bland. I think the fact that ccer is doing number theory a special kind of number theory makes it even better. I don't really understand the primary field though...</p>
<p>P.S. I think lack of induction refers to some rings and groups that can be created using abstract algebra. Number theory does not mean integers necessarily...just things that are LIKE integers.</p>
<p>I think that newyorker may have meant that quite a few people go into number theory compared to other fields (not sure about about RSI applicants, but I'd guess it's the same), let alone that "number theory" itself is simply such a broad field (analogous to saying stating topology).</p>
<p>
[quote]
sonar, do you mean optimization in the combinatorical sense?
[/quote]
</p>
<p>Yes, but I am interested in optimization in general (like network optimization [ties in with graph theory, etc]) so I simply stated "optimization" to cover both in one move.</p>
<p>Oh, and zogoto, your didn't add you fields!</p>
<p>hehe, If I pursue my next pet project I'm going to have to do some heavy duty combinatorial optimization possibly should I reach a certain stage in it. Specifically in the form of scheduling, and if I'm to get even tolerable execution times I'm afraid I'll have to use a heuristic (ick!).</p>
<p>Specifically, I'm planning on writing an optimizing compiler! (mwahaha!) Hard? yes! Do able? Definitely (assuming its possible to do over a man year of work in about a month or more)</p>
<ol>
<li>AltairAqua/ Biology: virology; Chemistry: organic/ LA</li>
<li>huangm/ Physics: nanotech; Mathematics: discrete math</li>
<li>Dmitriy_Y/ Engineering: mechanical engineering(robotics); physics: theoretical astrophysics / NJ / 800m 700v</li>
<li>New Yorker/ Psychology: cognitive neuroscience; Political Science: political behavior & socialization/ NY</li>
<li>schemer/ Computer Science : programming languages; Computer Science : theory & algorithms/ NY
6.Random^4/Physics : Cosmology; Physics : Astronomy/MN</li>
<li>Pygo/ Biology : marine; Chemistry : marine/ RI</li>
<li>tsr472/ Math: mathematical physics; Math: Set Theory (Order & Lattice Theory) / AR</li>
<li>tetrahedr0n/Math: combinatorial game theory; Math: additive number theory</li>
<li>ReasonableSon/ Computer Science: AI; Computer Science: Robotics / PA</li>
<li>smurf816/ Physics: quantum mechanics; Bio: biotechnology</li>
<li>mruncleramos/ Mathematics: Differential Geometry/Topology; Physics: Gravitational Waves and Singularities</li>
<li>intelliot / Computer Science: Search Algorithms; Engineering: Digital Signal Processing</li>
<li>kinglz/ Molecular Biology: Chaperones and protein transport; Molecular Biology: Neurodegenerative Diseases</li>
<li>Frankthetank314159/ Engineering: nano; Physics: optics, preferably holography, because holography is cool.</li>
<li>dualityim/Biology: Biochemistry; Computer Science: Computer Architecture.</li>
<li>DanHak/Physics: Particle Physics; Physics: Astrophysics (PSAT: 77V, 73M)</li>
<li>maverick27/Nanotech: Nanomaterials (organic membranes); Physics: Elementary particles/NJ.</li>
<li>sonar/Mathematics: Knot Theory; Computer Science: Optimization</li>
<li>puddinggirl/Chemistry: organic; Biology: biochemistry (SAT 790M 800V)</li>
<li>ccerforlife/Mathematics: Foundations of Geometry in the Non-Euclidean Plane and with Limited Axioms; Mathematics: Number Theory (in systems lacking induction)</li>
<li>adidasty/Biology: Cellular/Molecular Biology; Mathematics: Applied Math/Data Analysis (780M 690V, 76M 77W 63CR, 800 BioE/M)</li>
</ol>
<p>"Ok wow how could you say Number Theory is bland. Number Theory is THE hardest and most open branch of mathematics" I will have to disagree with that. Number Theory is not the hardest, nor the most open branch in mathematics. It is merely the most popularized. Besides, it is hard to assign a difficulty to a branch of advanced mathematics. When we speak of a field of mathematics, we refer to it's problems. However, the methods for solving these problems can come from many different fields. For example. In the proof of FLT, there are techniques used from fields such as Algebraic Geometry, not just Number Theory. If we look at it this way, almost every branch of mathematics is the "hardest branch" Besides, I think that when it comes down to it, it is a matter of opinion. In my opinion, I believe that number theory is quite boring. But that is just my opinion.</p>
<p>No, Godel proved in 1931 that any "yes or no" question can be answered over the reals, but it is impossible to know everything about the integers.</p>
<p>Zogoto, how does that work? Aren't integers a subset of reals? Or am I missunderstanding you?</p>
<p>Maybe I was unclear. hmm. ok</p>
<p>x^3 + y^3 = z^3 has infinite solutions over the reals right? But none for integers. Like that, there are even problems/conjectures that may not even be able to be proven in number theory, but you can always answer "does _____ happen over the reals?"</p>
<p>oops, silly me!
I was thinking about incompleteness/undecidability.</p>
<ol>
<li>AltairAqua/ Biology: virology; Chemistry: organic/ LA</li>
<li>huangm/ Physics: nanotech; Mathematics: discrete math</li>
<li>Dmitriy_Y/ Engineering: mechanical engineering(robotics); physics: theoretical astrophysics / NJ / 800m 700v</li>
<li>New Yorker/ Psychology: cognitive neuroscience; Political Science: political behavior & socialization/ NY</li>
<li>schemer/ Computer Science : programming languages; Computer Science : theory & algorithms/ NY
6.Random^4/Physics : Cosmology; Physics : Astronomy/MN</li>
<li>Pygo/ Biology : marine; Chemistry : marine/ RI</li>
<li>tsr472/ Math: mathematical physics; Math: Set Theory (Order & Lattice Theory) / AR</li>
<li>tetrahedr0n/Math: combinatorial game theory; Math: additive number theory</li>
<li>ReasonableSon/ Computer Science: AI; Computer Science: Robotics / PA</li>
<li>smurf816/ Physics: quantum mechanics; Bio: biotechnology</li>
<li>mruncleramos/ Mathematics: Differential Geometry/Topology; Physics: Gravitational Waves and Singularities</li>
<li>intelliot / Computer Science: Search Algorithms; Engineering: Digital Signal Processing</li>
<li>kinglz/ Molecular Biology: Chaperones and protein transport; Molecular Biology: Neurodegenerative Diseases</li>
<li>Frankthetank314159/ Engineering: nano; Physics: optics, preferably holography, because holography is cool.</li>
<li>dualityim/Biology: Biochemistry; Computer Science: Computer Architecture.</li>
<li>DanHak/Physics: Particle Physics; Physics: Astrophysics (PSAT: 77V, 73M)</li>
<li>maverick27/Nanotech: Nanomaterials (organic membranes); Physics: Elementary particles/NJ.</li>
<li>sonar/Mathematics: Knot Theory; Computer Science: Optimization</li>
<li>puddinggirl/Chemistry: organic; Biology: biochemistry (SAT 790M 800V)</li>
<li>ccerforlife/Mathematics: Foundations of Geometry in the Non-Euclidean Plane and with Limited Axioms; Mathematics: Number Theory (in systems lacking induction)</li>
<li>adidasty/Biology: Cellular/Molecular Biology; Mathematics: Applied Math/Data Analysis (780M 690V, 76M 77W 63CR, 800 BioE/M)</li>
<li>ArmenianInvasion: Engineering, Mechanical; Chemistry, Materials/Nanotechnology - reppin the MD</li>
</ol>
<p>yea
23 = jordan
i totally timed that</p>
<p>what's jordan?</p>
<p>michael jordan.</p>
<p>"what's jordan?"
that could potentially be very insulting. . .however ill excuse it</p>
<p>zogoto, i thought godel ensures that in ANY formal system (which would include R and the operations on it) there is undecidability, ie there may be true statements that cannot be proven. R is decidable?</p>
<ol>
<li>AltairAqua/ Biology: virology; Chemistry: organic/ LA</li>
<li>huangm/ Physics: nanotech; Mathematics: discrete math</li>
<li>Dmitriy_Y/ Engineering: mechanical engineering(robotics); physics: theoretical astrophysics / NJ / 800m 700v</li>
<li>New Yorker/ Psychology: cognitive neuroscience; Political Science: political behavior & socialization/ NY</li>
<li>schemer/ Computer Science : programming languages; Computer Science : theory & algorithms/ NY
6.Random^4/Physics : Cosmology; Physics : Astronomy/MN</li>
<li>Pygo/ Biology : marine; Chemistry : marine/ RI</li>
<li>tsr472/ Math: mathematical physics; Math: Set Theory (Order & Lattice Theory) / AR</li>
<li>tetrahedr0n/Math: combinatorial game theory; Math: additive number theory</li>
<li>ReasonableSon/ Computer Science: AI; Computer Science: Robotics / PA</li>
<li>smurf816/ Physics: quantum mechanics; Bio: biotechnology</li>
<li>mruncleramos/ Mathematics: Differential Geometry/Topology; Physics: Gravitational Waves and Singularities</li>
<li>intelliot / Computer Science: Search Algorithms; Engineering: Digital Signal Processing</li>
<li>kinglz/ Molecular Biology: Chaperones and protein transport; Molecular Biology: Neurodegenerative Diseases</li>
<li>Frankthetank314159/ Engineering: nano; Physics: optics, preferably holography, because holography is cool.</li>
<li>dualityim/Biology: Biochemistry; Computer Science: Computer Architecture.</li>
<li>DanHak/Physics: Particle Physics; Physics: Astrophysics (PSAT: 77V, 73M)</li>
<li>maverick27/Nanotech: Nanomaterials (organic membranes); Physics: Elementary particles/NJ.</li>
<li>sonar/Mathematics: Knot Theory; Computer Science: Optimization</li>
<li>puddinggirl/Chemistry: organic; Biology: biochemistry (SAT 790M 800V)</li>
<li>ccerforlife/Mathematics: Foundations of Geometry in the Non-Euclidean Plane and with Limited Axioms; Mathematics: Number Theory (in systems lacking induction)</li>
<li>adidasty/Biology: Cellular/Molecular Biology; Mathematics: Applied Math/Data Analysis (780M 690V, 76M 77W 63CR, 800 BioE/M)</li>
<li>ArmenianInvasion: Engineering, Mechanical; Chemistry, Materials/Nanotechnology - reppin the MD</li>
<li>sarkun: Engineering-neuroengineering brain computer interphases in particular- Engineering-robotics US citizen living in Turkey so have no idea as to how I will be considered :)</li>
</ol>
<p>tetrahedron
he wasn't talking about formal systems (as apparently both of us thought)
but instead about equations of the form x^3 + y^3 = z^3</p>
<p>On another note, I just found out that something I've been contemplating as a project is actually current research!</p>
<p>So 24 are brave enough announce that they have applied. I wonder how many will add thier names after the results are out? I see that additions happen all of the time on the college rosters.</p>
<p>obviously the places that are primes and perfect squares have an edge over the competition, so the longer one waits, the harder it is to take one of those coveted spots.</p>