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Your current IP address is 8.222.208.146. </p> <div class="paragraphbreak" style="margin-top:0.5em"></div><div style="font-size: 16px;"> <p>Even when blocked, you will <i>usually</i> still be able to edit your <a href="/wiki/Special:MyTalk" title="Special:MyTalk">user talk page</a>, as well as <a href="/wiki/Wikipedia:Emailing_users" title="Wikipedia:Emailing users">email</a> administrators and other editors. </p> </div> <div class="paragraphbreak" style="margin-top:0.5em"></div><div style="font-size: 16px;"> <p>For information on how to proceed, please read the <b><a href="/wiki/Wikipedia:Appealing_a_block#Common_questions" title="Wikipedia:Appealing a block">FAQ for blocked users</a></b> and the <a href="/wiki/Wikipedia:Appealing_a_block" title="Wikipedia:Appealing a block">guideline on block appeals</a>. 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Review the information below for assistance if you do not believe that you have done anything wrong.<div class="paragraphbreak" style="margin-top:0.5em"></div><div class="paragraphbreak" style="margin-top:0.5em"></div> <p>This block affects editing on all Wikimedia wikis. </p><p>The IP address or range 8.222.128.0/17 has been globally <a href="/wiki/Wikipedia:Blocking_policy" title="Wikipedia:Blocking policy">blocked</a> by <a href="/wiki/User:Jon_Kolbert" title="User:Jon Kolbert">‪Jon Kolbert‬</a> for the following reason(s): </p> <div style="padding:10px; background:var(--background-color-base, white); color:inherit; border:1px #666 solid;"> <p><a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/NOP" class="extiw" title="m:Special:MyLanguage/NOP">Open proxy/Webhost</a>: See the <a href="https://meta.wikimedia.org/wiki/WM:OP/H" class="extiw" title="m:WM:OP/H">help page</a> if you are affected </p> </div> <p>This block will expire on 15:12, 27 August 2028. Your current IP address is 8.222.208.146. </p> <div class="paragraphbreak" style="margin-top:0.5em"></div><div style="font-size: 16px;"> <p>Even while globally blocked, you will <i>usually</i> still be able to edit pages on <a href="https://meta.wikimedia.org/wiki/" class="extiw" title="m:">Meta-Wiki</a>. </p> </div> <div class="paragraphbreak" style="margin-top:0.5em"></div><div style="font-size: 16px;"> <p>If you believe you were blocked by mistake, you can find additional information and instructions in the <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/No_open_proxies" class="extiw" title="m:Special:MyLanguage/No open proxies">No open proxies</a> global policy. Otherwise, to discuss the block please <a href="https://meta.wikimedia.org/wiki/Steward_requests/Global" class="extiw" title="m:Steward requests/Global">post a request for review on Meta-Wiki</a>. You could also send an email to the <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/Stewards" class="extiw" title="m:Special:MyLanguage/Stewards">stewards</a> <a href="https://meta.wikimedia.org/wiki/Special:MyLanguage/VRT" class="extiw" title="m:Special:MyLanguage/VRT">VRT</a> queue at <kbd>stewards@wikimedia.org</kbd> including all above details. </p> </div> <p>Other useful links: <a href="https://meta.wikimedia.org/wiki/Global_blocks" class="extiw" title="m:Global blocks">Global blocks</a> · <a href="/wiki/Help:I_have_been_blocked" title="Help:I have been blocked">Help:I have been blocked</a> </p> </div></li></ul><hr /> <div id="viewsourcetext">You can view and copy the source of this page:</div><textarea readonly="" accesskey="," id="wpTextbox1" cols="80" rows="25" style="" class="mw-editfont-monospace" lang="en" dir="ltr" name="wpTextbox1">== The 1984 list == Simon listed the following problems in 1984:<ref name=":2" /> {| class="wikitable sortable" !No. !Short name !Statement !Status !Year solved |- | rowspan="2" |1st |(a) Almost always global existence for Newtonian gravitating particles |(a) Prove that the set of initial conditions for which Newton's equations fail to have global solutions has measure zero.. |Open as of 1984.<ref name=":2" />{{Update inline|date=June 2021}} In 1977, Saari showed that this is true for 4-body problems.<ref>{{cite journal |last1=Saari |first1=Donald G. |title=A global existence theorem for the four-body problem of Newtonian mechanics |journal=Journal of Differential Equations |date=October 1977 |volume=26 |issue=1 |pages=80–111 |doi=10.1016/0022-0396(77)90100-0 |doi-access=free |bibcode=1977JDE....26...80S }}</ref> |? |- |(b) [[Painlevé conjecture|Existence of non-collisional singularities in the Newtonian N-body problem]] |Show that there are non-collisional singularities in the Newtonian N-body problem for some N and suitable masses. |In 1988, Xia gave an example of a 5-body configuration which undergoes a non-collisional singularity.<ref>{{cite journal |last1=Xia |first1=Zhihong |title=The Existence of Noncollision Singularities in Newtonian Systems |journal=Annals of Mathematics |date=1992 |volume=135 |issue=3 |pages=411–468 |mr=1166640 |doi=10.2307/2946572 |jstor=2946572 }}</ref><ref>{{cite journal |last1=Saari |first1=Donald G. |last2=Xia |first2=Zhihong |title=Off to infinity in finite time |journal=Notices of the American Mathematical Society |date=April 1995 |volume=42 |issue=5 |pages=538–546 |url=https://www.ams.org/journals/notices/199505/saari-2.pdf }}</ref> In 1991, Gerver showed that 3n-body problems in the plane for some sufficiently large value of n also undergo non-collisional singularities.<ref>{{cite journal |last1=Gerver |first1=Joseph L |title=The existence of pseudocollisions in the plane |journal=Journal of Differential Equations |date=January 1991 |volume=89 |issue=1 |pages=1–68 |doi=10.1016/0022-0396(91)90110-U |bibcode=1991JDE....89....1G |doi-access=free }}</ref> |1989 |- | rowspan="3" |2nd |(a) Ergodicity of gases with soft cores |Find repulsive smooth potentials for which the dynamics of N particles in a box (with, e.g., smooth wall potentials) is ergodic. |Open as of 1984.{{Update inline|date=June 2021}} Sinai once proved that the hard sphere gas is ergodic, but no complete proof has appeared except for the case of two particles, and a sketch for three, four, and five particles.<ref name=":2" /> |? |- |(b) Approach to equilibrium |Use the scenario above to justify that large systems with forces that are attractive at suitable distances approach equilibrium, or find an alternate scenario that does not rely on strict ergodicity in finite volume. |Open as of 1984.{{Update inline|date=June 2021}} |? |- |(c) Asymptotic abelianness for the quantum Heisenberg dynamics |Prove or disprove that the multidimensional [[quantum Heisenberg model]] is asymptotically abelian. |Open as of 1984.{{Update inline|date=June 2021}} |? |- |3rd |[[Turbulence]] and all that |Develop a comprehensive theory of long-time behavior of dynamical systems, including a theory of the onset of and of fully developed turbulence. |Open as of 1984.{{Update inline|date=June 2021}} |? |- | rowspan="2" |4th |(a) Fourier's heat law |Find a mechanical model in which a system of size <math>L</math> with temperature difference <math>\Delta T</math> between its ends has a rate of heat temperature that goes as <math>L^{-1}</math> in the limit <math>L\to\infty</math>. |Open as of 1984.{{Update inline|date=June 2021}} |? |- |(b) Kubo's formula |Justify Kubo's formula in a quantum model or find an alternate theory of conductivity. |Open as of 1984.{{Update inline|date=June 2021}} |? |- | rowspan="4" |5th |(a) Exponential decay of <math>v = 2</math> classical Heisenberg correlations |Consider the two-dimensional classical Heisenberg model. Prove that for any [[Thermodynamic beta|beta]], correlations decay exponentially as distance approaches infinity. | rowspan="4" |Open as of 1984.{{Update inline|date=June 2021}} | rowspan="4" |? |- |(b) Pure phases and low temperatures for the <math>v\geq 3</math> classical Heisenberg model |Prove that, in the <math>D = 3</math> model at large beta and at dimension <math>v\geq 3</math>, the equilibrium states form a single orbit under <math>SO(3)</math>: the sphere. |- |(c) GKS for classical Heisenberg models |Let <math>f</math> and <math>g</math> be finite products of the form <math>(\sigma_{\alpha}\cdot\sigma_{\gamma})</math> in the <math>D = 3</math> model. Is it true that <math><fg>_{\Lambda, \beta}\geq<f>_{\Lambda, \beta}<g>_{\Lambda, \beta}</math> ?{{Clarification needed|date=June 2021|reason=unclear notation}} |- |(d) Phase transitions in the quantum Heisenberg model |Prove that for <math>v\geq 3</math> and large beta, the quantum Heisenberg model has long range order. |- |6th |Explanation of [[ferromagnetism]] |Verify the Heisenberg picture of the origin of ferromagnetism (or an alternative) in a suitable model of a realistic quantum system. |Open as of 1984.{{Update inline|date=June 2021}} |? |- |7th |Existence of continuum phase transitions |Show that for suitable choices of pair potential and density, the free energy is non-<math>C^1</math> at some beta. |Open as of 1984.{{Update inline|date=June 2021}} |? |- | rowspan="2" |8th |(a) Formulation of the [[renormalization group]] |Develop mathematically precise renormalization transformations for <math>v</math>-dimensional Ising-type systems. | rowspan="2" |Open as of 1984.{{Update inline|date=June 2021}} | rowspan="2" |? |- |(b) Proof of universality |Show that critical exponents for Ising-type systems with nearest neighbor coupling but different bond strengths in the three directions are independent of ratios of bond strengths. |- | rowspan="2" |9th |(a) Asymptotic completeness for short-range N-body quantum systems |Prove that <math>\oplus~\text{Ran}~\Omega_a^+ = L^2(X)</math>.{{Clarify|date=June 2021|reason=unclear notation}} | rowspan="2" |Open as of 1984.<ref name=":2" />{{Update needed|date=June 2021}} | rowspan="2" |? |- |(b) Asymptotic completeness for Coulomb potentials |Suppose <math>v = 3, V_{ij}(x) = e_{ij}|x|^{-1}</math>. Prove that <math>\oplus~\text{Ran}~\Omega_a^{D, +} = L^2(X)</math>.{{Clarify|date=June 2021}} |- | rowspan="5" |10th |(a) Monotonicity of ionization energy |(a) Prove that <math>(\Delta E)(N - 1, Z)\geq (\Delta E)(N, Z)</math>.{{Clarify|date=June 2021|reason=unclear notation}} | rowspan="5" |Open as of 1984.{{Update inline|date=June 2021}} | rowspan="5" |? |- |(b) The Scott correction |Prove that <math>\lim_{Z\to\infty} (E(Z, Z) - e_{TF}Z^{7/3})/Z^2</math> exists and is the constant found by Scott.{{Clarify|date=June 2021|reason=unclear notation}} |- |(c) Asymptotic ionization |Find the leading asymptotics of <math>(\Delta E)(Z, Z)</math>.{{Clarify|date=June 2021|reason=unclear notation}} |- |(d) Asymptotics of maximal ionized charge |Prove that <math>\lim_{Z\to\infty}N(Z)/Z = 1</math>.{{Clarify|date=June 2021|reason=unclear notation}} |- |(e) Rate of collapse of Bose matter |Find suitable <math>C_1, C_2, \alpha</math> such that <math>-C_1 N^{\alpha}\leq\tilde{E}_B(N, N; 1)\leq C_2 N^{\alpha}</math>.{{Clarify|date=June 2021|reason=unclear notation}} |- |11th |Existence of crystals |Prove a suitable version of the existence of crystals (e.g. there is a choice of minimizing configurations that converge to some infinite lattice configuration). |Open as of 1984.{{Update inline|date=June 2021}} |? |- | rowspan="5" |12th |(a) Existence of extended states in the Anderson model |Prove that in <math>v\geq 3</math> and for small <math>\lambda</math> that there is a region of absolutely continuous spectrum of the Anderson model, and determine whether this is false for <math>v = 2</math>.{{Clarify|date=June 2021}} | rowspan="5" |Open as of 1984.{{Update inline|date=June 2021}} | rowspan="5" |? |- |(b) Diffusive bound on "transport" in random potentials |Prove that <math>\text{Exp}(\delta_0, (e^{itH}\vec{N}e^{-itH})^2\delta_0)\leq c(1 + |t|)</math> for the Anderson model, and more general random potentials.{{Clarify|date=June 2021}} |- |(c) Smoothness of <math>k(E)</math> through the mobility edge in the Anderson model |Is <math>k(E)</math>, the integrated density of states{{Clarify|date=June 2021}}, a <math>C^{\infty}</math> function in the Anderson model at all couplings? |- |(d) Analysis of the almost Mathieu equation |Verify the following for the almost Mathieu equation: * If <math>\alpha</math> is a [[Liouville number]] and <math>\lambda\neq 0</math>, then the spectrum is purely singular continuous for almost all <math>\theta</math>. * If <math>\alpha</math> is a [[Roth number]] and <math>|\lambda| < 2</math>, then the spectrum is purely absolutely continuous for almost all <math>\theta</math>. * If <math>\alpha</math> is a Roth number and <math>|\lambda| > 2</math>, then the spectrum is purely dense pure point. * If <math>\alpha</math> is a Roth number and <math>|\lambda| = 2</math>, then <math>\sigma(h)</math>has Lebesgue measure zero and the spectrum is purely singular continuous.{{Clarify|date=June 2021}} |- |(e) Point spectrum in a continuous almost periodic model |Show that <math>-\frac{d^2}{dx^2} + \lambda\cos(2\pi x) + \mu\cos(2\pi\alpha x + \theta)</math> has some point spectrum for suitable <math>\alpha, \lambda, \mu</math> and almost all <math>\theta</math>. |- |13th |Critical exponent for [[Self-avoiding walk|self-avoiding walks]] |Let <math>D(n)</math> be the mean displacement of a random self-avoiding walk of length <math>n</math>. Show that <math>v := \lim_{n\to\infty}n^{-1}\ln D(n)</math> is <math>\frac{1}{2}</math> for dimension at least four and is greater otherwise. |Open as of 1984.{{Update inline|date=June 2021}} |? |- | rowspan="4" |14th |(a) Construct [[Quantum chromodynamics|QCD]] |Give a precise mathematical construction of quantum chromodynamics. | rowspan="4" |Open as of 1984.{{Update inline|date=June 2021}} | rowspan="4" |? |- |(b) Renormalizable [[Quantum field theory|QFT]] |Construct a nontrivial quantum field theory that is renormalizable but not superrenormalizable. |- |(c) Inconsistency of [[Quantum electrodynamics|QED]] |Prove that QED is not a consistent theory. |- |(d) Inconsistency of <math>\varphi_4^4</math> |Prove that a nontrivial <math>\varphi_4^4</math> theory does not exist. |- |15th |[[Cosmic censorship]] |Formulate and then prove or disprove a suitable version of cosmic censorship. |Open as of 1984.{{Update inline|date=June 2021}} |? |} In 2000, Simon claimed that five{{Which|date=September 2021}} of the problems he listed had been solved.<ref name=":0" /> </textarea><div class="templatesUsed"></div><p id="mw-returnto">Return to <a href="/wiki/Simon_problems" title="Simon problems">Simon problems</a>.</p> <noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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