Comments on: Did Anyone Invent Some New Math Stuff So They Could Solve A Problem Which Then Lead To a Technological Breakthrough?
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Comments on Ask MetaFilter post Did Anyone Invent Some New Math Stuff So They Could Solve A Problem Which Then Lead To a Technological Breakthrough?Wed, 06 Apr 2011 13:16:19 -0800Wed, 06 Apr 2011 13:18:19 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: Did Anyone Invent Some New Math Stuff So They Could Solve A Problem Which Then Lead To a Technological Breakthrough?
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough
Can you cite any examples where a technological breakthrough wasn't possible until there was some sort of mathematical breakthrough? <br /><br /> I've been told that Egyptians were able to forge ahead in geometry, which better allowed them to figure out the areas of their fields. I'm not exactly sure how useful this is, but this is the best example I can think of.<br>
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I'm also somewhat familiar with Leibniz and Newton and calculus, but did either of them start with a problem to solve, "figure out" integral calculus and then use it to solve their problem?<br>
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Did anyone else make a breakthrough once they figured out new mathematical techniques?post:ask.metafilter.com,2011:site.182770Wed, 06 Apr 2011 13:16:19 -0800Brian PucciomathmathsmathematicsBy: unixrat
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630156
Asymmetrical encryption is the basis for much of modern secure telecommunications.comment:ask.metafilter.com,2011:site.182770-2630156Wed, 06 Apr 2011 13:18:19 -0800unixratBy: the mad poster!
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630159
Bayesian statistics is the basis for all bayesian filtering systems (e.g. spam filters)comment:ask.metafilter.com,2011:site.182770-2630159Wed, 06 Apr 2011 13:19:08 -0800the mad poster!By: Brian Puccio
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630167
Bayesian statistics seems to go back to Thomas Bayes (1702–1761), so it doesn't look like some dude looking to write a spam filter figured out this branch of maths and was able to write a spam filter, it looks like the math was here before the technology. Thanks though!comment:ask.metafilter.com,2011:site.182770-2630167Wed, 06 Apr 2011 13:21:54 -0800Brian PuccioBy: Lutoslawski
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630177
Boolean Algebra and the computer?comment:ask.metafilter.com,2011:site.182770-2630177Wed, 06 Apr 2011 13:28:14 -0800LutoslawskiBy: zamboni
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630180
So your actual question is "did anyone, looking to solve a specific problem, come up with new mathematical techniques which allowed them to solve their problem?".comment:ask.metafilter.com,2011:site.182770-2630180Wed, 06 Apr 2011 13:29:17 -0800zamboniBy: kirkaracha
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630186
<a href="http://en.wikipedia.org/wiki/History_of_nuclear_weapons">Nuclear weapons.</a>comment:ask.metafilter.com,2011:site.182770-2630186Wed, 06 Apr 2011 13:30:16 -0800kirkarachaBy: Eyebrows McGee
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630199
Didn't Isaac Newton run into some unsolvable problems with his physics theories, so invented calculus to move forward?comment:ask.metafilter.com,2011:site.182770-2630199Wed, 06 Apr 2011 13:39:26 -0800Eyebrows McGeeBy: jasper411
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630203
I gather that CT scanning required certain math principles in order to accurately construct images emerging from the multiple scans. <br>
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from <a href="http://en.wikipedia.org/wiki/X-ray_computed_tomography">wikipedia</a>:<br>
<em>Tomography has been one of the pillars of radiologic diagnostics until the late 1970s, when the availability of minicomputers and of the transverse axial scanning method – this last due to the work of Godfrey Hounsfield and South African-born Allan McLeod Cormack – gradually supplanted it as the modality of CT. Mathematically, the method is based upon the use of the Radon Transform invented by Johann Radon in 1917. But as Cormack remembered later,[27] he had to find the solution himself since it was only in 1972 that he learned of the work of Radon, by chance.</em>comment:ask.metafilter.com,2011:site.182770-2630203Wed, 06 Apr 2011 13:43:37 -0800jasper411By: StickyCarpet
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630219
Bomb and artillery siting.comment:ask.metafilter.com,2011:site.182770-2630219Wed, 06 Apr 2011 13:55:23 -0800StickyCarpetBy: jchaw
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630221
E = mc^2comment:ask.metafilter.com,2011:site.182770-2630221Wed, 06 Apr 2011 13:58:24 -0800jchawBy: zug
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630226
Shannon information theory was a huge innovation that made the internet possible, as well as a pile of other technologies.<br>
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From <a href="http://en.wikipedia.org/wiki/Information_theory">wikipedia</a>:<br>
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"Applications of fundamental topics of information theory include lossless data compression (e.g. ZIP files), lossy data compression (e.g. MP3s), and channel coding (e.g. for DSL lines). The field is at the intersection of mathematics, statistics, computer science, physics, neurobiology, and electrical engineering. Its impact has been crucial to the success of the Voyager missions to deep space, the invention of the compact disc, the feasibility of mobile phones, the development of the Internet, the study of linguistics and of human perception, the understanding of black holes, and numerous other fields[citation needed]. Important sub-fields of information theory are source coding, channel coding, algorithmic complexity theory, algorithmic information theory, information-theoretic security, and measures of information."comment:ask.metafilter.com,2011:site.182770-2630226Wed, 06 Apr 2011 14:02:00 -0800zugBy: anaelith
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630240
<a href="http://en.wikipedia.org/wiki/John_von_Neumann">John von Neumann</a>. Especially his work in computer science and economics--although he was a pioneer in a bunch of fields.comment:ask.metafilter.com,2011:site.182770-2630240Wed, 06 Apr 2011 14:09:21 -0800anaelithBy: Chocolate Pickle
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630243
The development of <a href="http://en.wikipedia.org/wiki/Chaos_theory">chaos theory</a> has opened a lot of doors.comment:ask.metafilter.com,2011:site.182770-2630243Wed, 06 Apr 2011 14:11:03 -0800Chocolate PickleBy: muddgirl
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630251
<i>Didn't Isaac Newton run into some unsolvable problems with his physics theories, so invented calculus to move forward?</i><br>
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Sort of. Here's the question, as I understand it:<br>
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I roll a ball across a flat surface, and measure the distance it travels after time t_1, t_2, t_3, etc. I want to know the velocity at which it's traveling, but all I can come up with is the <i>average</i> velocity over some length of time (d2-d1)/(t2-t1). Newton wanted to know the <i>instantaneous</i> velocity. He pretty much had to invent calculus to get that. Calculus answers the question "what happens when (t2-t1) gets really, really, really small.<br>
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But really, he wasn't starting from a physical problem per se. Rather, he was starting from a foundation of geometry and arithmetic curves.comment:ask.metafilter.com,2011:site.182770-2630251Wed, 06 Apr 2011 14:17:24 -0800muddgirlBy: Brian Puccio
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630262
<blockquote>So your actual question is "did anyone, looking to solve a specific problem, come up with new mathematical techniques which allowed them to solve their problem?".</blockquote><br>
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Exactly. Problem, new maths, breakthrough.<br>
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Thanks everyone for your feedback, these are all excellent jumping off points!comment:ask.metafilter.com,2011:site.182770-2630262Wed, 06 Apr 2011 14:25:57 -0800Brian PuccioBy: Chocolate Pickle
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630266
<i>did anyone, looking to solve a specific problem, come up with new mathematical techniques which allowed them to solve their problem?</i><br>
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That would be <a href="http://en.wikipedia.org/wiki/Claude_E._Shannon">Claude Shannon</a>'s <a href="http://en.wikipedia.org/wiki/Information_Theory">Information Theory</a>. He was working at Bell Labs and needed to answer the basic question, "How much information can we reliably pump through one of our wires?"comment:ask.metafilter.com,2011:site.182770-2630266Wed, 06 Apr 2011 14:29:09 -0800Chocolate PickleBy: harmfulray
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630280
It's not exactly what you asked, but Chua's prediction of the <a href="http://spectrum.ieee.org/semiconductors/design/the-mysterious-memristor">memristor</a> is in the ballpark:<br>
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<blockquote><br>
Chua's theory [...] is framed in terms of the basic equations of electric circuits. Those equations link four quantities: voltage (v), current (i), charge (q) and magnetic flux (φ). Each equation establishes a relation between two of these variables. For example, the best-known equation is Ohm's Law, v=Ri, which says that voltage is proportional to current, with the constant of proportionality given by the resistance R. If a current of i amperes is flowing through a resistance of R ohms, then the voltage measured across the resistance will be v volts. A graph of current versus voltage for an ideal resistor is a straight line whose slope is R.<br>
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Equations of the same form but with different pairs of variables describe two more basic electrical properties, capacitance and inductance. And two more equations define current and voltage in terms of charge and flux. That makes a total of five equations, which bring together various pairings of the four variables v, i, q and φ. Chua observed that four things taken two at a time yield six possible combinations, and so a sixth equation could be formulated. The missing equation would connect charge q and magnetic flux φ and would describe a new circuit element, joining the resistor, the capacitor and the inductor. Those three devices had all been known since the 1830s, so the new element would be a very late and unexpected addition to the family. Chua named it the memristor.<br>
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No law of physics demanded that such a device exist, but no law forbade it either; the existing theory of circuits with resistance, capacitance and inductance could be augmented in a straightforward way to include memristance as well. Chua argued for the plausibility of the memristor on grounds of symmetry and completeness, suggesting an analogy with Dmitri Mendeleev's construction of the periodic table. Nature is not required to fill every square of this table, but a blank spot is certainly a good place to look for a new chemical element—or a new circuit element.<br>
</blockquote>comment:ask.metafilter.com,2011:site.182770-2630280Wed, 06 Apr 2011 14:38:10 -0800harmfulrayBy: harmfulray
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630285
Oops, here's the <a href="http://www.americanscientist.org/issues/pub/2011/2/the-memristor/3">cite</a> for that quote.comment:ask.metafilter.com,2011:site.182770-2630285Wed, 06 Apr 2011 14:41:41 -0800harmfulrayBy: Chocolate Pickle
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630301
von Neumann studied the Prisoner's Dilemma and things like it in Game Theory in part because he was developing the doctrine of Mutually Assured Destruction as a way of preventing an intercontinental nuclear war.comment:ask.metafilter.com,2011:site.182770-2630301Wed, 06 Apr 2011 14:56:37 -0800Chocolate PickleBy: Chocolate Pickle
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630312
I mentioned Chaos Theory above. That's actually an example of what you seek. The guy who came up with the foundation of Chaos theory (the idea of extreme sensitivity to initial conditions) was trying to explain why his computer programs couldn't predict weather a long time into the future. Chaos theory made clear that it isn't possible to predict chaotic systems accurately a long way out because you can never know the initial condition sufficiently accurately. Any error, however infinitesimal, in how you set up your model would cause it to diverge from reality eventually.<br>
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It didn't <i>solve</i> his problem, though. What it did was demonstrate that it was impossible to do what he was attempting to do.comment:ask.metafilter.com,2011:site.182770-2630312Wed, 06 Apr 2011 15:03:49 -0800Chocolate PickleBy: Blazecock Pileon
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630320
Seconding nuclear weapons.comment:ask.metafilter.com,2011:site.182770-2630320Wed, 06 Apr 2011 15:10:30 -0800Blazecock PileonBy: Chocolate Pickle
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630323
I just thought of another one. <a href="http://en.wikipedia.org/wiki/John_Snow_(physician)#Cholera">John Snow</a> developed what we now would think of as "epidemiology", an application of statistics to analysis of causes and spread of disease, in response to a cholera epidemic in London in the 1850's.<br>
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He had available to him a huge listing of cholera deaths, with information about all the victims, and tried slicing the data in all sorts of different ways in order to see if he could find correlations with other things. One thing he did was plot deaths on a map of the city, and in doing so he found one cluster, all centered around a single water pump. He was thus able to show that cholera was being spread by drinking water contaminated with human sewage. (This is all the more noteworthy because his work predated the Germ Theory of disease.)comment:ask.metafilter.com,2011:site.182770-2630323Wed, 06 Apr 2011 15:14:41 -0800Chocolate PickleBy: teraflop
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630367
Nuclear weapons are definitely not a good example of this at all. Einstein came up with the principle of mass-energy equivalence in 1905, almost 40 years before the Manhattan Project began. At the time, nobody even knew there was such a thing as an atomic nucleus. Furthermore, nuclear fission does <i>not</i> convert matter into energy; it breaks apart atoms to release some of the binding energy that holds the nucleons together. The fact that this energy has a small but measurable mass is beside the point. Nuclear weapons were based on physical research on the properties of atoms, not on any new mathematical breakthroughs.<br>
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With a few notable exceptions, like Newton's development of calculus, I think this is more common in fiction than in real life. For instance, in Ursula Le Guin's novel <i>The Dispossessed</i>:<br>
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<blockquote>"What is the ansible?"<br>
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"It's what he's calling an instantaneous communication device. He says if the temporalists—that's you, of course—will just work out the time-inertia equations, the engineers—that's him—will be able to build the damned thing, test it, and thus incidentally prove the validity of the theory, within months or weeks."</blockquote><br>
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TV Tropes has a page on <a href="http://tvtropes.org/pmwiki/pmwiki.php/Main/FormulaicMagic">"formulaic magic"</a> which is a similar idea.comment:ask.metafilter.com,2011:site.182770-2630367Wed, 06 Apr 2011 16:00:50 -0800teraflopBy: benzenedream
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630387
<a href="http://en.wikipedia.org/wiki/William_Sealy_Gosset">Gosset (better known as Student)</a> developed the T-test for brewing and agricultural work.<br>
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<a href="http://en.wikipedia.org/wiki/Ronald_Fisher">Fisher</a> basically developed much of modern statistics for use in population genetics.comment:ask.metafilter.com,2011:site.182770-2630387Wed, 06 Apr 2011 16:27:30 -0800benzenedreamBy: scalespace
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630716
Cracking of the Enigma machine using the<a href="http://en.wikipedia.org/wiki/Banburismus"> Banburismus</a> procedure, which is related to the <a href="http://en.wikipedia.org/wiki/Sequential_analysis">sequential analysis</a> technique in stats.comment:ask.metafilter.com,2011:site.182770-2630716Wed, 06 Apr 2011 22:19:51 -0800scalespaceBy: palindromic
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630873
<a href="http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html">GPS and relativity?</a>comment:ask.metafilter.com,2011:site.182770-2630873Thu, 07 Apr 2011 06:49:47 -0800palindromicBy: teraflop
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2630884
Again, the theory of relativity was formulated long before GPS was conceived -- probably before such a thing was even imaginable. The question asks for mathematical breakthroughs that happened <em>in response to</em> a technological problem.comment:ask.metafilter.com,2011:site.182770-2630884Thu, 07 Apr 2011 07:11:11 -0800teraflopBy: DU
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2631298
I don't know if I'd say that logarithms were invented to make hand-calculations easier, but they were certainly more exploited than they would have been because of that. Like, hand-calculations are hard, logarithms exist and that's good, but then someone is like "but I need to do THIS thing which is SO CLOSE to what we can already do...I think I'll figure out something extra about logs and BLAMMO! now I can do it!"comment:ask.metafilter.com,2011:site.182770-2631298Thu, 07 Apr 2011 11:53:04 -0800DUBy: TwelveTwo
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2631642
Usually the fruits of one field are food for another. A result in one field may be a solution in another. Autotrophic disciplines are few and far between.comment:ask.metafilter.com,2011:site.182770-2631642Thu, 07 Apr 2011 15:31:10 -0800TwelveTwoBy: TwelveTwo
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2631660
That is, it is rare for an answer resulting from a given line of inquiry to also be the very question that is posed to produce the answer in the first place. Instead, you must shift focus and aim at a different problem, then reframe the original problem according to the results borne from the alternative side problem. If the problem doesn't require such a shift then it isn't much of a problem, you can just continue unspooling the consequences out from what is already known. So, yeah, a mathematical result allowing for a technological problem to be solved and a technological result allowing for a mathematical problem to be solved are both just as likely. The absence of such cross-pollination would be the real shocker. It would imply that the discipline is perfectly self-contained and devoid of theoretical problems and gaps.comment:ask.metafilter.com,2011:site.182770-2631660Thu, 07 Apr 2011 15:46:44 -0800TwelveTwoBy: TwelveTwo
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2631677
And to more directly answer the question, a good example is Feynman's path integral. A mathematical tool invented to resolve a physics problem that to this day is still a big of a bugaboo for mathematicians seeking to form a rigorous definition of it. This is a quite a bit different than the survey of existing mathematical techniques and discovering that one or a few of them are immediately applicable to a problem exterior to its origin. That is, the path integral was a mathematical tool that was originally<em> foreign</em> to mathematics, and I so should fit the example you ordered.comment:ask.metafilter.com,2011:site.182770-2631677Thu, 07 Apr 2011 15:56:19 -0800TwelveTwoBy: Brian Puccio
http://ask.metafilter.com/182770/Did-Anyone-Invent-Some-New-Math-Stuff-So-They-Could-Solve-A-Problem-Which-Then-Lead-To-a-Technological-Breakthrough#2633560
I'm aware that it's quite rare for the math to not already exist/be known when a problem arises, which is why I came here. Thanks to those of you who came up with exactly what I was looking for.comment:ask.metafilter.com,2011:site.182770-2633560Sat, 09 Apr 2011 06:25:54 -0800Brian Puccio