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'To Live Your Best Life, Do Mathematics' (quantamagazine.org)
Excerpts from an article on Quanta Magazine, rearranged for clarity and space: Math conferences don't usually feature standing ovations, but Francis Su received one last month in Atlanta. In his talk he framed mathematics as a pursuit uniquely suited to the achievement of human flourishing, a concept the ancient Greeks called eudaimonia, or a life composed of all the highest goods. Su talked of five basic human desires that are met through the pursuit of mathematics: play, beauty, truth, justice and love. Su opened his talk with the story of Christopher, an inmate serving a long sentence for armed robbery who had begun to teach himself math from textbooks he had ordered. After seven years in prison, during which he studied algebra, trigonometry, geometry and calculus, he wrote to Su asking for advice on how to continue his work. After Su told this story, he asked the packed ballroom at the Marriott Marquis, his voice breaking: "When you think of who does mathematics, do you think of Christopher?" If mathematics is a medium for human flourishing, it stands to reason that everyone should have a chance to participate in it. But in his talk Su identified what he views as structural barriers in the mathematical community that dictate who gets the opportunity to succeed in the field -- from the requirements attached to graduate school admissions to implicit assumptions about who looks the part of a budding mathematician. When Su finished his talk, the audience rose to its feet and applauded, and many of his fellow mathematicians came up to him afterward to say he had made them cry. [...] Mathematics builds skills that allow people to do things they might otherwise not have been able to do or experience. If I learn mathematics and I become a better thinker, I develop perseverance, because I know what it's like to wrestle with a hard problem, and I develop hopefulness that I will actually solve these problems. And some people experience a kind of transcendent wonder that they're seeing something true about the universe. That's a source of joy and flourishing.
>> some people experience a kind of transcendent wonder that they're seeing something true about the universe
Those would be the ones that took an illegal substance before solving for x.
Transcript: https://mathyawp.wordpress.com/2017/01/08/mathematics-for-human-flourishing/
Audio Recording: https://www.dropbox.com/s/55i43l2irm57y9c/01%20Mathematics%20for%20Human%20Flourishing.mp3?dl=0
Good thing for most of us in fields that are lumped into that acronym, the difficulty of the work generally selects for who ends up in those careers. Maybe if we encourage more people to stand and deliver then we simply won't need to import talent and we could legitimately scale back totals on H1B quotas citing graduation rates and test scores as why we don't need ao many foreign skilled workers.
Do not look into laser with remaining eye.
Those would be the ones that took an illegal substance before solving for x.
Not all, but Erdos I think definitely fell into that category.
SJW n. One who posts facts.
... since they didn't have the numbers for it. Still their aqueducts lasted centuries and millennia. Nassim Taleb says a side effects mathematics is to optimize and cut corners, making things fragile. He also quoted a science historian that before the 13th century no more than five persons in Europe knew how to perform a division. But their architects made all those cathedrals that are more or less still standing. (They apparently didn't know geometry either: a triangle was visualized as the head of a horse.)
Not saying don't use mathematics, that would be insane, just listing counterexamples to the claim that life is best lived with mathematics. Any boxing in becomes counterproductive at some level.
Those would be the ones that took an illegal substance before solving for x.
Not all, but Erdos I think definitely fell into that category.
Probably not. Were amphetamines illegal then? For most of human history, the War on Drugs would have been an absurd concept (because it is an absurd concept). We have to make sure that genius mathematicians don't take all the amphetamines. Otherwise what will we pump our elementary school children full of!?
I think one of the problems with mathematics is that it's pretty hard to get the average person to see it as anything other than a tool. Maybe that's how it's taught, but how do you get average students interested in math the same way mathematicians are? Where is the hook in people's minds that turns them on to it as something other than a bunch of formulas and operations? I know it's a cop-out to say I suck at math, but I really do feel I'm mathematically challenged. I wonder if it was just because I didn't get some magic spark early on. I remember all of my elementary and high school math being a long slog of memorization with very little understanding. I was never very good at it and just learned enough to handle the exams. Like every high school student, I still remember to this day that x = -b +/- (sqrt(b^2 - 4ac)/2a) but I have no idea why that is or what it's good for other than getting the answers to a quadratic equation. I think my lack of math background kept me out of civil or chemical engineering, despite a huge interest in both.
One reason why I think proper teaching may play a role is because I had a similar experience studying chemistry in college. I had a very good introductory chemistry teacher and something just clicked. Almost everyone saw it as a bunch of nonsense formulas and equations for various phenomena that had to be memorized for the exams and forgotten, but somehow I got a little more out of it and it was interesting enough that I got a degree in it. Good thing too -- by the second year of engineering school I knew I wasn't going to be able to keep up with my poor math background and didn't want to end up a generic business major!
It will make solving difficult computer problems much easier.
Even better with atl-math you can make up you own truths...
What you've just described is not alt-maths, it is in fact actual regular maths.
For example, you can make up your own truth about how 1+1 isn't really 2 and you wind up with Galois theory and finite fields. Or invent something impossible like x*x=-1 and you end up with complex numbers.
Or you can invent absurd things like "infinity" and so find that 1-2+3-4+5-... to infinity ends up rather oddly as 0.25 (don't even look at 1+2+3+4+...).
Mathematics is in fact all about making up the rules and seeing where they lead. There are basically 3 outcomes:
1. trivial (and therefore not interesting).
2. inconsistent (and therefore not interesting).
3. interesting.
SJW n. One who posts facts.
Arithmetic is less than .01% of math.
Why is the mathematics profession dying?
Fixed that for you. Short answer: It's not. Long answer: Purists don't like applied mathematics, but the modern world is applied not theoretical.
Good thing for most of us in fields that are lumped into that acronym, the difficulty of the work generally selects for who ends up in those careers.
Simply not true. Those of us who are most passionate about STEM are those who never enter the field, because careers are made by mediocre morons who manipulate their way into positions of power and close ranks to keep talented upstarts out. If we're lucky, we end up working dead-end jobs while blogging about our STEM-related hobbies. If we're unlucky, we end up committing armed robbery and studying STEM in a prison cell.
Maybe if we encourage more people to stand and deliver
To which meaning of "stand and deliver" are you referring here?
"A phrase traditionally used by a highwayman commanding victims to hand over their valuables."
That would be armed robbery, after which you could study STEM in a prison cell.
"Stand and Deliver is a 1988 American drama film based on the true story of high school math teacher Jaime Escalante."
That would be showmanship, with heavy subtext that if you study STEM, you will end up at a dead-end job teaching STEM in high school instead of applying anything you learned.
I have a math degree, I went into medicine. I can honestly say very very little math that I learned has been useful in any meaningful way (only really some basic stats), Analysis, partial differential equations, algebras and all that stuff while enjoyable (and incredibly work/ time intensive in undergrad) have really not improved my life in any way and really it seems like a sad waste as most of it has just faded away (although epsilon and delta will always cause a small smile in my heart) but damn you Ji and eta
Have a great day.
The problem with test scores is that they don't mean shit except that you have either been an ass-kiss student who was used by a professor,
For the literature teacher who wants you to exalt their favorite author or the history/civics teacher who will give you a higher grade for parroting their political point of view, you might have a point.
One of the better points of science and math is that it's not quite as subject to that sort of kiss-assery. When you answer "What's 2+2" with the number 4, your teacher can't dock you points because they don't like the way you wrote the 4.
Inconsistent need not be uninteresting. Many things that at first glance are inconsistent need a minor change to behave consistently. sqrt -1 was inconsistent until a new perspective was imposed that made a newly consistent system.
That's just... bullshit.
Is walking "accessible to anyone who really tries"? What if they have no legs?
Lots of people simply do not have the intellectual facilities -- not training, I'm talking about capacity here -- to even begin to approach mathematics beyond various levels. Every person is a mix of capacities and limits. To claim that undertaking X is accessible to any person who "really tries" demonstrates nothing more than that the claimant has very little understanding of people in general.
Or to look at it from the other end of the stick, you're not going to become Einstein just because you "really try."
We're not identical cupcakes spewed out by a cupcake factory, some of us missing the icing just because we went down a different conveyor belt.
Not yet, anyway.
I've fallen off your lawn, and I can't get up.
Inconsistent need not be uninteresting. Many things that at first glance are inconsistent need a minor change to behave consistently. sqrt -1 was inconsistent until a new perspective was imposed that made a newly consistent system.
I don't think sqrt -1 was inconsistent. Inconsistent is where you can for example prove both a and not a from the same axioms.
SJW n. One who posts facts.
The ugliness of the real world in comparison to that mathematical beauty can unfortunately be a bit too much.
"I bless every day that I continue to live, for every day is pure profit."
Numbers have been nothing but logic for me.
Those five basic human needs are what I have found in reading and writing. There you deal with emotions and subjectivity.
Write and/or read. https://scifurz.wordpress.com/
Math conferences don't usually feature standing ovations, ...
That's because the usually ask people to limit their applause, but as the number of people still standing approaches zero, there's always one guy who keeps clapping for *way* too long...
It must have been something you assimilated. . . .
Or I could be referring to the history of the Calculus program that the high school that Olmos' character portrayed as having built and nurtured...
Do not look into laser with remaining eye.
Seriously. This sounds like a sad sad man.
Actually, it sounds like a very happy man. The thing that is missing though is that he doesn't seem to realize that just because something makes him happy it doesn't mean that it will make everyone else happy. Everyone is wired a little different. I'm pretty good at math but I find it boring. I enjoy programming which is similar but for whatever reason I find it a lot more interesting and can get lost for hours in a tedious problem that would drive other people crazy. I have a good friend who can't stand to be at a desk job. He *loves* pouring concrete which is about the worst job I can think of but after 4 years at a desk job (as a co-owner of the company no less), he quit and went back to pouring concrete because that is what he enjoys.
And the difference being?
You've probably never seen the film. It's a direct reference to students who were considered by society to somehow be unable to learn those mathematics, not only being able to learn that material, but also being able to demonstrate their knowledge and mastery when the world decided there was no way those poor dregs could have actually amounted to anything and learned the material for themselves. It's a pretty clear indication that the U.S. has plenty of capable workers, but that our education system fails them and that society fails to recognize their potential for success.
Also, it's pretty damned elitist to think that someone in education has a dead-end job or one that they couldn't possibly enjoy.
>> desires met through math: ...truth
Clearly, he's never met a statistician.
And the difference being?
er huh? The difference being that they're different?
If you limit yourself to the reals, how can you prove some proposition P and also prove not P?
SJW n. One who posts facts.
What? This is like the best Slashdot summary I have seen in years. Congrats to the Department of the Pursuit of Happiness (No editor was credited?)
This is very much News for Nerds, and pure mathematics is stuff that matters to the whole universe.
I'm pretty good at math but I find it boring. I enjoy programming which is similar but for whatever reason I find it a lot more interesting
Me too. I think the big difference is the lack of feedback in math. If I work for hours or days to construct a proof, I don't really know if it is valid or not, and maybe it was all a waste of time because I made an error in the first few steps. With programming, I can test incrementally, fix errors as I go, and I can see the end result is valid because the program works. The feeling of accomplishment is much better.
Also, programming pays better.
I have a math degree and then got a PhD in EE. I drifted into software development of physics codes and have to say that my undergraduate math degree has been very useful. It basically taught me how to think and approach problems. I see code as a theorem and every step needs to be examined for logical errors and implicit assumptions. As a result, I have been able to catch bugs by reading my and other peoples codes before testing. While I would never have been happy as a mathematician, the skills it provides can still be valuable for other occupations.
some people experience a kind of transcendent wonder that they're seeing something true about the universe
Isn't the same math true in any universe?
Could there be an alternative universe where 1+1=3?
Or where 4 is prime?
This statement is a lie starts off with no value. It then evaluates to false and remains so, for it can never mister the credulity to ever be a lie. Perhaps you were thinking of, This statement is false, which starts off with no value, becomes false and then alternates between true and false.
The ugliness of the real world in comparison to that mathematical beauty can unfortunately be a bit too much.
The profession with the highest suicide rate is farming.
The lowest are teachers and librarians.
Mathematicians are in the middle.
Farmers tend to be old, they often work alone, and one bad season can ruin them financially.
These are all aggravating factors for suicide.
How much effort was put into helping him understandthe concepts behind which operator to use? Even going bact to two dimensions and illustrating what happens when you take three rows of three and multiply them as opposed to adding them and explaining that the word "by" can signla a multiplication may scratch deeper than what he has picked up on so far. You have to get his attention first though, and there are lots of other unexplored details. So we know too little about how people work and fail to work to adequately address the situation of what people can and cannot do.
Thank you.
Some argue that programming is merely a form that an expression of math can take.
When you answer "What's 2+2" with the number 4, your teacher can't dock you points because they don't like the way you wrote the 4.
They can, however, dock you points for getting the wrong answer if, for example, you're supposed to be working in GF(3).
SJW n. One who posts facts.
2* 3 is different from 3*2 and 3+3. That doesn't mean they can't all equal 6. I meant, what was the difference thst makes your example inconsistent and my example not inconsistent.
Ah yes, prison rape joke.
Prison rape jokes are a GOOD THING. You should look at them as a sign of progress. Remember the old adage: First they ignore us, then they laugh at us, then they fight us, then we win. Jokes about prison rape mean we have moved from stage 1 (ignoring) to stage 2 (laughing). The brutality of our prison system is a horrific stain on our civilization, and the current rate of incarceration (America's rate is four times higher than either China or Russia) is appalling. Prison reform and sentencing reform are noble causes, and even the incremental progress of getting people to acknowledge the issues with humor is encouraging.
Thanks... you know I felt a bit guilty about posting such a trollish comment but now reading your interesting post made it worth.
Breaking news: thinking rationally using logic makes you less irrational. Wow, Slashdot is full of insight these days...
Help! I am a self-aware entity trapped in an abstract function!
Enjoyed the math enough but decided to go in a different direction like Computer and Information Science, Information Security etc. It's where I went.
I meant, what was the difference thst makes your example inconsistent and my example not inconsistent.
Pretty much the definition of inconsistent is when, for some proposition, P, you can prove P and prove not P from your axioms.
You haven't proven any proposition let alone its inverse, so you example is not one of inconsistency. I don't follow what you consider to be inconsistent about 2*3=6 and 3*2=6 and 3+3=6.
SJW n. One who posts facts.
The flexibility allows you to store more energy and launch the weapon faster.
https://www.youtube.com/watch?v=BkK2vEZ5bTk
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
<-- kr5ddit.com
Linked site collects user data and is suspected to harbor malware.
Often causes shark attacks.
Site owner is vindictive and abusive.
Site prone to fail when accessed by more than five users simultaneously.
Approach with Caution
Why is it incumbent on him to even give a shit? Personally, I'd let the co-worker flounder. He's had plenty of time in life to learn. More likely, he's just lazy. Not like it's difficult to slap a sticky on the wall that says "package volume takes multiplication".
Untrue. We *can* be adequate about it, just not perfect. I'll wager that even *you* will tell at a glance that this guy is not going to be doing any significant math.
Unless you want to know what your actual acreage is.
That's not true, I had two 1st grade math teachers. : I was doing multiplication problems and powers of 2 in with my first one (a continuation of stuff I learned from my father). Then my family moved. My second 1st grade math teacher docked me for writing fours with a triangular top (4) as opposed the accepted fours that look like an upside down 'h'. I was also docked for writing 9's that look like upside down 6's, instead of the accepted nines that look like mirrored P's. As punishment, I was required to fill up a notebook page of with hundreds of mirror-P shaped 9's.
Many of my teachers were more focused on indoctrinating me rather than improving my mind.
Reflecting; it is funny that the fonts I use today depict numbers the way I learned to write them from my Dad rather than the way I learned to write them in school.
-- Each tock of the Planck clock is a new world and here we are still life. --
No, he just likes AKB48.
My second 1st grade math teacher docked me for writing fours with a triangular top (4) as opposed the accepted fours that look like an upside down 'h'. I was also docked for writing 9's that look like upside down 6's, instead of the accepted nines that look like mirrored P's.
I've heard similar stories, but it's always in the early grades of elementary school, where the teachers aren't expected to understand specific subjects -- the school is more about fitting in than knowing or learning. After the first few years, you should have proper subject teachers. In contrast, the GP's points about kiss-assery in certain subjects is a lifelong issue.
Escher was the first MC and Giger invented the HR department.
What is with these nonsensical postings, almost always as AC? There seem to be more and more of them over the last few months, and pretty much on any article. My guess is /. is an easy way to inject output by scripts that generate pseudo-random phrases, and possibly monitor the replies (like this one).
Starting to /. needs an always-available way to tag nonsense posts rather than having to wait for mod points so it can be marked Offtopic.
Just the other day, aliens from Rijel 9 plucked him up and retrained his neural net to fly their hypertrasnwarp gizmo home instead of running his body.
But seriously, I don't know what he is capable of. We don't even know how what he does have allows him to perform the tasks he seems capable of performing in the photo.
Math is not an empirical concept. It's not a property of our universe. It's a set of first principles, plus a set of principles of deduction, like any other formal system.
Math works shockingly well in predicting our universe, though. Handy, that.
Socialism: a lie told by totalitarians and believed by fools.
I was on my phone and several times circumstances ate my post. I'm fairly certain that some of the other times I had it right. The shortcomings involved with making these posts offer lots of opportunities for errors to creep in other than being unable to spell. And since we seem to have a difference of opinion as to whether my assertion was a pedantic nitpick or a somewhat solid refutation of his claim, anyone else wish to chime in?
Mathematicians Agree That Mathematics Is The Best
As a general rule, people do not listen to music because it is useful. They listen to it because they can appreciate it on many levels, from the poetry of the words, the emotional tenor of the melodies and harmonics, the driving urge of the rhythms, and the overarching story told by the composer. Nobody (or almost nobody) argues that listening to music is a waste of time because it did not help them on their job. Music is the reward not the labor, though for musicians and composers it can be both.
I think what the story about Christopher is trying to say is that mathematics can have a similar appeal for those who can learn to appreciate it. But looking at music also shows something else. People's tastes in music vary greatly. One person's greatest and most moving musical performance can be on another person's "hate list" (I am thinking of Disco when I say this). Similar things can be said about art, dance, movies, architecture, games, and sports (and probably much more can be added to this list). In my view, one of the points of a good education is to learn how to see at least a few of these things as rewards instead of as labors. For a mathematician, math is its own reward and there is an argument to be made that a large part of the world truly cannot understand that fact, especially if they have never had an intimate understanding (full on with the proofs using limits) of a theorem like the Fundamental Theorem of Calculus.
But to say that anybody can or should appreciate math is nonsense, just as saying that all persons should love Disco or Abba.
"Data" is not the plural of "anecdote."
I've fallen off your lawn, and I can't get up.
At first, when I read the title I thought to myself, "how arrogant." What about people who are primarily verbal - and don't do math, or don't care to do math? Are they not equally fulfilled in their lives? How rich - a scientist who makes sweeping generalizations in a scientific journal.
If he had prefaced it with, "I have observed in some people that...blah blah blah," then yeah, that would be defensible.
Lodragan Draoidh
The more you explain it, the more I don't understand it. - Mark Twain
That's... not true. Like at all. You can group the terms and then argue it comes out to negative infinity. Or positive infinity. But I don't see any way to make it come out to 0.25.
Your ad here. Ask me how!
I wish I had mod points for you and ShanghaiBill. Couldn't be more correct, unfortunately.
Hanlon's Razor -- Never attribute to malice that which is adequately explained by stupidity.
I thought it was Air Traffic Controllers.
Complex analysis and google isn't being very helpful.
i am so very tired....
All the math teachers I ever had tended to be be very precise and open about the algorithms that they use to arrive at your final grade. Of all the teachers I had, I would generalize that they were the least likely to grade on feeling or hunches. Partially because they have a subject that is very discreet in nature (you are generally either right or wrong, with little opinion in the process) and because the sort of person who is attracted to math likes structure and order.
You could be correct, but your story has a odd smell.
HA! I just wasted some of your bandwidth with a frivolous sig!
The aqueducts that lasted millennia are only those that you can see now. You should take into account all the aqueducts that crumbled after earthquakes and all those that would have crumbled if the locals hadn't quarried them.
__
Men with no respect for life must never be allowed to control the ultimate instruments of death.
GW Bu
Sounds as if you can find an excuse for any sort of abuse.
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Pity the poor CEO of Microsoft. He's in a dead-end job; he can never be promoted.
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The cost of teaching algebra is pretty close to the cost of teaching "Dick and Jane". Allocating more money to teach advanced subjects K-12 is wasting money, because the actual costs for the advanced subjects (unless they require additional expensive equipment and consumables) is the same as basic subjects.
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If you're trying for humor, you failed. If you're aiming for bitter incoherence, you've succeeded.
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You're not arguing education or not, you're arguing the extent.
The counter-argument is that people should be educated or have the opportunity to be educated to the extent that they're willing to pursue it.
Calculus itself may not be of-use to most people, but learning how to learn Calculus is itself a skill which may translate into other learning that the individual as an adult will need, especially when it is now the norm that people will change careers potentially several times through their working lives.
I don't use calculus even in my technical job, but I do have to devise complex plans that require lots of data collection and analysis and whose subsequent steps are based on prior results. I also do kinds of math at work that I never learned to do in school, like number base conversion and binary arithmetic. Complex math has been helpful for me even if I don't use the original material.
Kids should have the opportunity to have this education in high school and should be encouraged to pursue it. Obviously not all will take the opportunity and not all will be qualified to take it even if they want it, but we should attempt to at least have our kids start out with the same opportunities.
Do not look into laser with remaining eye.
Mathematician presents some "Math(s) is bwetiful auwsome" nonsense at a math(s) conference and gets a standing ovation from other mathematicians.
I'm stunned, I tell you!
There is an odd but persistent correlation between mathematics and insanity. A prison math program could convert an ordinary robber into a crazed serial killer who becomes a political hero to other wackjobs: https://www.google.com/search?...
Who choosed that there are exactly five platonic solids in a 3D universe?
Plato.
Duh.
A lot of math has utility. We humans need to eat and we like to be comfortable. Choosing the sort of math that allows us to do those things is in large part not arbitrary.
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Then who wins? The prison rapists?
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Similar story here, although I can't remember (it *was* almost 60 years ago) whether I got points off for writing your kind of 4 and 9 (and a 2 that looked like the printed 2, rather than some kind of curly-cue thing), or whether I just gave in so I wouldn't lose points. It wasn't until drafting class in High School that I reverted to my father's 2, 4 and 9. (He was an engineer, and in those days being an engineer meant hand-written numbers and words on your blueprints: drafting.)
Another movie you might like, with similar point of view, is "Spare Parts" (http://www.imdb.com/title/tt3233418/). Also a book. A Wired article tells the story more briefly (https://www.wired.com/2014/12/spare-parts/).
I took algebra, geometry, trig, and calculus in High School, and a smattering of linear algebra; finished with a semester of calculus and a semester of probability and statistics in college. The latter was a very theory-oriented course: we learned that there is a theorem that says it's possible to cut up a solid object and put it back together in such a way that it's twice as big (radius, volume, doesn't matter) with no space. (Of course it only works if the sphere is infinitely divisible, i.e. not atomic.)
What have I actually needed since then? Well, I studied linguistics, and now work in computational linguistics. Geometry was eye opening: the notion of proof from axioms. Basic algebra and trig were of some use; advanced algebra and calculus never really helped. But I sure wish I knew more about linear algebra and statistics.
YMMV, of course; engineers, especially electrical engineers, probably need the rest, and of course there are science disciplines that need other kinds of math. But IMHO *everyone* should know a lot more about probability and statistics. And that includes students who never go to college. Very little algebra is needed to get a working knowledge of statistics.
In sum, I think the math that's taught (past arithmetic) is upside down. (Most) people need more statistics, and far less algebra, trig, calculus...
Coffee was illegal?
Oops, I guess that saying was wrongly attributed to Erds. But Erds is said to have drunk a lot of coffee.
As a linguist, I guess I have to agree with you about skyscrapers. (There's a story about a certain skyscraper and some languages...) And you're right in lots of what you say. But I guess there are other things you can't describe with math, but you can with language. The beauty of a sunset, the uglyness of a burned out car; love, hate; joy, sorrow. We would not be human if we had math but no language.
Math is not the better language, nor is language the better math. I'd say they were orthogonal, but that's not quite true either. But they certainly serve different purposes in different ways.
Oops, I guess that saying was wrongly attributed to Erds. But Erds is said to have drunk a lot of coffee.
Indeed. He attributed it to someone else. Nevertheless he did drink a lot of coffee and also took a lot of amphetamines.
SJW n. One who posts facts.
If you use automated proof verifiers, like HOL, Metamath, Mizar, etc., the experience is the exact opposite from what you suggest. When a proof is automatically verified, you KNOW the math is 100% correct, even if you spent days working out the proof. That provides a tremendous sense of accomplishment. When writing a computer program of any complexity, while it can be satisfying to see it run, you will never know (barring formal verification) that there aren't still hidden bugs not yet uncovered.
On a semi-related topic, I guess /. doesn't do Unicode (I recall seeing that in someone's sig line). When I typed in my post, I had an umlauted 'o' in Erdos' name, and I see it's gone now. Weird, I wonder why /. can't get with the times? It's not like Unicode is new...
Just for reference the important caveat is no logic that can encode basic Peano arithmetic can be consistent and complete. There are plenty of axiomatic systems that are complete and consistent, even complicated mathematical ones (the first order theory of complete ordered fields, a.k.a. the real numbers is complete and consistent). Also a stronger logic can prove the consistency of a subset contained within it. Thus the first order theory of Peano arithmetic can be proved to be consistent via second order logic. Finally you may also want to look up Tarski's indefinitability of truth -- a theorem which gives the results you have here as a corollary, but is simpler: in sufficiently power logical systems you can't even define a truth predicate.
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