Hacker News new | past | comments | ask | show | jobs | submit login
Paul Erdős: a life that added up to something (1996) (osu.edu)
246 points by michaelhoffman on Oct 7, 2016 | hide | past | favorite | 64 comments



Here's the first chapter of a book on him: https://www.nytimes.com/books/first/h/hoffman-man.html. Interesting insight into his personality (generous, warm, eccentric, curious), obsession with mathematics, reliance on amphethamines, and wide-spread collaboration with peers (Erdös number).

> To communicate with Erdös you had to learn his language. "When we met," said Martin Gardner, the mathematical essayist, "his first question was `When did you arrive?' I looked at my watch, but Graham whispered to me that it was Erdös's way of asking, `When were you born?'" Erdös often asked the same question another way: "When did the misfortune of birth overtake you?" His language had a special vocabulary--not just "the SF"[1] and "epsilon"[2] but also "bosses" (women), "slaves" (men), "captured" (married), "liberated" (divorced), "recaptured" (remarried), "noise" (music), "poison" (alcohol), "preaching" (giving a mathematics lecture), "Sam" (the United States), and "Joe" (the Soviet Union). When he said someone had "died," Erdös meant that the person had stopped doing mathematics. When he said someone had "left," the person had died.

[1] "The SF is the Supreme Fascist, the Number-One Guy Up There, God, who was always tormenting Erdös by hiding his glasses, stealing his Hungarian passport, or, worse yet, keeping to Himself the elegant solutions to all sorts of intriguing mathematical problems."

[2] "Epsilon was Erdös's word for a small child; in mathematics that Greek letter is used to represent small quantities"


I've heard this same thing and I just think he was a nerd and that was one of his gags. I don't understand why someone would write about it like it's deeper than that.


I never interpret this as anyone trying to say it is deep, but just that it shows insight into the kind of person he was.


Paul Erdos published over 1,500 papers during his lifetime. That's about one paper every 2 weeks during his career! Average professional mathematician publish about 2 papers a year. And... still he couldn't beat Euler in total number of pages published in mathematics :).

Fun fact from Wikipedia:

Erdős signed his name "Paul Erdos P.G.O.M." When he became 60, he added "L.D.", at 65 "A.D.", at 70 "L.D." and at 75 "C.D."

P.G.O.M. = "Poor Great Old Man"

L.D. = "Living Dead"

A.D. = "Archaeological Discovery"

L.D. = "Legally Dead"

C.D. = "Counts Dead"


For anyone with kids, there's a great children's book about Erdös called "The Boy Who Loved Math". I read it to my kid for the first time when he was 2 or 3, and he loved it. It got us to start talking about prime numbers in a fun way long before I would have started talking to him about them. It also made enjoying math perfectly normal; my kid is 5 now and has no idea some people don't like math.

https://www.amazon.com/Boy-Who-Loved-Math-Improbable/dp/1596...


My cousin's five year old daughter loved this book. Learned what prime numbers are :)


I took a combinatorics class that was hellish. Over half the class dropped out, including all of the graduate students after two weeks and almost all of the honour students almost immediately.

I ended up looking at our library catalog to look for a book that might help with the class. I noticed our professor had a book out that was a collection of Erdos papers. I signed out the second copy. After that I was getting high 90s while the rest of the class was getting barely 50s. The marks had to be scaled, it was the teacher's intention not to fail us but to see how far he could push it.

It was brutal.


It's interesting, but perhaps not surprising, that that obituary does not mention how critical Erdős felt his amphetamine use was to his work. A famous anecdote:

"After 1971 he [Erdős] also took amphetamines, despite the concern of his friends, one of whom (Ron Graham) bet him $500 that he could not stop taking the drug for a month. Erdős won the bet, but complained that during his abstinence, mathematics had been set back by a month: "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper." After he won the bet, he promptly resumed his amphetamine use."


As an ADD diagnosed Adderall user I can vouch for this. It's like super coffee that lasts all day. It makes you more tenacious. But tolerance builds quickly. Taking a break from it causes me to sleep 12 hours per day and eat twice as much and I get NOTHING done even when trying to supplement it with crazy amounts of coffee. Even after a week of abstinence taking my normal dose again I get 2 weeks worth of work done in a day, then I come home and clean my whole house and learn a new song on my bass.


For me (with a normal prescription), it just never worked like that.

I felt the side effects too strongly and while I did many, many things, I could only crank out unimportant widgets and the executive functions of my brain were diminished as to whether this thing I can do at an incredible [speed / pace] actually mattered.

One example from college is reading chapters of a physics book and copying the vocabulary and definitions for a hundred or more words in a single session. In an unaltered state, I could maybe do half to a whole chapter and 1–2 dozen words before feeling saturated.


An interesting Freudian slip.

You wrote: "...whether this thing I can do at an incredible actually mattered."

leaving out the word "speed" (another term for amphetamines).

It reminds me of Jung's word association experiments, where his data showed that people would pause for longer periods of time when the words in the test hit on subjects that held a strong emotional charge for them.


Whoops; corrected. I probably ought to stop trying to write multiple sentences at a time on mobile.


And people argue there is no market for the old Blackberry style phones. Hah.


For those that want to focus without as much jumpiness, Evekeo is a good choice. It's not as much of an upper since has less dextro, but still works fine.


I hadn't heard of Evekeo, and was surprised to find out that it is just Amphetamine Sulfate. Is it supposed to be an immediate release preparation?

I've been taking Vyvanse for a while now. Lysine-dextroamphetamine is really working great for me. Lasting almost 10 hours, not over- or under-stimulating.


I liked Vyvanse more than Evekeo. I had much less depression, was much more motivated and able to focus during the day as well as evening, and I still could get to bed easily and sleep well-enough. But, I acted too hyper on it.

Perhaps I could try to practice more self-control and continue taking it or could try taking 1/2 the dose, but after I had problems, my doc put me on Evekeo. I take one in the morning and mid-day, and I'm much more even-keeled than on Vyvanse. The downside is that it's not time-released. I have ups and downs and my brain is not working as well in the evening like Vyvanse. I also don't get sleepy as much at night when I should. But, it's much, much better and safer for me than not taking anything. I might start taking a low dose of Zenzedi in the afternoon to see if that helps problems getting to sleep.

Evekeo is 50/50 dextroamphetamine/levoamphetamine; in some sources it's just called amphetamine sulfate, but the ratio is important.

Zenzedi is also made by Arbor Pharmaceuticals and is pure dextroamphetamine sulfate (which is the really addictive one).

Adderall/Adderall XR is 75 percent dextroamphetamine (the regular Adderall is a mixture of dextro salts in that 75 percent) and 25 percent levoamphetamine.

In comparison, Vyvanse is the prodrug lisdexamfetamine that is converted to dextroamphetamine and lysine by the hydrolytic activity of red blood cells, so it's time-released.

I'm told the levo form is for increased wakefulness and improved focus and dextro is for energy and speeding up executive function. I don't know if it's really that simple, but that seems to mirror my experience.


That's what happens when you live your life on speed.


Unfortunately, maybe it is ?

With apologies if I've misunderstood your intent, but what you said came across as quite condescending, and that's being generous.

In any case, for some of us it is the only way we can live at all, and without becoming outcasts at the fringes of society as used to be the case. To some extent we still are, as witness by many trying to hide their problems, not rarely because of the (apparent) intent and position you express in you comment. Yes it's a drug for many, for me it's a necessary evil. It's a locked and completely boarded up door becoming only locked with a rather shitty lock.

Our problems might not appear real to you, or it might be that you think chemistry is the wrong solution, it's hard to know from your comment, but I can assure you that while I would love to be without my chemical 'wheelchair', it's not realistic. Being able to be a decent father, keep a job, and tons of other things simply wasn't possible. I tried so hard I completely burned myself to the ground, while really only trying to do the things others take for granted. Like doing dishes.

If you call being allowed a decent life is being 'on speed', then by all means call it that. But understand that it's no different than throwing slurs at the quadriplegic, the blind, the deaf or the dyslexic.

In a different world I might not have needed my medication, who knows ? But as I can't change the world completely in my lifetime, I have to change myself, at significant risk.


I couldn't agree more. This is a perfect description.


Was that meant to sound judgmental? My prescription doesn't say "speed", and I'm fairly certain I couldn't get a meaningful therapeutic benefit from anything called "speed".

It seems that you're implying that someone using Adderall should be stigmatized because they're taking medication to improve a deficiency in their brain's biochemical systems...Are you?


>I'm fairly certain I couldn't get a meaningful therapeutic benefit from anything called "speed".

Sure you can. Desoxyn, Ritalin, and all the others work about the same, and have largely the same side effects. The only reason Methamphetamine is preferred over Amphetamine (i.e. Adderall) for recreational use is that Methamphetamine is much easier for an illicit drug kitchen to cook up from extracted ephedrine.

When amphetamine was more widely available supply side as an antidepressant and prescribed by general physicians as a placebo in the same way that SSRI's commonly are today, the vast majority of illegal amphetamine products seized by police had a pharmaceutical origin. Addicts can't tell the difference between the various drugs in this class. (http://theinfluence.org/neuroscientist-meth-is-virtually-ide...)

That having been said, like all things related to the drug war there's a lot of fighting and bickering and double think involved here. People are scared of these drugs because of their narcotic potential, and the frightening effects they have at medically inadvisable doses. They seem safer than some of the other commonly prescribed pseudo-narcotics like painkillers or benzodiazepines.

Disclaimer: I take Adderall.


Ritalin has a different mode of action on dopamine and noradrenaline, and tends to "wear off" a lot faster for many patients. I understand there are higher rates of side effects with Ritalin as well. My own "anecdata" supports that: I became an anger-ball when I came down from Ritalin. I remember some studies that suggested it can cause schizophrenia.

Desoxyn? I didn't realize it was still prescribed, given the profoundly negative effect it has when used recreationally (esp when homemade). Meth terrifies me, honestly, because it has such a wide-reaching range of effects on the body compared to amphetamine.

I never got the "easier" part. My understanding is that it's not difficult to get a prescription for Adderall if one "studies" for the appointment, and it's certainly a lot cheaper. And less likely to ruin one's life.


>I remember some studies that suggested it can cause schizophrenia.

Pretty much every drug in this class can do that.

https://en.wikipedia.org/wiki/Stimulant_psychosis

The more you take (acutely, not chronically) the closer the probability gets to one that you'll develop psychotic symptoms.

>Desoxyn? I didn't realize it was still prescribed

I've met at least one person in the last two years who had a prescription for it. In their case it was for severe narcoleptic symptoms, they slept 14 hours a day without it.

>I never got the "easier" part. My understanding is that it's not difficult to get a prescription for Adderall if one "studies" for the appointment, and it's certainly a lot cheaper. And less likely to ruin one's life.

If you're a middle class white person, sure. But for people who don't have the advantage of being pretty or well educated or come from a stigmatized minority class, interactions with doctors where pharmaceutical prescriptions are involved generally get written off as drug seeking. (Of course, that's what it is right?)


>Sure you can. Desoxyn, Ritalin, and all the others work about the same, and have largely the same side effects. The only reason Methamphetamine is preferred over Amphetamine (i.e. Adderall) for recreational use is that Methamphetamine is much easier for an illicit drug kitchen to cook up from extracted ephedrine.

Perhaps op was suggesting that, generally speaking, regulated sellers don't call those drugs speed. I would argue that because 'the dose makes the poison' is probably the biggest factor here, buying from a regulated seller is a really good idea, and is probably going to make more difference than which particular drug in this class you choose, just because my perception is that the quality control of unregulated sellers is such that the actual amount of the drug you are getting is going to vary a lot, which makes maintaining a therapeutic dose rather difficult.

Also, while they are all broadly similar drugs, little changes in chemical structure can make a rather large difference when trying for cognitive enhancement. This is a very complex thing. I mean, these are all in the same class of drugs, sure, they are broadly similar, but they are not the same. methamphetamine metabolizes to amphetamine, for example. From talking to both patients and doctors, at least for the treatment of ADHD? it is quite common for one of those drugs to work, while the others don't help a particular patient at all. In my own case, methylphenidate seems to work at child-sized dosages, while amphetamine doesn't seem to help focus much at all.

>Addicts can't tell the difference between the various drugs in this class. (http://theinfluence.org/neuroscientist-meth-is-virtually-ide...)

First, the link claims to have tested methamphetamine vs amphetamine; it did not claim to test methylphenidate. (as a side note, my own experiences line up with the conventional medical wisdom that methylphenidate is significantly less euphoric than amphetamine. I haven't tried methamphetamine) - next, the 'addicts choice' test might go to addictiveness, but even if they are similarly addictive, it doesn't at all address the concerns about neurotoxicity.

Now, I'm no doctor; I don't know if the claims of methamphetamine neurotoxicity are true or not, or if they are true or not at dosages one might reasonably use to enhance cognitive function (which is a rather different question) but... the neurotoxicity concerns are one of the larger differences between amphetamine and methamphetamine, and in my mind, one of the stronger reasons to choose the former over the latter.


Completely agreed. I glossed over this aspect because I felt like it distracted from discussing the core claim that amphetamine lacks potential as a recreational drug, or that calling it 'speed' is somehow fundamentally inaccurate. (It's inaccurate in the sense you describe, that of regulated versus unregulated dosage. But saying you can't get a therapeutic benefit from what 'speed' refers to, often methamphetamine, triggered my pedant senses.)

I've been told the same thing about meth's neurotoxicity, and that the major difference between the two drugs is that amphetamine is slightly neurally beneficial and methamphetamine is slightly neurotoxic at therapeutic doses.[0] I figure any neurotoxicity involved has to be slight enough for Desoxyn to stay out of Schedule I in the US. As a counterpoint, there's evidence that points to brain damage from antipsychotics and those are still definitely prescribed with regularity. (http://www.psychiatrictimes.com/articles/antipsychotics-and-...)

Of course, to my knowledge there's no real therapeutic replacement for antipsychotics whereas if methamphetamine was doing significant damage to patients it could almost always be swapped out for a safer drug. (Not to mention that methamphetamine was invented in the east and amphetamine in the west, so historically amphetamine has always been more popular than meth in western medicine to begin with.)

[0]: A quick check of wikipedia corroborates.


If your definition of speed is methamphetamine, that is available by prescription for therapeutic use under the name Desoxyn.

As somebody who also takes legally prescribed Adderall myself (begrudgingly...I've been on a years-long hunt for practical counseling/coaching help w/ focus), I think it's important not to kid ourselves - we are consuming amphetamines. Uppers. Speed. Greenies. Apart from the assurance of purity, the drug isn't magically safe or without other pleasurable/terrible effects because prescribed by a doctor.

Also would like to add: the "brain biochemical deficiency" theory has been called into question for ADD (and other mental health diagnoses).

http://psychcentral.com/news/2013/11/02/chemical-imbalance-i...


How did you first found you have ADD? I suspect I have ADD but don't know how I should bring it up with my doctor?


You may want to take the Wender-Utah Adult Rating Scale:

http://www1.psykiatristod.se/Global/Psykiatristod/Bilagor/AD...


I was diagnosed as a kid in the early 90s. didn't try any medications till around 2006. Ask your doctor for a referral to see a psychiatrist or specialist in add.


Indeed, I found this NYT article a more meaningful summary of Erdős' life (with amphetamines): https://www.nytimes.com/books/first/h/hoffman-man.html


That made me think of this article from a few years ago: https://www.madinamerica.com/2012/02/why-anti-authoritarians...


> It's interesting, but perhaps not surprising, that that obituary does not mention how critical Erdős felt his amphetamine use was to his work. A famous anecdote:

I personally don't find this particularly remarkable or relevant to a discussion of the man himself. It would be relevant to a discussion of amphetamines, or of performance enhancing drugs, sure, but it's not really relevant to an obituary.

I have a good friend who says that he can't think as well if he doesn't eat enough meat. If he somehow went from 'above average' to 'legendary' in some field of endeavor, sure, the story about the meat would make for an amusing personal anecdote, and would become commonly cited by omnivores when arguing with vegetarians, but is something that would probably be left out of a one-page obituary.


This seems very significant.


If he responded so well to amphetamine, I would simply think he had ADHD, not a drug problem. I take amphetamines every day, and I also have a hard time working without them.

(Adderall is "mixed amphetamine salts", for those that may not know)

Folks with ADHD respond to stimulants in way that is quite different to those with more typical attention steering skills.


"Folks with ADHD"

ADHD symptoms are a matter of degree in most individuals so presenting it as a binary is a fallacy. The vast majority of people can experience some benefits from some dose of stimulants (see the widespread use of coffee which has different effects but is analogous). I believe the reason the idea that people with ADHD respond differently is popularized is to legitimize ADHD in the eyes of people who would be judgmental regarding medication that causes cognitive enhancement in "healthy" individuals as well. (Because using performance enhancing drugs is cheating or some such nonsense)

Edit: See http://www.nature.com/nature/journal/v456/n7223/full/456702a... http://www.nature.com/news/2008/080409/full/452674a.html


No they don't. Adderall is speed it just floods your brain with dopamine. Everyone feels more focussed. It's all propaganda pushed by the drug companies.

With all due respect, I am baffled at how people can believe this.


Yes, they do, because the baseline availability of dopamine and noradrenaline (it affects both of them) as well as 5-HT is considerably lower in someone with ADHD than without, though 5-HT doesn't have much of a role to play in attention disorders. It also has a sympathetic serotonergic effect (edit: that is to say, that the increase in 5-HT is similar to taking an SSRI. 5-HT is serotonin.)

The fact is, there are proven anatomical changes that are strongly correlated with attention disorders, and the efficacy of the dopamine/noradrenaline systems in the brain is significantly impaired by someone with such a condition. And, as someone with such a condition, I can attest to my baseline being very different from someone without an attention disorder. Further, the effect that I experience from taking Adderall is one of calmness and focus, while friends who have taken diverted pills say they feel "edgy" and focused, because its effect on me is to increase a low-baseline of the relevant neurotransmitters, and someone without a related attention disorder would have their baseline availability increased far above the therapeutic levels I experience. Self-reports from recreational users on web sites devoted to nootropics or to recreational drug use seem to agree with that assessment with considerable frequency.

Maybe that helps explain why people persist in saying that someone with ADHD has a different experience with stimulants?

Edit: I'll also add that my level of focus on stimulants still requires me to be somewhat interested in what I'm doing, and that doesn't seem to be the case with non-affected users, who seem to hyperfocus on whatever catches their attention first. Almost as if taking the drug gives them an attention disorder because they have too much dopamine and noradrenaline.


It effects people without ADHD the same way it effects people with it. The only difference is that people with ADHD have a lot more to gain from taking them then someone without it. (Keep in mind that stimulants can have negative effects to performance such as focusing excessively on specific tasks, or as someone else in the thread mentioned - causing you to lack discretion in choosing what to spend your time on.) What you're saying regarding neurotransmitters is speculation since we don't really know how levels of neurotransmitters affect performance in concrete ways.

Edit: punctuation


I read an amazing theory of this on reddit: https://www.reddit.com/r/Nootropics/comments/4z8znn/can_one_...

>As far as I know, when ADHD individuals are treated with amphetamine(s) even long-term, the dopamine D4 receptor in the prefrontal cortex does not down-regulate. This means that the pro-cognitive benefits of the amphetamines, namely executive function improvement [ability to organize thoughts, plan your day and exhibit sustained attention] are all improved.

>However, what most people experience when they first start Adderall or any amphetamine is the massive surge of motivation and in particular energy. This energy can be massively addictive as it is basically anxiolytic first time around while simulteanously giving you big bouts of motivation and pro-sociability. Neuropsychopharmacologically speaking, these effects are due to dopamine D2 and D3 receptor stimulation in the nucleus accumbens (and effects in the ventral tegmental area, accounting for some of the motivating experience, most likely), however, what is important to note, is that after somewhere around 1-3 weeks, these receptors down-regulate and dose-escalation is needed to retain the pro-social, pro-energetic, pro-anxiolytic effects.

>In other words, while amphetamines may be a piss poor choice of drug for sustained energy production long-term, the pro-cognitive benefits for individuals with executive function deficit (whether diagnosed ADHD, drug abuse, or traumatic brain injury) do exist in long-term. I think this is one of the reasons that some ADHD individuals are capable of staying at the same dose for a long period of time and still reap the benefits.

In other words, the 'high' that drug users get from doing speed once, is very different than the effect that benefits people with ADHD. While the high tolerates over time and requires higher and higher doses, the beneficial effects don't seem to tolerate and last long term.


Possibly because they're molecular biologists, geneticists, and bioinformaticians who study the specific interaction of amphetamines with specially bred mice and observe markedly different responses in the amphetamine dosed knockout mice vs. the amphetamine dosed control mice?

With all due respect, I am baffled at how strongly you're exhibiting the Dunning-Kruger effect.


Scientists who have a monetary incentive to prove that the drugs feel different for people with ADHD. Ever hear about how most depression drugs don't beat the placebo? But we're still told all about the "science" of chemical imbalance. We've got a population here that is drugging themselves...



If this interests you, his biography My Brain is Open, is a great read:

https://www.amazon.com/MY-BRAIN-OPEN-Mathematical-Journeys/d...


I'm surprised by the author -- I never would have pegged Krauthammer as a math enthusiast. I wonder what the backstory is there.


I only looked at the author once I had finished reading the full article and was indeed very surprised. We're often quick to ridicule people in the spotlight but most of them got there on more than just luck.


Anyone here with an Erdős number less than 3? I have a 4, which is probably not going to change (I work in research engineering rather than research mathematics these days).


My dad has a 2.

Erdős stayed at my dad's house so that they could work together. The first morning at breakfast, Erdős asked my dad to butter his toast for him. My dad refused.

That's why he doesn't have 1!


Poor choice in hindsight haha!


But do you have an Erdos-Bacon number, the true test of a polymath?

https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Bacon_numbe...


I admit I geeked out and calculated this a couple months ago, after I was credited on my first academic paper (my career is in programming)

If you count video games, I have a Bacon number of 3 because I was credited on Tiger Woods 2003-2005 with an artist named Sylvain Doreau, who is credited on Shrek. John Lithgow was in Shrek and in Footloose with Kevin Bacon.

My former coworker Li Zhang has an Erdos number of 2 and we worked together on this paper: https://arxiv.org/abs/1607.00133 (with him doing a lot more work than me).

So putting that together is an Erdos-Bacon number of 3 + 3 = 6.


Years ago I was first author on a paper with this chap, who gives his Erdös number as 4, which would presumably make mine 5:

https://www.linkedin.com/in/mario-cortina-borja-2b98ab47

Also, I was in a film with Donald Sutherland (even managing to get on screen at the same time) so I think that's a Bacon number of 2.


I have 2, through Neil Calkin.


I have a 5 - i published in ocean engineering / statistical signal processing.

You can use https://www.csauthors.net/distance/mandar-chitre/paul-erdos to find yours.


I currently have a 5 - I only have 1 conference paper - but once I publish with my advisor, I'll bump that down to a 4. The 2 levels below my advisor are both professors at my institution, so I can do better if I try. I'm in ECE btw, which is probably why it's not that great.


I have a 3, so at least I published with people that have a 2 (e.g., John Tate, Barry Mazur).


I have a 3, through Bruce Berndt. One used to be able to progress to a 2 without doing additional work, but nowadays that has become close to impossible.


I only published one paper (which in undergrad... never got into research after that) but it got me a 5.


I often think of a (probably not entirely correct) quote I read in a book about Erdös. Something like, "the purpose of life is proof and conjecture." The progression of technology seems to me to confirm this in some ways...


Maybe something to consider when then next "I am 28yo and a senior software developer. Is $170k salary enough or should I ask for more?" thread pops up.


Friggin 'A.

I'm 27 with 2 years experience and nowhere close to that pay in my company. FML.


Inb4 a million comments on Erdõs' amphetamine use...discussions of his life inevitably boil down to people talking about the famous bet. Rarely his contributions.


Why not talk about his contributions instead of bringing up his amphetamine use then?


Very few people are qualified to comment on his mathematical work, but lots of people have done speed.


This is probably one of the best examples of "bike shedding" I've seen yet.




Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: