Albert Einstein:
“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”
Mathematician: It is impossible to know precisely what Einstein meant by this quote without being able to ask him. It is often taken to mean that he did not have a strong understanding of math or that he was bad at it when he was young. It is simply wrong, however, to say that Einstein was bad at math. Some of his papers were quite mathematically sophisticated, involving advanced subjects such as stochastic differential equations and tensor calculus. What’s more, he excelled in math as a youth.
The following Einstein quote may help us gain a bit more perspective:
“Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.”
(source: In A. Sommerfelt “To Albert Einstein’s Seventieth Birthday” in Paul A. Schilpp (ed.) Albert Einstein, Philosopher-Scientist, Evanston, 1949.)
Perhaps what Einstein meant when he claimed to have difficulties in math is that he felt as though it was a struggle to learn some of the very advanced math necessary for formulating his theories, or that (compared to mathematicians or mathematical physicists) his math skills were not exemplary. However, he certainly was far, far more gifted at math than your average person. All of this being said, the original quote was actually directed at young students, so it may have reflected little more than an attempt to encourage them to persevere despite their perceived difficulties.
Physicist: Here’s my guess. Einstein witnessed the end of what might be considered the “intuitive physics” of the 19th century and before. Most of that was his own damn fault. In 1905 (Einstein’s “miracle year“) he introduced the world to both quantum mechanics (QM) and special relativity. Up until that time (most of) modern physics was something that could be easily pictured and intuited. You can draw the trajectories of moving objects, electric and magnetic fields can be modeled using field lines, you can picture heat flowing like a fluid, etc.
Electric field lines (in blue). Easy to picture.
Another Physicist: I am not familiar with the quote. I only have a wild guess. In the period between the publication of special relativity and general relativity he took some time to learn enough differential geometry to develop his ideas. This apparently did not come easily to him, and involved a lot of consultation with other people in Europe. He and Levi-Civita were in very frequent communication for example. So he may have been responding to someones comment of the sort we all hear that they we’re having a hard time with math.
Awesome coincidence. When I was in math grads’ office @ Columbia U yesterday, I saw that they have a poster of the dude, with this quote, posted on the door. I stared at it long and hard imagining what it means.
…At some point I content myself with the interpretation that he meant “The math problems I’m working on are harder than yours.”
That’s a better answer. He was pretty famous and a little self-important after a while.
I came to say that I also think it essentially means, “The math problems I’m working on are harder than yours.”
I don’t think it’s self-important, though. I think an advanced math problem is still harder even for someone who is good at it than a simple problem is for someone who has trouble with math.
Interesting answers, but my understanding has been a motivational one. I think Einstein’s intent was that when you push beyond your boundaries, you invariably struggle. I use this quote (and others) with my students to combat the common notion that having difficulty understanding something necessarily equates to a lack of capability.
I think he wanted to say that he wanted to now the math at another level and his problem with math are more greater because is another level of Knowledge
It seems pretty obvious to me. It’s like he’s saying
“Oh, the FOIL method getting you down? Well come take a look at MY chalkboard; then we’ll talk about who is having math troubles!”
Life (just like math) is a continuous Learning. If you are worry now on difficulties of your early Life, How much more the greater difficulties that you will face in the future. I think this is a word of encouragement from a person who start for none to greatness. Who witness difficulties in his early life but didn’t surrender/worry and pursuing his goal (with happiness) and became successful.
Our life is a continuous struggle like mathematical problem that if you always look on difficulties, you might lost focusing how to resolve it.. that there is a formula or pattern on our life that might resolve it, if we just not focus on difficulties but on our goal and the way to reach it.
I think it means that the more you learn about math, the more you realize how much you don’t know. Because he knew more than most people, he realized he “didn’t know that much” more than most people (duh).
Well I’ve always though it was very simple – Abit like John says.
Maybe we can compare it to 1 graders maths and university maths – the first grader struggles with the simplest of maths, but what Einstein is saying is that the university student also struggles, but with much more complex maths. And the more complex the maths is, the greater problems. Its like ‘What? You can’t do sums? Well I’m having a bit of trouble with vector spaces, so don’t you worry’
If that makes sense 😀
Well! i am not a scientist yet, am a 12th pass student. i think he means that…’there is no end to mathematics!!! if u get a solution, next problem is always waiting! and at every level, there is next level which seems difficult at that level. so, we should not worry at our level, just move forward, even if u reach his level, there are much bigger problems to face as at greater level,problems too becomes greater!’
i am on my level, trying to reach his. at present, my problems are just some little calculus but with time, they becomes greater and always have something which will keep me busy in my favorite field…’MATHEMATICS!!!”
Einstein was no genius. He openly admitted that he did not understand his theory.
http://claesjohnsonmathscience.wordpress.com/article/did-einstein-not-understand-math-yvfu3xg7d7wt-70/
What is really amazing is how others claim they understand it… Sigh, the biggest liars are academics.
If understanding something means that you can make accurate predictions about it’s behavior, and can parse what is and isn’t involved with it, then Einstein and most modern physicists definitely understand relativity and the basic nature of spacetime very well. While mind-blowing, they’re not particularly complicated.
However, if understanding means holding it all in your head at the same time and seeing every possible repercussion, then you could make the argument that nobody understands anything.
I can’t understand why this is so much tough to understand 😉
He means, everything is relative.
My understanding is always the hardest. Because only I exist.
You exist in my imagination. I can only imagine how hard mathematics is for you. I can never know how hard it is for you.
And still my difficulties are greater than the imagination about how much hard mathematics is for you.
The link “he excelled in math as a youth” doesn’t work.
Love Long and Prosper
Hi! …. sorry for the bad interpretation about the Einstein’s words.
I think that when Einstein make refer about the math, he refer about like the math help to the physic people with his understanding, however I don’t think that Einstein would thinking first the math and after, he understand about the fenomenal phisic for describe.
Is all!! …. because the math is only a lenguage, don’t the form of thinking the people that work in physic. However, if you have the best idea for explain the universe and you don’t have the necesary instruments for explain this idea: you have nothing.
i m so depressed that i m the weakest in maths , when my teacher taught me maths ,i understand everything but when i try to resolve that same question , it takes tooo much time to solve that same question , i have no confidence in maths n solving numericals in physics n chemistry but theoretically many questions arise inside my mind , like if only earth’s moon has perfect sphere shape ,y not deimos n phobos have , why?
The beginning of this post talks about that a little. Basically, Mars’ moons aren’t large enough to collapse under their own gravity. They’re each only a couple dozen km across, whereas our moon (the Moon) is about 3,500 km across.
I think it means… oh, you are having difficulties with math ? Me too buddy! Get over it.
when i read this quote it feels more like he’s speaking of his personal turmoil with mathematics.
not just an “i’m smarter than you” type of a quote, but more along the lines of:
your problems with math are only superficial, however my problems arise from something deeper, a personal relationship with mathematics. raising more questions/”problems” than answers.
(saying he didn’t understand his own theories is a hint to this interpretation of the quote)
einstein was no high-flyer.
hell, he didnt even understand “his own” theories.
the info was given to him when he became a satanist in switzerland. (the devil always demands a child).
he worked for one world government, married his cousin and was permanently chaperoned by mathematical high flyer ernst straus.
the balfour declaration, whose work was based on e=mc2, was written by (not to) lord rothschild.
he was at the same time sponsoring the third reich and the communist party and was the agent responsible for einstein’s inexplicable rise to fame, fortune, power and guilt and regret.
What a silly point of view!
He ment exactly that the more deep you go to mathematics the bigger problems you discover! The longer you are on the way the harder the difficulties become! The better you are the higher goals you should give to you.
I believe the quote was simply a joke that was put into perspective through his eyes that could be used for encouragement. With math comes the difficulties of understanding it, no matter what level. It is simply a trial and error until you realize your mistakes and improve upon them until you master a technique… and then endlessly repeating these steps as you move on to a higher level of mathematics. Each higher level of mathematics comes with more difficulty. He could have just been saying it gets harder as it goes on. Especially in his case where his theories created new fields of mathematics.
i think this will be silly ….but still i want to say….
1)maths is considerd as physics language or speech ……it may be that Sir would understand many things like a child who understands but can not explain it in words …..in the same way he knew what his understanding is but he might be feeling difficult to explain it in mathematics….because people like Sir Einstien would live in world of science…..
This was Einstein’s reply to his 8-year-old neighbor, when she knocked on his door asking him to help her with her math.
I think it’s a joke. Einstein was a wit.
Nope, he just meant that math is tricky, ask any mathematician 🙂 And some assumptions form the math introduced in relativity are mind blowing indeed, especially when the math is applied without considerations for the observations we’ve made so far, as ‘time travels’.
I would guess the to be the question if mathematics is a ‘universal language’, fitting all we observe, or if it us, ‘picking’ those answers that fits best, ignoring other. Einstein had to go looking for ‘new math’ to express some of his ideas for example. And I guess he found some applications of his equations to become increasingly weird, although based on the same mathematics he himself had used.
I don’t expect us to ‘time travel’ ever 🙂 myself. A time dilation needs two frames of reference, your local one including that ‘local clock’, relative measuring some other frame. But your local clock will always give you a same measure relative your life span, so you going to some neutron star won’t change that. Although you might define a universe to ‘accelerate’ as you are there, it won’t change the years you have.
Ahh Tom, didn’t know that one 🙂 if it was in that context I too think he meant it as a harmless joke. But who saved that reply for history? The eight year old?
I love reading all these attempts to understand what my good friend Einstein meant with this quote. Truly I can explain it to you.
Mathematics has set laws and terms in which to decipher. That is constant. On the other hand, the human nature with regard to love, God, good & evil, emotions, truth, wisdom, intelligence, intelligence of the heart, etc. These are the things that are quite puzzling and have no definite lines of solving. He, however refused to accept this(like many great minds) and in trying to come to absolute truths on these matters, he looked back at mathematics as silly in comparison to knowing the Self.
Waters run deep my friends.
He spent the latter half of his life trying to figure out “The Theory of Everything”.
It would be hard to top that “Math Problem” …
my name is md ali reza sir albert einstein 5 mathematics to send my email
I am a high school drop out. I believe what Einstein meant by this quote was not in a rude way, (my math is harder than yours), I think what he meant by this is that the difficulties he had trying to understand and comprehend the material was much more difficult for him than he thought it was for the average person, or more so he may be saying it was very difficult for him to achieve an understanding of the mathematics he was involved in compared to others ability near his level, perhaps. Einstein had the mindset to always keep pushing forward and never let negative emotions with no benefit get in the way.
i think there is something wrong in this quotes of einstein. so we explain it simply.. there’s a letter scribbled in the word “mine” in one single blink of an eye.. that will change everything. “mind”
I think by “Mine are still greater” i think he meant the math problems he is facing at his level, That his math problems at his level was greater than the math problems we think of as problems. Anyone with me?
There is a saying in mathematics:
“Dividing the world into continuous equations and non-continuous equations is like dividing the world into bananas and not-bananas.”
I would argue the same about human knowledge vs what is possible to know.
Just because the “pile of bananas” you know about is larger than someone else’s pile… it’s still all just bananas, and there’s always more to discover.
Although I must guess as everybody else, and we all see what we want to see, but it seems clear to me that Einstein is saying “Don’t worry about your math problems – we ALL have math problems because math is only a ‘problem’ when we’re working at the edge of our ignorance. We all have math problems, and we always will. Stop fretting about the problems and keep working on them.”
Let’s give Mr. Einstein the benefit of the doubt.
I’ve interpreted this much like a story about Lance Armstrong. Someone asked him if bike racing ever got easier. “No,” he said, “You just go faster.”
Einstein had the strength to carry some heavy problems. That did not mean they were not difficult problems; they were just within his capabilities.
To me it says that he had some seemingly impossible problems in his work (that he probably worked through).
That part is very probably truth.
On the other hand he doesn’t want to be arrogant and so he can claim his difficulties were greater than others’ (who can disprove it) and thus not discourage his listeners with his celebrity.
I am not brightest button in the draw for sure…but most of you are supposed to study science at uni and still don’t’ get it?!?!
It is all about relativity.
Your difficulties in maths are subjective and NOT absolute.
Even if you think you are struggling, in HIS reality, struggles are fare greater as he explores uncharted/untested theories.
In a tongue-in-cheek kind of way so typical of his explanations.
Although his theories might collapse one day, him as a philosopher still hasn’t got the recognition he deserves.
Anyone bother to read the freaggin book?
There are some good answers here. The simplicity of his answer is that the problem of solving for a consistent Theory of Everything (TOE) is the greatest life swallowing problem that one can aspire to solve . . . and yet, relative to Einstein, I have probably changed more diapers than he. Relativity, hmmm?
I believe Einstein meant what he said.
There is some question of Einstein having some type of “learning disability”. I put it in quotes because anyone who learns differently is labelled disabled, and it may be due to lack of teacher understanding. He was highly visual…he saw himself riding on a curved beam of light, he often talks of how he does not use words to think. This is indicative of dyslexia.
My own son is dyslexic in math. He scores at the 1%tile in mathematical calculations, mainly because of speed. His fingers can’t work that fast…BUT, he consistently qualified for gifted in Math. Of course, they never let him in the classes, thinking….I don’t know what they thought. He has a grand understanding of higher order math languages, without having the basics of calculation down.
In grade school, when I was so worried about his lack of ability to rote memorize math facts, his pediatrician noted that rote memorization is not true understanding, and that in the long run, he may be better off.
I’m just saying…
Einstein, His statement is simple to understand, or is it? we know, the more we know, the more we know we do not know. Regardless of one’s interest and quest to know as much as possible about that interest, with each question answered, many more questions unfold. Einstein made his transition harboring more questions than answers…..relax and learn, there is no correct answer, the goal is to learn to be comfortable knowing that behind each answer there is a door to many more questions. At any point in one’s life while on this plane of reality, we have the choice to open the next door or just be content with the doors you have already opened and sit quietly knowing you do not know. this life is a door…or is it?
I think Einstein is trying to assure students, ‘They could be more successful in solving Maths problems that they are dealing with, in comparison to the chances of Einstein solving his Maths problems ‘.
Understanding Einstien’s quote “Circle of Knowledge” may lead to understanding the quote in question……..inner peace profound
Hurrah! At last I got a web site from where I can really take helpful facts regarding my study and knowledge.
Perhaps what Einstein meant by the comment – “Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore” is that mathematicians literary takes every solution of his relativity equations as possibility in Physical world. This may not be true.
Perhaps building mathematics before realizing truth about underlying Physics may be the reason we are grappling with some problems in interpretation of prevalent Physics theories like relativity. For example, relativity forbids formation of trapped surfaces and yet we assume every black hole has singularity.
Einstein has always been a mystery to me on a certain points.
The main one his that he had decided to fight Newtons gravitational notion of “attractive masses”, which was the most solid notion in science at the time (and still is), with his simple notion of gravity being only a “consequence” of deformed géométry of space-time. That was promising to be quite a “fracas” to get into but he didn’t hesitate.
On the other hand, instead of facing a simple evidence, shown in his formula, that universe was dynamic, which couldn’t be so bad a “fight” after all, he decided to “cheat” is formula in order to make the universe static.
This simply doesn’t make sense to me.
As I think about another quote by Einstein, I am lead to believe that he is suggesting that his quest for knowledge of math has and always will, lead to more difficult questions or problems. Perhaps to understand his quote, we should see it as a simple metaphysical statement that applies to any interest of science and nature.
Einstein was remarkable in that he pondered and questioned (we good Catholics are not supposed to question! Screw that – I question and if I’m a sinner, so be it – OK enough of that little rant. But, asking questions is how we humans grow. I prefer to think for myself). The status quo of Newtonian physics which was widely accepted, and still is (no doubt Newton gave much to physics and mathematics), but it didn’t answer that annoying question. If the speed of light in a vacuum is the fastest known speed and a constant, then what accounts for the difference when a stationary observer sees a distant stationary source of light (travelling toward him at light speed, c) and another distant, but moving, source of light, say that headlamp of a train going 60mph (whose light also travels toward him at c). In either case light comes toward the stationary observer at the same speed (c) despite that fact that one source is moving relative to the other. Let’s assume the medium is a vacuum and not air where light can propagate at < c. There must be something different about the two light sources to account for this. Einstein did some remarkable thought experiments simply because they were too impractical or impossible to be whipped up in a lab. What happened if the train could move much faster, say closer to the speed of light? What then? Since speed of light is constant in a vacuum, irrespective of the speed of the light source, then what needs to change to make this possible? Einstein concluded that time must change. Remarkable! Why didn’t I think of it… it seems so obvious! Oh, yea, I was born well after Einstein… guess I’ll have to work on other problems like what existed on the other side of Planck’s wall). No one thought of this before him. Time slows down for the moving light source. The faster it goes, the slower its time relative to the stationary observer. Yet, if I could get on the train and move at incredible speeds, I wouldn't notice my own time changing. But, relative to the stationary observer, I would age at a lower rate (think of all the Hollywood stars that would jump at this opportunity? Where can they board such a train?) No one thought of this until Einstein because we all reside in a relatively low speed world where Newtonian physics works just fine for practically all everyday experiences. Weird Al spent the next decades of his life trying to find a grand, unifying theory but, unfortunately, never got to one despite his efforts. String Theory seems to have come to the fore as a unifying theory with little-known, quiet and humble geniuses like Ed Witten at the helm, another Princeton professor, as was Einstein. Thank God he abandoned history studies and took up math and physics. If I had not become an engineer, I surely would have pursued physics and plucked a few strings like Ed and like Al (violin).
My best guess is that it is that Einstein’s speaking of his intuition/imagination. He quotes, “Logic will take you from A to B. Imagination will take you everywhere.”
My best guess is that Einstein’s speaking of his intuition/imagination. He quotes, “Logic will take you from A to B. Imagination will take you everywhere.”
Einstein has read Tobias Dantzig’s Book on “Numbers”, it deals with the problem of infinitesimals.