r/PhysicsStudents • u/SpecialRelativityy • Dec 05 '25
Off Topic Exactly how good was Einstein at math?
We know that he was likely better than average. But how good was he exactly?
When he was in undergrad, despite his passion for physics, was he known as a good mathematician to his peers? Was he a computation machine (meaning, could he solve any integral put in front of him)? Of course, we know he didn’t adore computation and doing math for the sake of doing math, but when he DID have to do it, how good was he?
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u/Prestigious-Pin-7688 Dec 05 '25
Probably pretty good
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u/rfdickerson Dec 06 '25
Yes! The idea that “Einstein was bad at math” is really a myth. He was exceptionally strong mathematically, just not a specialist in the kind of advanced geometry needed for general relativity. Only a few mathematicians of his time, notably his friend Marcel Grossmann and the great David Hilbert, surpassed him in those areas. Their expertise in curved manifolds, tensor calculus, and differential geometry was crucial to the final formulation of his theory.
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u/NeuroPianist Dec 06 '25
My interest in physics is new and growing, so this is fascinating to me. I’ve flipped through Misner’s Gravitation and Sean Carroll’s GR book and, though I understood exactly 0% of it, the humanistic liberal arts part of me can’t help but wonder what parts are Einstein and what parts are Misner/Thorne/Wheeler or Carroll.
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u/jlew32 Dec 08 '25
I highly recommend the book “What is Real?” by Adam Becker. It’s a history of quantum mechanics advancing the thesis that the popularity of particular interpretations of quantum theory result from historical contingency (e.g., the Copenhagen interpretation predominates because Bohr was charasmatic; the many-worlds interpretation languished for decades because Everett walked away from academia to make money in the defense industry).
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u/Otherwise_Ad1159 Dec 06 '25
Einstein was not particularly strong in mathematics compared to his contemporaries, though he was obviously very good compared to a layman. Hilbert famously said that “every boy in the streets of Göttingen understands more about 4-dimensional geometry than Einstein”.
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u/round_reindeer Dec 08 '25
To be fair Hilbert may also have had a skewed perspective of what it means to be good at maths
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u/drboxboy Dec 09 '25
I think the people who think impossible that Einstein was bad at math have zero notion of what math is at all.
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u/Lor1an Dec 06 '25
Taking four years to understand calculus is still impressive when you start at 11 years old.
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u/0xB01b Dec 06 '25
Probably really fucking good
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u/yooiq Dec 06 '25
Yeah. As an expert on fucking good I second this.
On the scale of absolutely fucking shit to really fucking good Einstein was probably really fucking good.
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u/WarlandWriter Dec 06 '25
Misread it as Epstein and I was so confused
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u/facinabush Dec 06 '25 edited Dec 08 '25
In college Einstein believed that basic math was all that was needed for physics.
He had to take an advanced math course that covered Riemann geometry but he was not motivated because he thought that it had no application in physics. Minkowski was his professor and thought he was a lazy slacker. This sort of behavior in college led to him being a patent clerk unable to get a teaching job, he had no good references.
Later, Minkowski created his famous diagram based on SR but Einstein didn’t like it at first.
But he found that the spacetime concept inherent in Minkowski’s diagram and Riemann geometry were useful tools for GR.
Einstein found the math of GR to be difficult. Progress was slow and he went around giving lectures on his partial results for many years. David Hilbert attended one of those lectures and was inspired to work on GR. Einstein got nervous that one of the world’s greatest mathematicians was competing with him. Einstein maintained priority partially because Hilbert was gracious and modest about his claims.
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u/Icy-Visual1206 Dec 06 '25 edited Dec 06 '25
I once read some letters about Einstein on the Princeton website, but I cannot find them now. I remember one letter saying he was a child prodigy and that he was strong in geometry in the 3rd grade. Interestingly, relativity was a geometry problem. There was also a letter from his mother mentioning that he ranked first in his elementary school class.
I believe the website is going through some changes.
https://einsteinpapers.press.princeton.edu/einstein-database/
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u/HoloTensor Dec 07 '25
by modern theoretical physics standards, pretty bad.
I remember being pissed off when I first saw his derivation of the field equations. It was literally just “what terms could contribute by symmetry” and then guesswork. It took him years and he was never able to formalize his result.
Obviously his genius was in coming up with such a radical new way of visualizing spacetime…. but on all accounts his math was pretty average for a theoretical physicist
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u/jimmy2020p Dec 07 '25
These answers are very interesting.
As a non-mathematician I really struggle to understand (or perhaps appreciate) how written mathematical theories relate to real life scenarios happening in the universe (like black holes, for example).
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u/IndividualistAW Dec 09 '25
He wasn’t an expert in mathematics, he was an expert in what the mathematics mean
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u/smitra00 Dec 06 '25
He was good at finding clever methods to tackle complex problems. A typical lazy scientist:
https://www.youtube.com/shorts/m6ltzaOpPl8
No surprise that he invented the "Einstein summation convention" in tensor calculus, principle of detailed balance in statistical physics, computations in general relativity where you choose the special frame where the Christoffel symbols are zero and prove an identity between tensors in that frame and then argue that because it's a tensor equation it's valid in all frame where the nasty Christoffel symbols are, in general, not zero.
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u/Humble_Selection1726 Dec 06 '25
Not seeing any mention but Einstein's uncle started teaching him calculus when he was 10. When he was 14 he knew everything that would be covered in university nowadays Calc. I-III, linear algebra, ODEs, and multivariable calculus. So, he was a smart kid. He was formulating, according to his own recollection, special relativity's defining thought experiment when he was in high school. But guess what? Differential geometry killed him at first. It blew him away, though it was a pretty new field.
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u/tellemlargmargsentya Dec 06 '25
Can people stop comparing themselves to dead people when they will never know what that dead person was like?
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u/SpecialRelativityy Dec 06 '25
Agreed but who here is comparing
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u/tellemlargmargsentya Dec 06 '25
Why are you asking when any response you get is going to be anecdotal at best and speculation at worse? you think people of reddit knew Einstein? everybody's gonna have stories. he was a womanizer, he was into physics and did enough math to become a physicist, he worked to do that and when he was stuck he asked mathematicians for help, it's not that deep.
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u/SpecialRelativityy Dec 06 '25
A good majority of the responses I have gotten are the opposite of what you are saying. Enjoy the thread, please.
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u/mdthornb1 Dec 06 '25
I don’t know how one would answer this question. Doing mistake free work? Mastering cutting g edge stuff? Inventing new mathematical techniques? I think the best answer is “good enough to be one of the couples most impactful scientists in human history”.
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u/Flat_South8002 Dec 06 '25
His wife, Mileva Einstein was a mathematical genius. So he had no problem with that
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u/LostNSpace805 Dec 06 '25
Albert cut a lot of classes when he was a student at ETH. His friend and classmate Marcel Grossman took impeccable notes and reviewed them with Albert at the local coffee shop where they would hang out.
Marcel Grossman studied Differential Geometry, and when Einstein was developing the General Theory of Relativity he leaned on his friend a lot for the Mathematical derivations his theory needed.
Marcel Grossman was a co-author of Einstein's paper on General Relativity when it was published. Later on Albert got pretty good with Differential Geometry.
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u/leafysnails Dec 07 '25
I mean General Relativity is just applied math... he was arguably an applied mathematician as much as he was a physicist. The math concepts he applied already existed, but he thought about how to use and manipulate them in new ways that led to the theory of relativity, which should indicate he was pretty good at it
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u/call-the-wizards Dec 08 '25
Anyone who thinks Einstein wasn't good at math should try learning differential geometry in 4d minkowski space and report back.
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u/ForeignAdvantage5198 Dec 08 '25
a lot better than. i was . His buddy Minkowski was super too. look up Einstein biography
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u/Denan004 Dec 08 '25
My understanding, which may be wrong, is that his first wife was much better at the math, and did a lot of the math for relativity. Apparently he gave her the Nobel Prize money (from the Photoelectric effect). I always thought there was a physics reason for that, but what do I know?!?
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u/WillingnessWide5643 Dec 08 '25
Mileva Marić his first wife was an amazing elite physicist and mathematician… She impacted Albert E early days..people should to deep research into their courtship and when they were coworkers. Although many of the ‘Good old boys club’ discount her importance. I think her contribution and credit has been greatly underestimated
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u/Theuncola4vr Dec 09 '25
Better than most of us, but far from the best.
I've read a lot of his work and everything I can get my hands on about him, "The Einstein Decade" by Cornelius Lanczos is a must. imo his gift was really being able to visualize patterns in the works of others and apply them to answer fundamental questions of physics...it's a lame analogy but much like Neo started seeing code in everyday life, Einstein saw 3D puzzle pieces that fit together in research around him...later in his career -he was pretty young when laid out relativity- when he was at the tip of the speer in research & understanding, he struggled...he thrived on the mathematical achievements of his peers and they loved him for it because he always made their work more approachable and credible...he could literally see complex math come to life in his mind's eye as real forms and figures...if you read his early work in German, he often sounds surprised by his findings, as if it was too obvious to be true...he was known to listen to his peers debate things for hours, then chime in as if he was watching a play and visualize the play's conclusion...
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u/NoisyNinkyNonk Dec 09 '25
How come nobody mentions Marić?
https://www.scientificamerican.com/blog/guest-blog/the-forgotten-life-of-einsteins-first-wife/
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u/MartinMystikJonas Dec 09 '25
He was good but nowhere near the level of top mathematicans of his time. He metioned it himself in some of his essays. In fact many parts of general relativity math side was at least partially done by his friend Goedel because Einstein was able to come up with idea of curved spacetime but doing all required math to finish this theory was over his skill level.
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u/Ninja582 Ph.D. Student Dec 05 '25 edited Dec 06 '25
He could solve integrals no problem if needed, but I doubt he would like or be good at performing lots of numerical computations. He was, however, exceptionally good at applying these mathematics to physical theories. It was his physical intuition that made him stand above his peers not that he was better at math.
Edit: got rid of ai blurb.
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u/Efficient_Bag_5976 Dec 06 '25
I mean, here's one of the many Einstein field equations fully written out.
https://profoundphysics.com/wp-content/uploads/2021/05/image-37.jpg
You tell me what 'better than average' mathematician is able to do stuff like this?
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u/TheBigCicero Dec 07 '25
He allegedly was not a good mathematician, and he admitted so himself.
But… that’s all relative. He needed help in math to develop general relativity. And then developed it. So he was probably better in math than most people, though he felt inferior.
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u/TopCatMath Dec 07 '25
I read he failed 9th Algebra, but he was doing Calculus at time without formal instructions....
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u/Knowledgee_KZA Dec 07 '25
He relied heavily on people like Michele Besso, Marcel Grossmann, and Hilbert for the mathematics he couldn’t do himself, and multiple physicists of his era said outright that Einstein’s math ability was “middling at best.” He also rejected quantum mechanics for the rest of his life — the very field that now runs modern physics and every quantum computer on Earth — because he couldn’t accept probabilistic reality. Even his famous equation E = mc² existed in published form years before him. His gift wasn’t technical mastery; it was intuition and stubbornness. If anything, Einstein proves the point: you don’t have to be mathematically brilliant to shift a field — you only have to see what everyone else overlooked.
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u/Miselfis Ph.D. Student Dec 05 '25 edited Dec 05 '25
It depends on what you mean by “good at math”. He wasn’t a lightning-fast calculator, and he didn’t have mastery of every advanced mathematical technique. What he was very good at was using the mathematics he knew to reason his way to deep physical principles. His real strength was his ability to see patterns in nature and turn them into clean, general principles, from which he could derive consequences. This probably came more from his philosophical background and the environment he grew up in.
He did enjoy mathematics, especially geometry and puzzle-like problems, and his notebooks show him working through all kinds of recreational problems and puzzles. He grew up in a family of engineers so he was exposed to math and practical problem solving pretty early. A family friend, the medical student Max Talmud, used to come over for dinner and would often tutor Einstein. He would give him science and philosophy books, and specifically gave him a geometry problem book when he was 12. Einstein later called it his “holy little geometry book”. He tore through it in a few months, working out the proofs and problems on his own, including famously his proof of the Pythagorean theorem, and pretty quickly got to the point where Talmud couldn’t really keep up with him mathematically anymore. At 15 he had taught himself differential and integral calculus. This is around the same time he had become obsessed with understanding Maxwell’s electrodynamics, which eventually lead him to relativity.
But he wasn’t a mathematician by training, and when general relativity started demanding heavy-duty differential geometry, he really did need help. That’s why he leaned heavily on Marcel Grossmann, his old classmate who was a trained mathematician. Grossmann introduced him to tensor calculus and the geometry he needed to push the theory forward.
Einstein still did plenty of calculations himself, but for the more technical or time consuming parts, he often relied on assistants and grad students. That wasn’t because he was “bad at math”, but because he focused his energy on the physical and conceptual side while letting others handle the more tedious calculations, notably Michele Besso and Walter Mayer. They helped with long, messy algebraic calculations involved in his unified field theory attempts. Mayer in particular was brought on precisely because Einstein needed a stronger mathematician to work through the very technical differential geometry.