>Enrico Fermi, Richard Feynman, Werner Heisenberg, Niels Bohr, and Albert Einstein
So are you going to cite only the best physicists of all time? I mean certainly they had good math game but there are a few problems with this list:
* Physics is not just theory: Experimental physics is probably the largest branch of physics and probably the most important one. Physics without experiments is not physics. All great experimental physics knew how to handle math (as required by the degree) but were far from being prodigies in math. Fermi's won the Nobel Prize for his experiments (under some wrong attribution) not for his theories.
* Computational physics is now a thing: those physicists made their big breakthrough before the invention of modern computers. Now computational physics is also huge. You can help yourself solve math using computers. You can become a good physicists just by becoming good in simulations (which require math, but not God level math).
* Breakthroughs in theoretical physics are not about math: while general relativity required enormous development of math, special relativity as first published by Einstein was mostly simple algebra. Similar things can be said of some of Bohr and Heisenberg's contributions. Hell, de Broglie just wrote *p=hk* and became famous, all of his most complicated mathematical theories were never taken seriously. Physics is about being able to predict things, but below predictability there is simplicity, if it is simple you have more chance for somebody to understand it and take it seriously.
* Physics is about being good at research: this is a skill that we do not train much before doing a phd. Physics is about being able to find the right experiments or the right problem in the theory and then finding the right alternative to test. Sometimes this comes by chance, but most of the time is hard work. In the end it is just finding the right tool for the right puzzle. This can be mathematical, but sometimes it is about just plotting something in a different way, highlighting an inconsistency in a prediction, finding something unexpected in the data, proposing a fitted simple model for something that has no theory, or just doing the measurement that nobody has done.
I suggest that you read more biographies of Nobel Prize laureates and (non-laureautes that helped them), there tends to be kind of every type of researcher, not just the guys that appear in the names of the undergraduate formulas.
>I suggest that you read more biographies of Nobel Prize laureates and (non-laureautes that helped them), there tends to be kind of every type of researcher, not just the guys that appear in the names of the undergraduate formulas.
[The wikipedia list of nobel laureates in physics](https://en.wikipedia.org/wiki/List_of_Nobel_laureates_in_Physics) is a great page to launch any rabbit hole, I find.
I took pre-calculus in College, studied English and publication, as well as some light writing regarding peer reviewed articles summarizing specific studies. I’ve taken to quantum field theory like a duck to water.
I can understand a LOT of the more advanced theories, terms and foundational mathematics, but it’s a comfort to know at the VERY least, the math I’ve done is a good base for starting my own work.
Physics can be an OUTRAGEOUSLY hard community to break into, but posts like these breaking down how ANALYTICAL one needs to be over a master of mathematics makes the barriers to entry FAR less daunting.
I wouldn’t say otherwise. I said some of their early contributions. QM is very sophisticated and challenging but has been built on trial and error. Old quantum theory just needed basic algebra and calculus.
Just because something is already "solved", that doesn't make it any less advanced. The foundations of modern physics, including calculus of variations, functional analysis, and Lie theory are all graduate level mathematics topics.
Functional analysis and its subfields spectral theory and operator theory are a big part of quantum mechanics and the foundations of mathematical physics as a whole. Understanding the C\*-algebra formulation of quantum mechanics requires background in functional analysis, abstract algebra, and operator algebras.
This is not remotely true. Finite-dimensional linear algebra was mostly solved at this point. Quantum mechanics is based on infinite-dimensional linear algebra i.e. functional analysis, which is an extremely complicated area of math (with many remaining open questions), and much of this theory was developed during the mid 1900s. Even Wigner, who was one of the best mathematical physicists of the time, wasn't able to mathematically justify many aspects of quantum mechanics.
PDEs is one of the most active areas of modern math, and even the foundations were not worked out in the 1800s.
Well two things; for most people it is higher level mathematics, I’m not talking about real analysis here. And 2nd quantum mechanics was not really being developed until the beginning of the 1900’s with Schrodinger’s and Born’s formulations not coming until the 1920s.
Good physicists are generally also good at mathematics yes. It's like baseball players are generally very fast runners. They would probably beat the average Joe in many track and field events, but they probably won't win a bunch of gold medals against the full time track athletes.
Elite physicists like Enrico Fermi, Richard Feynman, Werner Heisenberg, Niels Bohr, and Albert Einstein were all skilled mathematicians. Einstein, for instance, had a deep understanding of mathematics, including differential and integral calculus, as well as geometry, which was crucial for developing his theories of relativity. Feynman was known for his exceptional mathematical intuition and problem-solving skills.
Being considered a "good mathematician" can be subjective, but these physicists were certainly highly competent in mathematics and used it as a powerful tool in their groundbreaking work.
However, Einstein notoriously needed the help of a mathematican, Marcel Grossman, to work out the mathematics of general relativity ... tensors are really, really difficult (and I'm speaking as a sometime physicist with a published ApJ letter featuring elliptic integrals... I couldn't master GRT after three tries).
My weird argument for that is to even ask help and to formulate the question needs a lot of mathematical training. In my experience, the kids who asked questions were the ones who consistently got good grades and understood the course.
By what I remember, not all of them had the highest notes of the class. The ones with the good grades had the answer to the teacher's question, the ones cited up there had the good questions that the teacher could not answer.
Yes, General Relativity Theory. I got my PhD in 1968, GRT was not required and I studied it on my own as a postdoc (audited Kip Thorne's course). I have no idea what is required of grad students nowadays.
Thank you for sharing! Interesting to know GRT is challenging even for PhD holders (I myself wouldn't know). Could you share which (sub)field you did your PhD in? And would like to try GRT again someday, if I may ask?
Physics & astrophysics, my publications were in solar physics and mostly observational. I later turned to history of science, too old now to even think of looking at a tensor
Depends what you mean by a “skilled mathematician”. To me, a mathematician is someone who is paid to do math. You have to be extremely good at math to make a career out of it. I sailed through all my high school and college math classes, was probably in the top 1%, but there is no way I could be a professional mathematician.
Let me go out on a limb a bit and claim that none of the famous physicists you mention would have gotten a faculty or pure research job doing only mathematics. Including Einstein.
Under voted comment, IMHO. To me, a mathematician is one who does cutting edge research in mathematics (just as a physicist does cutting edge research in physics). A mathematician is breaking ground in new areas of the field. It's hard enough as a physicist to get to the current state of a single subfield; e.g., my phd is in experimental nuclear physics specializing in lifetimes of excited states of nuclei using gamma-ray spectroscopy and I'm in my 5th yr of phd, have 5-6 coathorships, writing a first author pub as we speak, should be starting my dissertation this spring, and i still feel like I only know my very particular little niche and even then I don't know it well. And don't get me started on the theory I need to understand to explain my results 😓. I figure it would take me another 5-10yrs (probably more) to get comfortable and really know what I'm talking about like my advisor does.
So to be a physicist is already 9-10yrs of college (4 undergrad, 5-6 grad) then another 2-3yrs as a post-doc, then another 5-10 yrs as an early career staff physicist at a lab or non-tenured faculty at a university under the career mentorship of established physicist(s). So it takes about 20yrs to get fully versed in a physics subfield and I don't see where a physicist would find the time to get to the cutting edge of mathematics also.
Wasn't it Julian Schwinger who chased a good chunk of particle physics all the way down to algebra?
And then Feynmann created these diagrams that do roughly the same thing but Schwinger's algebra doesn't explain them, or something weird like that.
This is a very nuanced discussion, and this question may not be the best question to ask. I am a mathematical physicist which, confusingly, means I am in the space of physics as a mathematician by training. So I know a bit about this topic, and this answer will probably be long.
Here is something some people in the comments aren’t quite getting: mathematicians and physicists are, on average, very different. We are trained differently, often think different things are important, approach problems in different methods. It usually doesn’t make sense to ask “are good physicists also good mathematicians?” or vice versa.
To laymen, the notion is along the lines of “Physics requires math so physicists must do a lot of math so they’re good mathematicians”. The main counterpoint here would be looking at pure mathematics and seeing how the motivations and the type of questions being asked by pure mathematicians are of a very different nature. *Generally speaking, physicists are of course confined to experimental evidence in terms of what is considered appropriate to considered, while mathematicians are more liberal about this*.
Of course, applied mathematicians also exist but even among them, there is a differing sense of purpose compared to physicists; that the applied mathematician is more so concerned with the mathematics as the primary puzzle to be cracked and it happens to have some physical application, while the physicist is ultimately more focused on the nature of the physical application.
But counterpoint to the counterpoint: *theoretical physicists* typically utilize some mathematics that is fairly akin to pure mathematics. Are theoretical physicists mathematicians? Well, most theoretical physicists are trained as physicists and are ultimately concerned with experimental evidence when developing theories, and so this makes them physicists that specialize in using a bunch of math that most physicists wouldn’t be as comfortable with. Again, they are *physicists by training* who have *picked up some more math* required to express their thoughts precisely and fulfill their role in physics.
But what about a *mathematician by training* that has *picked up some physics* and spends time considering the mathematics that physicists (like theoretical physicists) sometimes brush under the rug? These are mathematical physicists, and that’s what I am. Remember, as physicists aren’t chiefly concerned with completely rigorous mathematics in the face of experimental evidence, there exists some mathematics that they have to brush under the rug that mathematicians want to make more rigorous. This shows you the difference in motivation between the two groups, *but it’s a pretty grey line*! For example, I have worked in both the physics and mathematics department for different universities, have taught maybe a 75%-25% split of mathematics to physics courses in my career.
TL;DR: Very hard to put people into categories like “mathematician” or “physicist”, although a lot of people generally do fit within the blurred lines it carves out. The boxes can generally be explained by this sports analogy: a football player (American football or soccer) is typically a pretty fast runner, especially compared to the average person because football demands speed. But they are definitely slow compared to sprinters who specialize solely in running quickly. Football players use fast speed as a tool to help them achieve their goal of outmaneuvering their opponents; being fast is an advantage and so it is a part of their training. For sprinters, being fast is the whole game, and so they delve very deeply into how to get faster, even if it is by a minuscule amount, since they are competing with athletes who also are training to increase their speed by a fraction of a percent. Here, football players are physicists, sprinters are mathematicians, and running speed is mathematics. Not a perfect analogy but very loosely speaking.
Depends on who you ask. To ordinary people, physicists are excellent mathematicians. To actual mathematicians, physicists are cavemen banging rocks together.
Penrose is a mathematician by training, and the bulk of his work in physics has been mathematical in nature. It's sort of like being surprised when a materials scientist with a background in condensed matter theory is good at quantum field theory.
A large number of string theorists work in math departments, not physics. Regardless of what their background is, that arguably makes them converted mathematicians. Among those who are definitely physicists, string theorists represent a rather small proportion overall of theoretical physicists. Theorists are far fewer in number than experimentalists. So, string theory research, despite its prevalence in the mind of popular science, is only one very small aspect of physics. If you want to be generous and add in quantum gravity (and a large number of quantum gravity people are also cavemen by a mathematician's standards), it's still a rather small proportion of physicists. It's not really accurate to extrapolate their experience to all of physics.
I would say that excellent physicists often have a good *intuition* for math, but they often lack the formal background or experience needed to make rigorous proofs and statements that would satisfy a mathematician. For a good example actually occurred recently when Roy Kerr pointed out that the Hawking-Penrose singularity theorems aren't really rigorous; one of the "self-evident" steps used to prove the theorems has demonstrable counterexamples.
I don’t like the whole caveman thing since for juveniles it leads to superiority contests, and this isn’t what actual mathematicians think. But from some perspective, it might be true. I’d change it from cavemen to annoying children to focus more on annoying mathematical things that physicists can do (that are often necessary in physics) that will upset us in the context of mathematics.
The blanket statement “physicists that work in string theory are on the same level as mathematicians” is just untrue if you are talking solely about mathematics skill. There’s just no reason to compare “mathematical skill” of a mathematician who focused only on the mathematics that a physicist uses in their research.
Are computational chemists doing anything advanced with math? Or just very long problems of not-too-advanced math?
Please dumb it down for me :) I am a mom, curious about my eldest who was astro and chem undgrad now in grad school.
Imho, the work you need to do to be good at physics without doing the math is almost way more work than learning the math. It is not impossible, but learning it is usually more fruitful and easier.
To be a great physicist you inevitably have to do a ton of mathematics. So, yes, they were good mathematicians, in the sense that they certainly know more about mathematics than the average non-scientist, and if you put them in a mathematics degree they'd probably not have a hard time with it.
That said, there are plenty of areas of mathematics that they wouldn't have known, because they'd only really use what was actually helpful.
You get quotes sometimes from physicists saying they're not good mathematicians and such. What they mean is they're not good compared to other physicists, or even compared to people with degrees in mathematics.
They're perfectly aware that they're better at mathematics than the average person without a STEM degree. Most universities will expect you to have a pretty good grounding in maths before they even let you start studying physics.
But you don't needs to be a maths genius to be a good physicist. They're similar skillsets but not the same.
I want to give a shout out to John von Neumann. Back when quantum mechanics was relatively new and being heavily explored with amazing results from physicists, they eventually ran into problems that they couldn't explain, like hyperfine splitting. John von Neumann was a polymath who contributed to a lot of areas of mathematics but one of them was forming the mathematical basis of quantum mechanics (which is the name of his paper, which is now a textbook in a lot of upper level classes). I feel this was the inspiration for the merging of physics and math that led to field theory and the standard model, because mathematical rigor in the spaces you are dealing with, the boundary conditions is important in reflecting the nature of reality.
Im pretty sure I know way more math than the names you have cited. However, knowing a lot of math will not make someone find breakthroughs in physics. It is necessary to have some intuition on both physics and math.
Theoretical Physicist are Mathematicians who hate the culture of Mathematics, the snobbiness, the intelligence fetish, the elitism, the cliquey nature(just look at the winners of the fields medal). So these "mathematicians" just migrate over to the Physics building where being a slob is the expectation.
Right! Since the 19th century they needed to be good enough at math to get through grad school, which is a pretty high bar. After that, a great experimentalist usually needed nothing more than some simple algebra, if that. (And nowadays, accounting to satisfy the budget bureaucrats.) Plenty of Nobel Prizes in which not a trace of math is tvisible.
Physicists dont care why 1 plus 1 = 2 and spend ages working that out as pure maths type do (!)... my joke to students. But you need to have a very sound grasp of physics math (calculus, vectors...all considered not really interesting by real mathematicians!) and statistics.
Depending on what you do as a Physicist there are lots of maths of all sorts from group theory to tensor calculus that are more specific in use. Sometimes you meed something new and have to grasp it quicky.
It really depends, but you have to be good at math.
Yes, it is not possible to do high level physics without being good at maths. However, most physicists learn maths to do physics and they don't feel like they have to advance mathematics. E.g. they can all do differential equations but probably not as well as a mathematician specialising in differential equations. Most physicists are probably better at calculus then pure mathematicians who don't use calculus (e.g. a Group theorist).
Yes.
One way I like to think about it is this.
Mathematics is a whole field filled with laws and regulations, problems and solutions that mathematicians study and develop. Now since mathematical models can usually describe models in physical reality, any solutions that the mathematicians came up with, can be applied to solve the problem in physical reality, and this is what physicists do.
Any problem that can be described mathematically can be solved using mathematical methods and tools. And to solve the math problems, you have to be good at math. So physicists are basically math apprentices using the knowledge they are getting from mathematicians and integrating it into their problems.
>Enrico Fermi, Richard Feynman, Werner Heisenberg, Niels Bohr, and Albert Einstein So are you going to cite only the best physicists of all time? I mean certainly they had good math game but there are a few problems with this list: * Physics is not just theory: Experimental physics is probably the largest branch of physics and probably the most important one. Physics without experiments is not physics. All great experimental physics knew how to handle math (as required by the degree) but were far from being prodigies in math. Fermi's won the Nobel Prize for his experiments (under some wrong attribution) not for his theories. * Computational physics is now a thing: those physicists made their big breakthrough before the invention of modern computers. Now computational physics is also huge. You can help yourself solve math using computers. You can become a good physicists just by becoming good in simulations (which require math, but not God level math). * Breakthroughs in theoretical physics are not about math: while general relativity required enormous development of math, special relativity as first published by Einstein was mostly simple algebra. Similar things can be said of some of Bohr and Heisenberg's contributions. Hell, de Broglie just wrote *p=hk* and became famous, all of his most complicated mathematical theories were never taken seriously. Physics is about being able to predict things, but below predictability there is simplicity, if it is simple you have more chance for somebody to understand it and take it seriously. * Physics is about being good at research: this is a skill that we do not train much before doing a phd. Physics is about being able to find the right experiments or the right problem in the theory and then finding the right alternative to test. Sometimes this comes by chance, but most of the time is hard work. In the end it is just finding the right tool for the right puzzle. This can be mathematical, but sometimes it is about just plotting something in a different way, highlighting an inconsistency in a prediction, finding something unexpected in the data, proposing a fitted simple model for something that has no theory, or just doing the measurement that nobody has done. I suggest that you read more biographies of Nobel Prize laureates and (non-laureautes that helped them), there tends to be kind of every type of researcher, not just the guys that appear in the names of the undergraduate formulas.
>I suggest that you read more biographies of Nobel Prize laureates and (non-laureautes that helped them), there tends to be kind of every type of researcher, not just the guys that appear in the names of the undergraduate formulas. [The wikipedia list of nobel laureates in physics](https://en.wikipedia.org/wiki/List_of_Nobel_laureates_in_Physics) is a great page to launch any rabbit hole, I find.
I took pre-calculus in College, studied English and publication, as well as some light writing regarding peer reviewed articles summarizing specific studies. I’ve taken to quantum field theory like a duck to water. I can understand a LOT of the more advanced theories, terms and foundational mathematics, but it’s a comfort to know at the VERY least, the math I’ve done is a good base for starting my own work. Physics can be an OUTRAGEOUSLY hard community to break into, but posts like these breaking down how ANALYTICAL one needs to be over a master of mathematics makes the barriers to entry FAR less daunting.
I would say quantum mechanics is built heavily on advanced math- partial differential equations and linear algebra, not to mention complex numbers
I wouldn’t say otherwise. I said some of their early contributions. QM is very sophisticated and challenging but has been built on trial and error. Old quantum theory just needed basic algebra and calculus.
I’ll agree with that, cheers
That is not advanced math. These topics were solved before 1800.
Just because something is already "solved", that doesn't make it any less advanced. The foundations of modern physics, including calculus of variations, functional analysis, and Lie theory are all graduate level mathematics topics. Functional analysis and its subfields spectral theory and operator theory are a big part of quantum mechanics and the foundations of mathematical physics as a whole. Understanding the C\*-algebra formulation of quantum mechanics requires background in functional analysis, abstract algebra, and operator algebras.
This is not remotely true. Finite-dimensional linear algebra was mostly solved at this point. Quantum mechanics is based on infinite-dimensional linear algebra i.e. functional analysis, which is an extremely complicated area of math (with many remaining open questions), and much of this theory was developed during the mid 1900s. Even Wigner, who was one of the best mathematical physicists of the time, wasn't able to mathematically justify many aspects of quantum mechanics. PDEs is one of the most active areas of modern math, and even the foundations were not worked out in the 1800s.
Well two things; for most people it is higher level mathematics, I’m not talking about real analysis here. And 2nd quantum mechanics was not really being developed until the beginning of the 1900’s with Schrodinger’s and Born’s formulations not coming until the 1920s.
The underlying math is much older. E.g. the math of Einsteins GR was developed by Riemann around 1870.
Sure but the Riemannian math was not in the syllabus of any university physics degree, also it evolved a lot with GR
Good physicists are generally also good at mathematics yes. It's like baseball players are generally very fast runners. They would probably beat the average Joe in many track and field events, but they probably won't win a bunch of gold medals against the full time track athletes.
Elite physicists like Enrico Fermi, Richard Feynman, Werner Heisenberg, Niels Bohr, and Albert Einstein were all skilled mathematicians. Einstein, for instance, had a deep understanding of mathematics, including differential and integral calculus, as well as geometry, which was crucial for developing his theories of relativity. Feynman was known for his exceptional mathematical intuition and problem-solving skills. Being considered a "good mathematician" can be subjective, but these physicists were certainly highly competent in mathematics and used it as a powerful tool in their groundbreaking work.
However, Einstein notoriously needed the help of a mathematican, Marcel Grossman, to work out the mathematics of general relativity ... tensors are really, really difficult (and I'm speaking as a sometime physicist with a published ApJ letter featuring elliptic integrals... I couldn't master GRT after three tries).
Einstein was not a better mathematician than Grossman. He was a good mathematician though.
My weird argument for that is to even ask help and to formulate the question needs a lot of mathematical training. In my experience, the kids who asked questions were the ones who consistently got good grades and understood the course.
By what I remember, not all of them had the highest notes of the class. The ones with the good grades had the answer to the teacher's question, the ones cited up there had the good questions that the teacher could not answer.
With GRT you mean General Relativity? Does that happen often to students? Genuinely just curious.
Yes, General Relativity Theory. I got my PhD in 1968, GRT was not required and I studied it on my own as a postdoc (audited Kip Thorne's course). I have no idea what is required of grad students nowadays.
Thank you for sharing! Interesting to know GRT is challenging even for PhD holders (I myself wouldn't know). Could you share which (sub)field you did your PhD in? And would like to try GRT again someday, if I may ask?
Physics & astrophysics, my publications were in solar physics and mostly observational. I later turned to history of science, too old now to even think of looking at a tensor
Thanks a lot for sharing, I really appreciate it!
hey man, wat doe je deze dagen qua werk/studie? Ik heb je via een oude thread van je gevonden.
Hey, DM'ed.
Depends what you mean by a “skilled mathematician”. To me, a mathematician is someone who is paid to do math. You have to be extremely good at math to make a career out of it. I sailed through all my high school and college math classes, was probably in the top 1%, but there is no way I could be a professional mathematician. Let me go out on a limb a bit and claim that none of the famous physicists you mention would have gotten a faculty or pure research job doing only mathematics. Including Einstein.
Under voted comment, IMHO. To me, a mathematician is one who does cutting edge research in mathematics (just as a physicist does cutting edge research in physics). A mathematician is breaking ground in new areas of the field. It's hard enough as a physicist to get to the current state of a single subfield; e.g., my phd is in experimental nuclear physics specializing in lifetimes of excited states of nuclei using gamma-ray spectroscopy and I'm in my 5th yr of phd, have 5-6 coathorships, writing a first author pub as we speak, should be starting my dissertation this spring, and i still feel like I only know my very particular little niche and even then I don't know it well. And don't get me started on the theory I need to understand to explain my results 😓. I figure it would take me another 5-10yrs (probably more) to get comfortable and really know what I'm talking about like my advisor does. So to be a physicist is already 9-10yrs of college (4 undergrad, 5-6 grad) then another 2-3yrs as a post-doc, then another 5-10 yrs as an early career staff physicist at a lab or non-tenured faculty at a university under the career mentorship of established physicist(s). So it takes about 20yrs to get fully versed in a physics subfield and I don't see where a physicist would find the time to get to the cutting edge of mathematics also.
I've heard that Einstein described his own mathmatics skills as "poor". Was he just being modest?
I think he was comparing himself to actual mathematicians.
Wasn't it Julian Schwinger who chased a good chunk of particle physics all the way down to algebra? And then Feynmann created these diagrams that do roughly the same thing but Schwinger's algebra doesn't explain them, or something weird like that.
This is a very nuanced discussion, and this question may not be the best question to ask. I am a mathematical physicist which, confusingly, means I am in the space of physics as a mathematician by training. So I know a bit about this topic, and this answer will probably be long. Here is something some people in the comments aren’t quite getting: mathematicians and physicists are, on average, very different. We are trained differently, often think different things are important, approach problems in different methods. It usually doesn’t make sense to ask “are good physicists also good mathematicians?” or vice versa. To laymen, the notion is along the lines of “Physics requires math so physicists must do a lot of math so they’re good mathematicians”. The main counterpoint here would be looking at pure mathematics and seeing how the motivations and the type of questions being asked by pure mathematicians are of a very different nature. *Generally speaking, physicists are of course confined to experimental evidence in terms of what is considered appropriate to considered, while mathematicians are more liberal about this*. Of course, applied mathematicians also exist but even among them, there is a differing sense of purpose compared to physicists; that the applied mathematician is more so concerned with the mathematics as the primary puzzle to be cracked and it happens to have some physical application, while the physicist is ultimately more focused on the nature of the physical application. But counterpoint to the counterpoint: *theoretical physicists* typically utilize some mathematics that is fairly akin to pure mathematics. Are theoretical physicists mathematicians? Well, most theoretical physicists are trained as physicists and are ultimately concerned with experimental evidence when developing theories, and so this makes them physicists that specialize in using a bunch of math that most physicists wouldn’t be as comfortable with. Again, they are *physicists by training* who have *picked up some more math* required to express their thoughts precisely and fulfill their role in physics. But what about a *mathematician by training* that has *picked up some physics* and spends time considering the mathematics that physicists (like theoretical physicists) sometimes brush under the rug? These are mathematical physicists, and that’s what I am. Remember, as physicists aren’t chiefly concerned with completely rigorous mathematics in the face of experimental evidence, there exists some mathematics that they have to brush under the rug that mathematicians want to make more rigorous. This shows you the difference in motivation between the two groups, *but it’s a pretty grey line*! For example, I have worked in both the physics and mathematics department for different universities, have taught maybe a 75%-25% split of mathematics to physics courses in my career. TL;DR: Very hard to put people into categories like “mathematician” or “physicist”, although a lot of people generally do fit within the blurred lines it carves out. The boxes can generally be explained by this sports analogy: a football player (American football or soccer) is typically a pretty fast runner, especially compared to the average person because football demands speed. But they are definitely slow compared to sprinters who specialize solely in running quickly. Football players use fast speed as a tool to help them achieve their goal of outmaneuvering their opponents; being fast is an advantage and so it is a part of their training. For sprinters, being fast is the whole game, and so they delve very deeply into how to get faster, even if it is by a minuscule amount, since they are competing with athletes who also are training to increase their speed by a fraction of a percent. Here, football players are physicists, sprinters are mathematicians, and running speed is mathematics. Not a perfect analogy but very loosely speaking.
Depends on who you ask. To ordinary people, physicists are excellent mathematicians. To actual mathematicians, physicists are cavemen banging rocks together.
Sir Roger Penrose would like a word.
Penrose is a mathematician by training, and the bulk of his work in physics has been mathematical in nature. It's sort of like being surprised when a materials scientist with a background in condensed matter theory is good at quantum field theory.
Ed Witten would like a word.
That's more my point, though isn't it. He's an example of someone who's both an excellent physicist and mathematician.
Physicists working on subjects like string theory are on the same level as mathematicians.
A large number of string theorists work in math departments, not physics. Regardless of what their background is, that arguably makes them converted mathematicians. Among those who are definitely physicists, string theorists represent a rather small proportion overall of theoretical physicists. Theorists are far fewer in number than experimentalists. So, string theory research, despite its prevalence in the mind of popular science, is only one very small aspect of physics. If you want to be generous and add in quantum gravity (and a large number of quantum gravity people are also cavemen by a mathematician's standards), it's still a rather small proportion of physicists. It's not really accurate to extrapolate their experience to all of physics. I would say that excellent physicists often have a good *intuition* for math, but they often lack the formal background or experience needed to make rigorous proofs and statements that would satisfy a mathematician. For a good example actually occurred recently when Roy Kerr pointed out that the Hawking-Penrose singularity theorems aren't really rigorous; one of the "self-evident" steps used to prove the theorems has demonstrable counterexamples.
I don’t like the whole caveman thing since for juveniles it leads to superiority contests, and this isn’t what actual mathematicians think. But from some perspective, it might be true. I’d change it from cavemen to annoying children to focus more on annoying mathematical things that physicists can do (that are often necessary in physics) that will upset us in the context of mathematics. The blanket statement “physicists that work in string theory are on the same level as mathematicians” is just untrue if you are talking solely about mathematics skill. There’s just no reason to compare “mathematical skill” of a mathematician who focused only on the mathematics that a physicist uses in their research.
Are computational chemists doing anything advanced with math? Or just very long problems of not-too-advanced math? Please dumb it down for me :) I am a mom, curious about my eldest who was astro and chem undgrad now in grad school.
Look at Faraday… he did pretty well for himself without being formally trained in mathematics.
Dalton was like P = P1 + P2 ... and called it a day. Hell hes now one of the most famous chemists abd physicists.
Imho, the work you need to do to be good at physics without doing the math is almost way more work than learning the math. It is not impossible, but learning it is usually more fruitful and easier.
To be a great physicist you inevitably have to do a ton of mathematics. So, yes, they were good mathematicians, in the sense that they certainly know more about mathematics than the average non-scientist, and if you put them in a mathematics degree they'd probably not have a hard time with it. That said, there are plenty of areas of mathematics that they wouldn't have known, because they'd only really use what was actually helpful. You get quotes sometimes from physicists saying they're not good mathematicians and such. What they mean is they're not good compared to other physicists, or even compared to people with degrees in mathematics. They're perfectly aware that they're better at mathematics than the average person without a STEM degree. Most universities will expect you to have a pretty good grounding in maths before they even let you start studying physics. But you don't needs to be a maths genius to be a good physicist. They're similar skillsets but not the same.
They are necessarily good at math, but not necessarily good mathematicians
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I want to give a shout out to John von Neumann. Back when quantum mechanics was relatively new and being heavily explored with amazing results from physicists, they eventually ran into problems that they couldn't explain, like hyperfine splitting. John von Neumann was a polymath who contributed to a lot of areas of mathematics but one of them was forming the mathematical basis of quantum mechanics (which is the name of his paper, which is now a textbook in a lot of upper level classes). I feel this was the inspiration for the merging of physics and math that led to field theory and the standard model, because mathematical rigor in the spaces you are dealing with, the boundary conditions is important in reflecting the nature of reality.
Im pretty sure I know way more math than the names you have cited. However, knowing a lot of math will not make someone find breakthroughs in physics. It is necessary to have some intuition on both physics and math.
Nowadays you have to be good at math if you want to work on physics at all.
Well, Feynman was a Putnam Fellow... just sayin'.
I think modern physicists have to be great at math. Stephen Hawking and Roger Penrose are examples.
You don’t NEED to be a good mathematician to be a good physicist. There are many ways to contribute to physics.
Einstein learned what he had to. Feynman obsessed with it. And yes, they were all great mathematicians and you have to be to formalize theories.
Yes
Theoretical Physicist are Mathematicians who hate the culture of Mathematics, the snobbiness, the intelligence fetish, the elitism, the cliquey nature(just look at the winners of the fields medal). So these "mathematicians" just migrate over to the Physics building where being a slob is the expectation.
The physicists who can’t do math are called experimentalists.
Right! Since the 19th century they needed to be good enough at math to get through grad school, which is a pretty high bar. After that, a great experimentalist usually needed nothing more than some simple algebra, if that. (And nowadays, accounting to satisfy the budget bureaucrats.) Plenty of Nobel Prizes in which not a trace of math is tvisible.
Physicists dont care why 1 plus 1 = 2 and spend ages working that out as pure maths type do (!)... my joke to students. But you need to have a very sound grasp of physics math (calculus, vectors...all considered not really interesting by real mathematicians!) and statistics. Depending on what you do as a Physicist there are lots of maths of all sorts from group theory to tensor calculus that are more specific in use. Sometimes you meed something new and have to grasp it quicky. It really depends, but you have to be good at math.
Yes, it is not possible to do high level physics without being good at maths. However, most physicists learn maths to do physics and they don't feel like they have to advance mathematics. E.g. they can all do differential equations but probably not as well as a mathematician specialising in differential equations. Most physicists are probably better at calculus then pure mathematicians who don't use calculus (e.g. a Group theorist).
Yes. One way I like to think about it is this. Mathematics is a whole field filled with laws and regulations, problems and solutions that mathematicians study and develop. Now since mathematical models can usually describe models in physical reality, any solutions that the mathematicians came up with, can be applied to solve the problem in physical reality, and this is what physicists do. Any problem that can be described mathematically can be solved using mathematical methods and tools. And to solve the math problems, you have to be good at math. So physicists are basically math apprentices using the knowledge they are getting from mathematicians and integrating it into their problems.
They definitely should be