
Why is Maxwell's theory so hard to understand? (2007) [pdf] - sytelus
https://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf
======
sytelus
I actually have happened to delved quite a bit to "really" understand the
Maxwell's equations. I've bought original treatise, books with its commentary
and plain old "for idiots" sort of books. His original treatise is super dense
and unapproachable. Right now we can wear Maxwell's equations on t-shirt but
their original form were forbidding. Even with modern form you "really" need
to get concepts of differential geometry if you want to just play beyond
abstract. There are tons of hand wavy explanations of div and curl out there
but almost all can be broken with crafting clever question like “ok, so what
you think curl of that would look like?”. I don't think even today I can claim
I really get these concepts.

In any case, some of my biggest takeaways were these:

1\. There is no such thing as "proof" of Maxwell's equations. Just like
Einstein's field equations, Newton's laws and many other things in Physics,
Maxwell equations are also simply laid out as _lets assume these_. Vast
majority of “greatness” in Physics is simply assuming something without
needing to fully understand it and then cross your fingers to see if some good
predictions comes out of it.

2\. The major achievement of Maxwell's equations is that you can predict
velocity of light using other physical constants that have seemingly nothing
to do with light. A consequence that we only later realized was that this was
literally a constant and not relative to who is measuring it! This is easily
one of the most non-obvious achievement in Physics.

~~~
Certhas
You should try to understand differential forms, if you have those then
Maxwells equations in vaccuum really aren't strange any more.

But Differential forms aren't that strange really. They are the mathematical
objects that allow you to integrate along surfaces and curves. Of course their
theory hadn't been developed when Maxwell wrote them. And Maxwell was very
much concerned with EM in matter, which mixes the properties of the EM fields
and materials, and that can thus be expected to get a bit messy.

But I don't see what you are striving for when you say "really" understand
them. I think this is a psychological category, rather than a hard criterion.
Can you apply the formalism to calculate consequences? That's the main issue.
Maybe you can have a better or worse intuition about the consequences, but
that is often mainly due to practice. You can't expect to correctly intuit all
possible consequences of a system as rich as EM.

> Young man, in mathematics you don't understand things. You just get used to
> them. -- John von Neumann

~~~
tobinfricke
Could you recommend a good (accessible) reference on differential forms?

~~~
6gvONxR4sf7o
I'm late to the party and not the person you asked, but I've been trying to
work through
[https://smile.amazon.com/gp/product/0817683038](https://smile.amazon.com/gp/product/0817683038)
It's good so far.

------
scottlocklin
A lot of the early days failure of Maxwell was his notation was insane. As
others notice below; Heaviside notation[1] made it a lot easier to follow and
calculate things. Notation is underrated as increasing human power: I'm not
sure General Relativity would have been possible without Christoffel notation.
FWIIW fun stuff to read; Whittaker's theories of Aether and Electromagnetism
gives the detailed history of all this. Cheap from Dover books. Mind blowing
in how theoretical physics used to work.

[1]
[https://books.google.com/books?id=nRJbAAAAYAAJ&pg=PA109#v=on...](https://books.google.com/books?id=nRJbAAAAYAAJ&pg=PA109#v=onepage&q&f=false)

~~~
Balgair
Einstein Notation is similar in this regard. It makes the 'mechanics' of
tensor mathematics much easier to deal with. Kinda like how arabic numerals
are a lot easier to manipulate than roman numerals.

I'm not sure sure, but I believe that Helen Dukas, Einstein's secretary, is
the one who came up with Einstein notation originally. She was just trying to
get through his notes faster when writing things up and that method of
notation later became accepted. I can't find that citation though, so calling
it Dukas Notation is for the moment erroneous.

~~~
harry8
To hell with it. So much great work from lowly support, frequently women, has
been robbed of its rightful place. Call it Dukas notation until proved
otherwise. Crick and Watson still have their ill-gotten novel prizes and most
are unaware they are little more than thieves. (Wildly racist and sexist,
sure, hard to deny that nowadays so we don't talk about it as loudly as we
should).

tl;dr

"Dukas notation" just sounds good.

~~~
Balgair
I believe that you have misunderstood. I do not know if Helen Dukas in fact is
responsible for this.

~~~
harry8
I don't think so, fwiw.

"Call it Dukas notation until proved otherwise."

------
jiggawatts
Maxwell's theory is hard to understand because it's based on an almost-but-
not-quite-appropriate algebra. It's like stringly-typed programming. It
_works_ , but it's messy and hard to understand.

Maxwell's set of coupled differential vector electromagnetic equations
simplify to a hilariously short _single_ equation in Geometric Algebra.

A random Google turned up this paper comparing classic EM and the GA
formulation. It's not even the simplest possible representation, because that
uses natural units and a 4D GA to basically condense the entire set of EM
theory into about 4 characters worth of equation that is _fully relativistic_
for free:
[https://www.researchgate.net/publication/47524066_A_simplifi...](https://www.researchgate.net/publication/47524066_A_simplified_approach_to_electromagnetism_using_geometric_algebra)

It's almost a joke. To me it's reminiscent of looking at beginner programmers.
You see them do crazy things like calculate a date "next month" by taking
apart the pretty-printed date string, parsing to find the month, realising
that sometimes the day part is one digit and sometimes it's two, then having
to worry about m-d-y or d-m-y formats, building little tables of "days per
month" and leap years... and so on.

They can write pages and pages of _error free_ code and it's still Wrong
because the correct way is to just call "thedatevar.AddMonth(1);" and be done
with it.

PS: 3D game engine vector algebra libraries have all of this in common with
the physics maths. Things like the cross product being bizarre, having to pick
a basis, not being able to interpolate rotations, gymbal lock, rounding error,
having different maths for 2D and 3D, a bunch of special cases to worry about,
and so forth...

Watch Enki Mute's Siggraph 2019 presentation on Geometric Algebra. It's mind-
blowing how many stupid little quirks of vector algebra just _evaporate_ if
you're prepared to step outside of your comfort zone:
[https://youtu.be/tX4H_ctggYo](https://youtu.be/tX4H_ctggYo)

~~~
adamnemecek
The speaker in the video runs a community for people interested in geometric
algebra.

[https://bivector.net/](https://bivector.net/)

Check out the demo [https://observablehq.com/@enkimute/animated-
orbits](https://observablehq.com/@enkimute/animated-orbits)

Job the discord [https://discord.gg/vGY6pPk](https://discord.gg/vGY6pPk)

~~~
jiggawatts
GA _seems_ to be getting more popular, but I still see vector algebra used in
areas such as robotics where GA is _clearly_ superior. In that application the
small performance difference between GA and vector algebra is irrelevant, but
the advantages of GA are huge.

In game engines the vector algebra method is slightly faster, so the elegant
programming model is often sacrificed in the name of performance.

That, I can understand.

Why physicists use at least 4 separate formulations of the EM equations I
can't understand, especially considering the vector version is the _worst_ yet
the most popular.

~~~
devit
How can it be faster considering that they are equivalent?

~~~
gridlockd
Computers don't care about mathematical equivalence. For instance, dividing by
a number is generally slower than multiplying with the inverse of that number.
Also, memory access patterns can make a difference of night and day.

I'm not sure though where exactly the idea that GA is slower comes from. It's
all down to the application and implementation. Perhaps it's because GA
generalizes so well to higher dimensions that many libraries are overly
generalized and thus slower than vector algebra libraries that _need_ special
cases anyway.

~~~
jiggawatts
The 3D case is often handled using a conformal projective geometric algebra,
which is 5D and requires 2^5 = 32 elements for a general multivector. This is
twice that of a 4x4 matrix, and and eight times the size of a 4-element
homogeneous vector as typically used in most 3D engines.

Of course, there are all sorts of optimisations. Most GA libraries are
actually based on code-generation and support various "subsets" of the full GA
to efficiently represent things like vectors only. From what I've seen, even a
well-tuned library has approximately a 25% overhead for hot paths and 50-100%
is typical.

This is a bit like representing a simple rotation like the hand of a clock,
with either just one angle, or a two-element unit vector pointing in the
direction of the rotation. The one-element angle has a bunch of special cases,
like have to be checked to see if it goes past 360 degrees and then reset back
to the 0..360 range. Representing this with two numbers just requires
multiplication with a matrix, which involves no conditionals or modulo
arithmetic.

This is analogous to the vector vs geometric algebra. Typically, GA has no
special cases and "just works", but it does so by "uncompressing" the compact
vector representation. It's going to be slower.

------
tagrun
It appears no one here has actually read the essay. He's not talking about
mathematical complexity of Maxwell's equations (and no, you can use
differential forms, Clifford algebras, quaternions, vector calculus, but no
matter how you write it, it's still the same thing, and at the end of the day,
you will end up solving _exactly_ the same set of coupled partial differential
equations, to the letter --there's no magical mathematical notation that makes
this go away).

The difficulty he's referring to is in the physics (and not mathematics)
associated with the idea that fields are real, fundamental physical entities,
and cannot be reduced to mechanical models with "gears and wheels" permeating
the space (which was a popular idea back then).

~~~
mjfisher
You prompted me to read the actual essay. It was considerably more interesting
than the comments here would have suggested; which is not a surprise, given it
was penned by Freeman Dyson.

His insight that Maxwell's contemporaries lacked even the language to fully
describe what a transformative idea he had is acutely interesting. Once again
language both shapes and traps thinking.

He makes the same point with quantum mechanics as well - that we're
constrained by not having the proper language to describe the most fundamental
behaviour. I think it's fair to say that point still stands today.

------
ThePhysicist
Modern notation has contributed greatly to making Maxwell's equations more
understandable. I dare you to have a look at Maxwell's original paper
([https://royalsocietypublishing.org/doi/10.1098/rstl.1865.000...](https://royalsocietypublishing.org/doi/10.1098/rstl.1865.0008))
and try to understand it, I'd say even for a seasoned physicist it's not
trivial. Compare that to the modern differential form of the equations (e.g.
[https://en.wikipedia.org/wiki/Maxwell%27s_equations](https://en.wikipedia.org/wiki/Maxwell%27s_equations)),
which (IMHO) are really easy to understand even for second-year Physics
students (given that you understand the underlying vector operators).

Personally, I found the "flow analogy" always the most intuitive, and there
are some books that teach electrodynamics in that way. Typically one would
start with electrostatic problems and work one's way to the more complicated
stuff like magnetic fields.

I guess to derive a "complete" understanding of classical electrodynamics you
need to understand the concept of relativity as well. Magnetism is a
consequence of relativity and the finite speed of light, so if you accept that
it becomes easier to understand (IMHO). Of course you then have to
"understand" relativity, which just moves the problem to a different area. But
then again, it's always like that in Physics :)

~~~
jjdredd
> Magnetism is a consequence of relativity and the finite speed of light

That doesn't make any sense.

~~~
rovolo
Here's a video explainer:
[https://www.youtube.com/watch?v=1TKSfAkWWN0](https://www.youtube.com/watch?v=1TKSfAkWWN0)

Magnetism affects moving charges, but not stationary charges. A magnetic field
in your reference frame is really just an electric field in the moving
charge's reference frame.

------
lordnacho
With a lot of theories I find the breakthrough in discovery is separate from
the breakthrough in explanation.

How quickly was it that the familiar four vector equations were published?
When you come across them now in an undergrad class, it seems so simple
because a lot of work went into distilling the insight into the bits that
matter. When the theory was still being fleshed out, there were probably a
load of intermediate steps acting like a scaffolding.

Likewise with relativity, you can pick up a book and read about it because a
lot of people have looked at it over the years and figured out which
explanations actually work.

~~~
jart
Explanations that work for whom? I can't speak for electromagnetism or
physics. What I can say is that for years I felt like I didn't have the least
bit of clarity on color modeling until I referred to Maxwell's primary
materials, which are cited by just about no one sadly.

~~~
pas
Could you explain this a bit? (Excuse me if I'm asking too much, I don't
really know what you mean by color modeling, and how it connects to Maxwell -
or maybe you are talking about wavelengths?)

~~~
abecedarius
[https://en.wikipedia.org/wiki/Color_triangle#Maxwell's_disc](https://en.wikipedia.org/wiki/Color_triangle#Maxwell's_disc)

------
mannykannot
This is a wonderful essay, and I wish I had come across it as a freshman. For
example:

"Just as in the Maxwell theory, the abstract quality of the first-order
quantities is revealed in the units in which they are expressed. For example,
the Schrödinger wave-function is expressed in a unit which is the square root
of an inverse cubic meter. This fact alone makes it clear that the wave-
function is an abstraction, for ever hidden from our view. No-one will ever
measure directly the square root of a cubic meter."

That, of course, is an observation about quantum mechanics, and it is only on
rereading the essay today that I noticed its structure: Dyson begins with an
anecdote about Maxwell giving an address that spent most of its time
discussing some features of Helmholz's "splendid hydro-dynamical theorems"
(with a nod to Kelvin, who I guess was present), before briefly drawing
analogies to his electrodynamical theory. Dyson brings this up within an essay
in which he uses Maxwell's theory to make a point about coming to understand
quantum mechanics, though he spends rather more time on his ultimate topic
than Maxwell did in his talk.

------
antman
Maxwell's equations are an artifact of the Mathematical Formulation and they
can be written in a perhaps easer way. If one describes them in Geometrc
Algebra terms it is just one equation [0] and one can understand it in a
natural way.

During the nineteenth century and the discussions on different formal ways to
describe vector fields Hamilton's quartenion system prevailed. Maxwell had
reservations and presented his treatise of electricity and electromagnetism as
"the introduction of the ideas, as distinguished from the operations and
methods of Quaternions" [1], thus the formulation we know.

[0] Mathematical descriptions of the electromagnetic field
[https://en.wikipedia.org/wiki/Mathematical_descriptions_of_t...](https://en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field)

[1] The vector algebra war a historical perspective
[https://arxiv.org/pdf/1509.00501.pdf](https://arxiv.org/pdf/1509.00501.pdf)

~~~
llamaz
Currently with Maxwell's equations you can point to each one and couple it
with an experiment.

If you simplify the equations any further, it will be a result of mathematical
elegance rather than fundamental undergraduate-level physics.

~~~
jiggawatts
> and couple it with an experiment.

Only a handful of special cases that have obvious "paradoxes" that cannot be
explained with Maxwell's equations.

It's not even a fully general set of equations classically, it can only handle
a certain constrained motions at low velocities, short distances, and
generally without accelerations.

I mean sure, a map is simple to understand and is fine for navigating a city,
but let's not pretend the Earth is flat and then only introduce its spherical
geometry in 2nd year studies. That's not the right pedagogical approach.

~~~
pdonis
_> Only a handful of special cases that have obvious "paradoxes" that cannot
be explained with Maxwell's equations._

What are you talking about?

 _> It's not even a fully general set of equations classically, it can only
handle a certain constrained motions at low velocities, short distances, and
generally without accelerations._

Huh? Maxwell's Equations are relativistically invariant and cover all
classical electrodynamic phenomena. The only thing they don't cover is quantum
mechanics (although in quantum field theory Maxwell's Equations are still the
field equations of the quantum electromagnetic field, so even there they play
a role).

~~~
jiggawatts
Maxwell's equations only apply to static states, including steadily
circulating currents. It's not _generally_ applicable without extensions to
more complex scenarios such as handling time delays and arbitrary movement.

[https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_...](https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential)

[https://en.wikipedia.org/wiki/Jefimenko%27s_equations](https://en.wikipedia.org/wiki/Jefimenko%27s_equations)

The apparent "paradoxes" are literally the reason Einstein started on his
journey to develop Special Relativity.

[https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_pr...](https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem)

[https://en.wikipedia.org/wiki/Relativistic_electromagnetism](https://en.wikipedia.org/wiki/Relativistic_electromagnetism)

~~~
pdonis
_> Maxwell's equations only apply to static states_

Nonsense. Maxwell's equations are the equations of classical electro
_dynamics_.

 _> It's not generally applicable without extensions to more complex scenarios
such as handling time delays and arbitrary movement._

The equations for the Lienard-Wiechert potentials are mathematically
equivalent to Maxwell's Equations (when you put those equations in potential
form instead of field form and make an appropriate choice of gauge).

Jefimenko's equations are also mathematically equivalent to Maxwell's
Equations; their originator believed that the causality properties of those
equations would be clearer when put in his preferred form. Whether or not he
was right is a matter of considerable debate.

 _> The apparent "paradoxes"_

Are a result of lack of understanding on the part of the people claiming and
promoting them.

 _> are literally the reason Einstein started on his journey to develop
Special Relativity_

Nonsense. The problem Einstein had when he developed SR was not Maxwell's
Equations; it was _Newton 's_ equations. He realized that Maxwell's Equations
and Newton's equations were inconsistent. Every other physicist at the time
who realized that (and there were many) believed that the way to fix that
problem was to modify Maxwell's Equations and leave Newton's equations the
same. Einstein, however, realized that the way to fix the problem was to
modify _Newton 's_ equations and leave Maxwell's Equations the same. The
result was SR, and the rest, as they say, is history.

------
jwmerrill
This is a lovely essay, but I think it goes a little too far in claiming that
the electromagnetic field is intangible or immeasurable, in slightly forced
analogy with quantum mechanics.

> We now take it for granted that electric and magnetic fields are
> abstractions not reducible to mechanical models. To see that this is true,
> we need only look at the units in which the electric and magnetic fields are
> supposed to be measured. The conventional unit of electric field-strength is
> the square-root of a joule per cubic meter... This does not mean that an
> electric field-strength can be measured with the square-root of a
> calorimeter. It means that an electric field-strength is an abstract
> quantity, incommensurable with any quantities that we can measure directly.

A more conventional way to think of the dimensions of the electric field is
[force]/[charge] (e.g. units of Newtons/Coulomb), and you can observe the
electric field by observing the force it exerts on a charged particle through

f=qE

for example by observing the trajectory of an electron in a cloud chamber.

Dyson says that the square of the field is a measurable energy density, but
it’s arguably harder to measure an energy density than it is to measure a
force.

Dyson’s point is much more true for quantum mechanics, where the only
measurable things seem to be quadratic combinations of the wave function, and
I do like the analogy he points out with electromagnetism, but I think he
oversimplifies a bit to make his point.

~~~
mncharity
> not reducible to mechanical models [...] is much more true for quantum
> mechanics

Yes, but... a caveat.

How big is an atom? "Unimaginably small" is an oft repeated phrase. What is an
atom? "Definitions [...] models [...] skill at switching between models".
Electron behavior? Quantum... "unintuitive... the equation _is_
understanding".

So how well is "small" taught? Horribly, even by the lackluster baseline of
current science education research. Asking first-tier medical school graduate
students how big cells are, is not happy thing. But hey, maybe cells are
"unimaginable" too.

So how well are atoms taught? One challenge in teaching high-school
stoichiometry, is students not thinking of atoms as _real_ , as physical
objects. But hey, maybe that's a failure to "switch models".

So how well is electron behavior taught? Well, when students use the many
realistic interactives emphasizing molecular electron density... oh wait.
Well, when students view the many molecular dynamics videos showing electron
density... oh wait. They _do_ exist... now find them without using google
scholar and sending people email. :/ But hey, if students ever do see them
some year, maybe no understanding will result, given how unintuitive it all
is.

Punchline? Teaching things badly seems associated with failure attribution
errors. As with education research that's "we taught atoms really badly...
surprisingly that didn't work... so we draw the obvious conclusion... students
of this age aren't developmentally able to understand atoms".

And physics side... there often seems a blurred vision of objectives and their
properties. There are a great many plausible learning objectives between
"atoms are real" and "i∂_{t}ψ=Hψ". And the usefulness of "mechanical" models
varies greatly among them. So "the equation _is_ understanding" gets repeated,
in contexts where it's inappropriate, and where it distracts from a broad
long-term societal failure to improve wretched science education content.

------
0xff00ffee
This paper captured what I encountered as a TA in the 90's: students could
solve the integral forms, but had trouble with the differential due to fields.
I think this is because some students have a very difficult time going from
the mental image of fields as 2D arrows, to div, curl and grad in practice.
There's a big step function there in manipulating the equations. I wasn't a
very good TA because I didn't have much luck explaining to the struggling
students (still feel bad about that, sorry folks, I was getting my master's
degree and had no choice to be a TA). And students who didn't understand this
in second-year physics had even more trouble when their EE classes went into
field and waves classes (conductors, antennae, etc.).

TL; DR: I think this is more a problem with teaching advanced differential
calculus concepts than Maxwell.

------
LatteLazy
Once you understand VC operators (grad, div and curl) and the associated
intergals, Maxwells Equations are actually really intuitive and quit
beautiful. I was lucky that the maths course I was on covered those a few
weeks before we started electrodynamics. Plus I had Mary Boas Mathematical
Methods in the Physical Sciences which teaches this material (and Greens
theorem etc) very well.

------
m0zg
Theory of electromagnetic field (of which Maxwell's is a part) was one of my
favorite topics in the university. The other being digital signal processing.
I don't have very good memory, so I have to rely on things having a lot of
consistency and internal structure so they could be efficiently "compressed"
and "recovered". Both of these fields have that - the math is consistent,
beautiful, and somewhat more intuitive than in other fields. Theory of
electromagnetic field does assume that your integral and differential calculus
is pretty good though.

------
state_less
> Mathematics is the language that nature speaks.

Nature seems to speak in forces and had been doing so long before we arrived
and started honing our math skills.

Nature made an imprint on our math. Newton came up with new math to make more
accurate physical predictions.

There is a good reason to be an adherent to the mathematical descriptions. We
might want the photon to go through only one slit, To help make nature more
classical and understandable, but that’s not the nature we know and observe.
So we keep to the math and let it speak to us, lest our work-a-day
understandings of the world lead us astray.

------
UncleSlacky
I've seen the "another theory which I prefer" quote mentioned elsewhere
(possibly with reference to this paper) as being a form of modesty. I would
say that it looks to me like typical British understatement, which is often
misunderstood (particularly by Americans) and may have been simply an attempt
at humour on his part.

[https://en.wikipedia.org/wiki/English_understatement](https://en.wikipedia.org/wiki/English_understatement)

~~~
BeetleB
The author of this piece, though, is British.

------
sleavey
So not so much hard to understand (at least for trained physicists at the
time), rather too much modesty from Maxwell himself to shout about the
importance of his discovery.

------
peter_d_sherman
Excerpt:

"Maxwell explained how the ancient theory that matter is composed of atoms ran
into a logical paradox.

On the one hand, atoms were supposed to be hard, impenetrable and
indestructible.

On the other hand, the evidence of spectroscopy and chemistry showed that
atoms have internal structure and are influenced by outside forces.

This paradox had for many years blocked progress in the understanding of the
nature of matter. Now finally the vortex theory of molecules resolved the
paradox. Vortices in the aether are soft and have internal structure, and
nevertheless, according to Helmholtz, they are individual and indestructible.

The only remaining task was to deduce the facts of spectroscopy and chemistry
from the laws of interaction of the vortices predicted by the hydrodynamics of
a perfect fluid."

------
zethraeus
This is a lovely essay. Wonderful layers-of-reality analogy to quantum
mechanics.

~~~
elbear
Yes. That's the reason why I saved it. I don't know much about quantum
mechanism, but I could feel a vague intuition developing after reading this
essay.

------
robochat
We've all gotten used to the idea that Electric and Magnetic fields are real
but then we learn about the Aharonov-Bohm effect and suddenly, maybe it's the
electric potential and magnetic vector potential are what is 'real'. But then,
there's all the issue with gauges.

I think that the best way of teaching electromagnetism might still be in the
future.

------
gumby
This is fundamentally a sociological (or philosophy of science) essay rather
than about why Maxwell's equations are still so hard to understand for the
student. In that it's quite interesting but I found the jump to a parallelism
between the model of Maxwell's and quantum mechanical models a bit of a
stretch.

------
ajeet_dhaliwal
Very interesting article, I think there's a lot of parallels there to business
and startups. I'm a technical person who has always struggled to promote, and
it seems scientists/researchers face the same issues. The ideal is to be a
showman and technically brilliant.

------
montalbano
Previous interesting HN discussion on the same paper:
[https://news.ycombinator.com/item?id=18837677](https://news.ycombinator.com/item?id=18837677)

------
Vysero
" We, with the advantage of hindsight, can see clearly that Maxwell's paper
was the most important event of the nineteenth century in the history of the
physical sciences. If we include the biological sciences as well as the
physical sciences, Maxwell's paper was second only to Darwin's ``Origin of
Species''."

By what metric? How has Darwin's ``Origin of Species`` been even half as
prolific as Maxwell's work? Maxwell's work revolutionized our understanding of
the physical world and had lead to the creation of thousands upon thousands of
technological advances. It has literally forged the modern world.

~~~
AbrahamParangi
I think Darwin gets special note for the fact that while there are many
incredible works of theory in math and physics, there's really only one in
biology: _On the Origin of Species_ by Charles Darwin.

~~~
Vysero
Certainly not saying that it's not noteworthy, but if I had to make a top 5
list he wouldn't be on it. Apparently, my metric and the authors metric are
different.

------
arkj
Does the professor’s claim that the “origin of species” is more important than
Maxwell’s equations got any real takers? Or is it just his personal opinion?

------
bearsbearsand
what happened to Maxwells original quaternion based equations. the changes
made against his will by lorrentz and others to simplify after his death were
an affront to science and have set back humanity a hundred years.

------
dschuetz
Ah, yes. It's not the ignorant physicists' fault that Maxwell's theory hasn't
got the attention it deserved. It's Maxwell's modesty's fault that set back
the science of physics two decades. What a ridiculous notion.

------
vincent-toups
Try SU(3) Yang Mills!

~~~
jjdredd
Why not SUSY then? Once you understand the formalism you can derive any field
theory to your liking.

------
raxxorrax
> Modesty is not always a virtue

Seriously... where and when in the last 50 years in modern society was modesty
ever a virtue? I certainly wouldn't expect anything like that at Princeton in
the US.

Otherwise an interesting essay nevertheless, but I certainly don't agree with
all the points.

> Mendel's modesty setback the progress of biology by fifty years.

Hilarious conjecture.

