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Math wasn’t Einstein’s strong point, but how bad was he? Very, very bad, says a ruthless new book...

Publication Date: 2008-10-13

A book review from the Los Angeles Times, Oct.
12, 2008

Even the great genius of Albert Einstein stumbled
when it came to calculations.

Einstein's Mistakes: The Human Failings of
by Hans C. Ohanian

WHEN Donald Crowhurst's abandoned sailboat was
found adrift in the Atlantic in 1969, his
captain's log recorded the ravings of a man whose
mind had snapped. On page after page, he spouted
fulminations and pseudoscience, finally ripping
his chronometer from its mountings and throwing
it and then himself into the drink.

During the voyage, an around-the-globe sailboat
race, Crowhurst had been reading Einstein's book
"Relativity: The Special and the General Theory."
A chapter called "On the Idea of Time in Physics"
seems to have pushed him over the edge.

Einstein was pondering what it means to say that
two lightning bolts strike the ground
simultaneously. For this to be true, he
suggested, someone positioned halfway between the
events would have to observe the flashes
occurring at the same instant. That assumes that
the two signals are traveling at the same speed -
- a condition, Einstein wrote, rather oddly, that
"is in reality neither a supposition nor a
hypothesis about the physical nature of light,
but a stipulation which I can make of my own free
will in order to arrive at a definition of

"You can't do THAT!" Crowhurst, an electrical
engineer, protested to his journal. "I thought,
'the swindler.' " From there he descended into

Hans C. Ohanian, who tells this strange tale at
the beginning of "Einstein's Mistakes: The Human
Failings of Genius," sympathizes with poor

"The speed of light is either constant or not,
and only measurement can decide what it is,"
Ohanian writes. For Einstein to make a
postulation rather than propose it as a
hypothesis to be tested may seem like a fine
distinction. (Earlier in his book, Einstein does
cite an empirical basis for his assumption: the
Dutch astronomer Willem de Sitter's paper, "An
Astronomical Proof for the Constancy of the Speed
of Light," which was based on observations of
binary stars.) But to Ohanian, the act was as
outrageous as when Indiana lawmakers tried to
legislate the value for pi. And so he adds it to
his roster of Einstein's mistakes.

Ohanian, the author of physics textbooks and a
former associate editor of the American Journal
of Physics, sometimes seems to be overreaching in
his attempt to humble the great man, but the
book's quixotic approach -- retelling Einstein's
story by homing in on his blunders -- makes for
good intellectual entertainment. Having read two
books about Einstein just in the last year, I
wasn't sure I could take another. But with his
idiosyncratic style and cranky asides (at one
point he calls the young Einstein "an
incorrigible and tactless loudmouth"), Ohanian
kept me eagerly turning the pages.

We have all heard that math wasn't Einstein's
strong point, and Ohanian ruthlessly lays out the
details. A 12-page marathon calculation in
Einstein's doctoral dissertation, "A New
Determination of the Molecular Size," was "a
comedy of errors" based on "zany" physical
assumptions, such as treating sugar molecules
dissolved in water as though they were tiny
spheres sitting at rest instead of spinning like

"It is a total mystery why his thesis advisors
overlooked this glaring mistake," Ohanian writes.
"They were quite ordinary, dull professors at
what was then a dull, second-rate university, but
even the dullest of dull physics professors
should not have been this blind. Einstein's
dissertation should have been rejected."

Fumbling ever forward, Einstein went on to commit
more errors in the suite of famous papers he
wrote in 1905, what came to be called his miracle
year. The miracle, as Ohanian tells it, is that
Einstein could have been wrong on so many details
while coming through, in the end, with some of
the greatest insights of the century.

In his paper on the photoelectric effect, for
example, he claimed to prove that a phenomenon
called blackbody radiation behaves like a gas
made of light particles, or photons. Not so fast,
Ohanian objects: Though the theory worked for
high-frequency photons, Einstein glossed over the
fact that it didn't work for low-frequency ones,
"like a tailor who tells the customer how
beautifully the jacket fits at the shoulders, and
pretends not to notice that the sleeves are much
too long, ending somewhere near the knees."

Most of the errors Ohanian describes will be just
as esoteric for many readers, but his exasperated
outbursts make the book fun. E=mc2? Don't get him
started. No matter what you have been told, it
was not such an important equation, a trifle,
really. And not even original. Nevertheless, in
deriving the formula, Einstein left a hole in his
argument "almost big enough for a truck to drive
through." He proved the case for slow-moving
bodies and then extrapolated, without
justification, to fast-moving ones.

"The mistake is the sort of thing every amateur
mathematician knows to watch out for," Ohanian
scolds. Over the years, Einstein came up with
more proofs; they all contained errors.

Einstein buffs have read numerous times about
what he called his "biggest mistake" (introducing
a fudge factor in general relativity to avoid the
seeming absurdity of an expanding universe).
Ohanian gives us Einstein's "zaniest mistake." In
trying to nail down the equivalence between
energy and mass, he engaged in a mathematical
fraud as egregious as that "perpetrated by some
sleazy Italian purveyors of olive oil, who pour a
bottleful of genuine olive oil into a barrelful
of vegetable oil of unknown provenance and then
sell this mix as pure olive oil, extra vergine."

Sometimes, Einstein's friend Marcel Grossmann
tried to help him with his figures but not always
to good effect. When Einstein was trying to get
his mind around curved space-time, one of
Grossmann's bungled equations led him astray.
Einstein didn't notice. "In a performance worthy
of Elmer Fudd marching off to hunt 'wabbits' and
failing to notice that Bugs Bunny is sitting on
top of his hunting cap, Einstein failed to
recognize the mistake." In going through
Einstein's life, some of what Ohanian marks down
as errors seem more like philosophical disputes.
Einstein's quest to find a unified theory and to
expunge quantum craziness from physics ultimately
failed. But that doesn't mean it wasn't a noble

Ohanian assures us that his crankiness comes not
out of schadenfreude, "[b]ut, rather, because
these mistakes made Einstein appear so much more
human. They brought him down from the Olympian
heights of his great discoveries to my own level,
where I could imagine talking to him as a
colleague, and maybe bluntly say, in the give-
and-take of a friendly discussion among
colleagues, 'Albert, now that is really stupid!'

We can imagine Einstein responding favorably. "We
all must from time to time make a sacrifice at
the altar of stupidity," he once wrote to his
colleague Max Born, "for the entertainment of the
deity and mankind." Most important, Ohanian
notes, Einstein's instincts were dead on. Light
is made of photons. Mass is equivalent to energy.
Space-time is curved. Nothing can exceed the
speed of light. Einstein, Ohanian writes, had "a
mystical intuitive approach to physics" that led
him to the right answers -- if not always by the
right path.

George Johnson's most recent book is "The Ten
Most Beautiful Experiments."

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