Posted by: Dave Richeson | October 13, 2008

Einstein’s math

In a previous post I mentioned that I was hoping to write an article called Mythematics. The idea is that I will investigate famous mathematical myths and either give evidence that they are true or debunk them.

One that I had on my radar was the myth that Albert Einstein was bad at math.

I was hoping to juxtapose two different kinds of myths—those which deify our mathematical heroes (such as the baby Gauss story) and those which humanize our heroes by showing them to be flawed (Einstein’s struggles with mathematics).

You will be disappointed to find that I have not yet done my homework on the Einstein myth.  My hunch is that this myth is one that can be debunked, but I’m proceeding with an open mind.

The reason I’m blogging this myth right now is that I came across a new book on a related subject, Hans C. Ohanian’s Einstein’s Mistakes: The Human Failings of Genius. In it he writes:

Almost all of Einstein’s seminal works contain mistakes. Sometimes small mistakes—mere lapses of attention—sometimes fundamental failures to understand the subtleties of his own creations, and sometimes fatal mistakes that undermined the logic of his arguments.

The book was reviewed positively in a recent Wall Street Journal article.

A theoretical physicist by training, Mr. Ohanian doesn’t write like one. He recounts his chronicle of errors in clear and engaging prose, giving us in the process a short course in the history of modern physics and a witty and provocative account of his subject’s life. Anyone who has read the recent biographies of Einstein by Walter Isaacson or Jürgen Neffe may find some of the material familiar, but on the whole “Einstein’s Mistakes” is original and fresh. Nor is Mr. Ohanian one of those petty biographers who delight only in turning up the failings—or turning out the dirty laundry—of great men. Rather he notes Einstein’s errors for a purpose, showing us why his achievement was all the greater for them.

And a little less favorably in the Los Angeles Times.

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.

I’m looking forward to reading it myself.

Another well-known myth about Einstein is that much of his work is actually due to his wife, Mileva Maric Einstien. This was the subject of a PBS special. On the website they write:

Much of the debate centers on the words of Abram F. Joffe (Ioffe), a respected member of the Soviet Academy of Sciences and an assistant to W.C. Roentgen from 1902 to 1906, who saw the original version of Einstein’s three most famous papers (on Brownian motion, the photoelectric effect, and the theory of relativity) and said that they were signed Einstein-Marity (Marity being the Hungarianized version of Maric.) Whether that reference was to one author or two is the nub of the debate. Most researchers now agree, based on a memorial to Einstein, written by Joffe, that he was referring to a single author rather than a husband-wife team.

This story has its detractors as well.

I welcome references to get to the bottom of these myths. Post them in the comments below, or send me an email.

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Responses

  1. In his 1905 paper
    Einstein claims that velocities of less than the speed of light resolve to c.

    He substitues c-k and c-lamda into the previous equation which results in

    V=c(2c-k-lamda/(2c-k-lamda+klamda)/c)<c

    Completely wrong

    Should be

    V =c(c-k)+(c-lamda)/(c-k)+(c-lamda)/c)<c

    Basic high school stuff

    Secondly
    Magnitude for velocities calculating the angle between 0 and 90 degrees. Proving velocities greater than c also wrong.

    V=sqrt((v^2+w^2 +2vw cos(a)-(vw sin a/c)^2/1+vw cos a/c^2

    Sort of works for zero degrees but for 90 degrees the formula blows up.

    The bad part about these two equations is that they claim to be proof of restrictions on velocity to c. There are a dozen or so more elementary mistakes this is just two. I throw down the challenge to anyone to provide mathematical proof that the equations are correct, otherwise give up on Einstein.

    So I guess the myth is not a myth after all, he was just bad at mathematics.

  2. He was a man. Was he not? As much as physicists like to deify him, he was- in the end- just a man.

    I do not contend that Guiri is wrong. However, to say this man was “bad at mathematics” is a gross misstep.

    Talking about his blunder makes me wonder- if even his so-called greatest mistakes turn out to be mostly correct. Considering there was no paradigm at the time, I am still amazed at what he did- much like Newton, Kepler, et al.

    Take the CC as an example. The way it was described is wrong. But, shed a little dark energy “light” onto the subject and it is quite fascinating to see that essentially dark energy is the CC with some polish and a new set of equations.

    All great ideas begin in the “gut,” and I can think of no better gut. For someone with no super-computers, Hubble etc, he was able to peer into the beast and not lose his mind (or credibility) in the process.

    In the end, his ability to do thought experiments was his gift to humanity, not his Trig and Differential equations abilities.

    In this day and age, if he was alive, he’d have 20 or so undergrads doing all the heavy lifting. Such wasn’t the case at the turn of the 20th.

    Just my 10 cents.

  3. I take your point, but all that is needed is high school algebra not a computer, he doesn’t need undergrads all he needed was a bunch of schoolkids.

    His answers are not even mostly correct they are outright wrong.

    To address your next comment even his thought experiment is severly flawed.

    The first section of his paper describes a thought experiment using a basic concept velocity = light path/ time interval. Everything seems just hunky dory and indeed is all correct.

    In the next section he completely changes the experiment which is based upon velocity = length of rod/time interval. He even says so

    “rAB is the length of the rod” NOT the distance travelled.

    The problem is that most do not take the time to read and understand his theory, and if they do they all miss the all important line and wrongly assume it is distance not length of the rod.

    tB-tA = rAB/c-v and t’A=tB = rAB/c+v

    I challenge anyone to derive a different answer for the stationary rod and the rod at velocity c from his two equations. By this I mean absolutely anyone from professional theoretical physicists to the guy in the street. In four years I have not had one person who could do so, most just give up and go silent and there are some that finally declare that I am correct. If you are up for the challenge give it a go, as I said it’s high school algebra.

    Hint, the correct answer is; 0 and 2d.

    When the rod is stationary the length of the rod is ZERO it dissappears out of existence for no reason.

    When the velocity is c the length of the rod is TWICE THE DISTANCE TRAVELLED ludicrous.

    Remember that these are Einstein’s own equations upon which his whole theory is based, they perculate down all the way through the whole paper, invalidating all.

    http://stevepsmith.com/Special%20Relativity.pdf

  4. Guiri has no idea what he is talking about and is so lacking the fundamental understanding of the theory of relativity that its embarrassing that he posted here. You have misunderstood the concepts here as badly as the math.

    I can’t believe there are still people out there that continue with these silly arguments against Einstein’s math in the general theory of relativity. In fact, it is obvious that Guiri doesn’t even understand the calculations or the implied reasoning. It looks like he just went to the website of a person that is known to be out there trying to make a name for themselves that has made up this nonsense and copied here basically.

    For one thing, you obviously think that not only are you better at math than Einstein, but that you are better at math than the most brilliant of mathematical minds of the 20th century that not only published his paper, but argued against it and failed miserably and they had much better arguments than the ones you misunderstood here. Embarrassing. Go back to school.

    • Its real easy Rooster,
      Explain the error in the formulas, bear in mind that they are Einsteins own.
      It is obvious you have no idea and suck up any old junk thrown at you.
      What a gullible fool you are.

      Fyi. The results verified by a mathematician who works for JPL.

    • Rooster just read your rant again.
      A quick comment to show your ignorance. The comment was about Special Relativity 1905 not General Relativity which came later, or do you not know the difference?


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