back to article Croatian brainboxes deploy calculus-based CAPTCHA

Boffins at Croatia's Ruđer Bošković Institute are confronting surfers with difficult maths problems as an alternative to conventional CAPTCHA conundrums. Web users signing up for new accounts are typically asked to decipher the text in a jumbled up image and input the results into a dialogue box. The challenge-response test is …


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  1. Torben Mogensen


    I recall a story from the 80's, where an Eastern European student union wanted to keep the secret police out of their club rooms, so they instituted a password challenge: "What is the derivative of x squared?". After a while, the secret police figured out that "2x" got them in, so the student union changed the question to "What is the derivative of y squared?". Which worked.

  2. Mike 140

    My title is Mr.

    But the expression contains only the single variable, x, so why a partial derivative?

  3. Dom 3

    The first one is easier

    The first captcha is easier (as long as you can remember operator precedence).

    And it says:

    "Note: If you do not know the answer to this question,

    reload the page and you'll (probably) get another, easier, question."

    If you reload, then you start getting calculus.

  4. ph0b0s
    Thumb Up

    And I thought

    working in IT, I would never get to use my Physics Degree....

  5. Anonymous Coward
    Anonymous Coward

    easy, its 20

    although it looks a little daunting, its a really easy case, sin goes to cosine, and its evaluated at x=2pi. cosine of any multiple of 2pi is 1.

    therefore its just a case of getting the front number 4 x 5 - as d/dx of Asin(mx) = Am cos(mx)

    1. Liam Johnson

      I think you mean...

      it was easy, 20 years ago!

  6. spodula

    I cant answer that..

    I'm obviously not human!

    Dammit, been found out.

    Beep - Destroy all humans - Beep.

  7. Anonymous Coward
    Thumb Up

    Heh, that reminds me of.

  8. Anonymous Coward
    Anonymous Coward

    I suppose it could keep idiots out too.


    Someone should just hurry up and implement a Voight-Kampff though, job done.

    1. Anonymous Coward


      So someone who doesn't understand calculus or advanced math is an idiot then? Some of the world best artists, photographers, campaigners for world peace, etc are just lumped in with 90% of the world's population who would have to spend 10 mins to fathom out that question before even attempting an answer?

      Granted most of us would not be knocking on the door of an academic research institute but it's good to see academic snobbery alive and well on the Reg!

      1. Paul Smith

        Touchy today?

        "So someone who doesn't understand calculus or advanced math is an idiot then? "

        Artists, peace campaigners and any body else attempting to join a Croatian advanced math club without a good knowledge of advanced math is probably an idiot, yes.

      2. DavCrav Silver badge


        "So someone who doesn't understand calculus or advanced math is an idiot then?"

        Well, calculus is 300 years old, and is not exactly advanced maths -- it's fundamental and basic -- and it's the numerical equivalent of knowing who Tennyson is. In the UK at least (and I assume the US), knowing anything other than basic arithmetic (i.e., adding and multiplying single-digit numbers) is considered advanced, and this is generally innumerate people's way of trying to cover up the fact that they have a severe and gaping hole in their education.

        To see what I mean, replace "can't add up" with "can't read". People who can't read in the UK are either three or are considered mentally retarded, but people who cannot do arithmetic are just "not good with numbers", despite arguably arithmetic being a much more natural thing than language.

        Maybe this calculus problem, which actually is a fairly easy calculus problem (differentiation is a science, integration is an art) is an unreasonable captcha, but this post smacks of society's general belief that mathsy stuff is hard and dull, etc..

        (On a totally unrelated point, I remember getting one of these captchas ages ago for some forum, but I cannot remember which one...)

        1. John Wilson

          Only 300? Young'uns

          Calculus may be 300 years old, but arithmetic is much, much older. Not knowing calculus is hardly the same as "can't add up" A person who can't distinguish between arithmetic and calculus is in no position to lecture on comparisons with "can't read".

          1. Mike Richards

            I hope this catches on

            Physicists putting up X-ray diffraction challenges, biologists making you work out the species from a DNA sequence (all of it) and the geologists just threatening to take a hammer to your tender bits.

          2. DavCrav Silver badge

            I guess I should refine my comment

            I put it at about this sort of level:

            Basic arithmetic = learning the alphabet.

            More advanced arithmetic = learning to spell, read up to an 11 year old's level.

            Basic geometry = reading a few books.

            Calculus = reading Shakespeare.

            (If you actually think about it, that's about when people do it in school! However, it seems OK to people to forget the right-hand side, but not the left-hand side.)

            Back to your comment, I compared calculus to Tennyson, not reading. I later went on to say that not being able to do arithmetic is equivalent to to not being able to read. I moved away from the actual calculus point and on to generally bemoaning a society that considers anything numerical to be nerdy and uncool; this is really not going to help us in the coming, totally technological, reality.

      3. Paul RND*1000

        re: Nice!

        Actually makes sense. Yes I'd be firmly in the "idiot" camp on this one having had no desire to pursue calculus beyond what was strictly required of me (and even that turned out to be a complete waste of time based on precisely zero uses of that knowledge in the last 20 years), but let's face it, I'm not going to ever be signing up for an account on that system, am I?

        For specialist fields like this why *not* use specialist-field-related captchas? Not only would it help defeat spammers, it would also maybe help defeat the average basement-dwelling troll, too. Wouldn't be any worse than the capctha I saw recently which had accented characters in it.

        Of course it all falls apart if the field involves things which are more easily processed by computers than humans anyway but at the rate things are going with some captchas it won't be long before computers are the only things which *can* decode the bloody things.

    2. James Hughes 1


      Excellent reference!

  9. James 129
    Thumb Up

    It makes sense

    If theres one thing humans are good at, that computers could never be programmed for.. I'm sure its calculus!

    1. Mark 65

      @James 129

      Dare you to out-reduce or out-solve Maple or Mathematica. Perhaps they could just have a CAPTCHA system that asks what the current celeb-du-jour got up to recently?

      1. peyton?

        re: @james 129

        Your solution to non-nerds being excluded is to exclude the nerds??

        Not nice.


        A nerd that could not tell you who the celeb-du-jour even is, let alone what they are up to.

      2. DavCrav Silver badge


        "Perhaps they could just have a CAPTCHA system that asks what the current celeb-du-jour got up to recently?"

        Hang on, didn't this computer just beat(ish) a human at this sort of thing? Except, you need to say

        "This is the action that the current celeb-du-jour got up to recently."

    2. Anonymous Coward

      The CAPTCHA for politicians would have to be...

      ... based on lying. :)

      (with added score for well faked sincerity)

  10. fourth of three

    I could not remember ...

    whether Dsin is cos or -cos. (Sigh.)

    1. hamlet

      ...think graphically

      sine is increasing as it passes through 0, so Dsin must be +cos!

  11. Anonymous Coward

    My preferred CAPTCHA

    "what is the air speed veolicity of an unladen swallow"

    1. Loyal Commenter Silver badge


      or European?

  12. Graham Marsden

    To continue...

    ... please solve the P versus NP problem...

  13. Anonymous Coward
    Anonymous Coward

    Nerd Captcha

    x = 3;

    y = 71;

    x ^= y;

    y ^= x;

    x ^= y;

    What is x?

    1. Matthew 25

      What is x?

      x are what I have with bacon.

  14. Frank Bitterlich

    OK, so I may not understand calculus...

    ... but these so-called "brainboxes" don't understand CAPTCHAs. Using something that can be solved more easily by machine than by (some) humans is an epic fail.

    And now on to the service they're offering: A "random" bit generator. So, then, would you rely on the ability of these pranksters to build an even remotely reliable (P)RNG for your cryptography? Yeah, right...

    1. Anonymous Coward


      "a fast non-deterministic random bit (number) generator whose randomness relies on intrinsic randomness of the quantum physical process of photonic emission in semiconductors and subsequent detection by photoelectric effect. In this process photons are detected at random, one by one independently of each other. Timing information of detected photons is used to generate random binary digits - bits."

      A little more reading finds that it easily passes every test of randomness they've put it to.

  15. Kanhef

    re: machine processing

    Maple, Mathematica, etc. are great - if you give them the problem in a form they can understand. Presented as an image, it's a good bit more challenging. Conventional captcha-solvers can stop once they've identified all the characters. This requires also parsing the correct mathematical meaning, which is sensitive to the spatial layout (e.g., 112 is different from 11^2 (11 squared = 121) and from 11_2 (11 base 2 = 3), and then solve it.

    The best captchas I've seen are semantics-based, asking questions such as "what is the domain name of this site?". Answering them correctly requires understanding natural language, which is trivial for humans, but almost impossible for computers. Specialized knowledge also works well; in this case, anyone who needs truly random data has most likely studied calculus, and if necessary can look it up or ask a colleague who remembers it better.

  16. mhenriday

    It's a joke innit ?

    And besides, while a machine can easily be programmed to solve the problem itself, it (presumably) can't resolve the captcha, as it can't process the image - which, after all, is the point of a catcha. But I do agree with Mike 140, why is the problem expressed as a partial derivative ? Or is that part of the joke ?...


  17. kwikbreaks

    being lazy..

    .. I refreshed a couple of times to see just how easy a question would turn up.

    My third poser was simple arithmetic along the lines of...

    -2 * (-4) +7 =

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