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MIT Entrance exam (1869)

libraries.mit.edu

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Re: MIT Entrance exam (1869)

#61

Post by redthrowaway »

varjag wrote: post #55
redthrowaway wrote: post #27

Earlier quoted context omitted.

If you can't do arithmetic in your head, the other problems are considerably more involved. I can't see a time where the ability to do mental multiplication is not a prerequisite for higher maths.

The Greeks got by fine without it.

If by "fine", you mean, "with Bronze Age math", then sure. The Greeks figured some great things out in their time, but your average math undergrad would school their best in most things. We've done more with math in the last 20 years than they did in their entire 600 year history.

Re: MIT Entrance exam (1869)

#62

Post by migiale »

varjag wrote: post #56
trurl123 wrote: post #44

It's usual exercises for school in Russia. I don't find any difficult problems. I mean all except English.

True, but it wasn't typical Russian school level in 1868.

check this out http://upload.wikimedia.org/wikipedia/commons/a/a7/BogdanovB... this is a painting from 1895 pupils were supposed to do calculations like the one on the blackboard in their heads, without any writing

Re: MIT Entrance exam (1869)

#63

Post by redthrowaway »

shadowfox wrote: post #18
amelim wrote: post #6

Earlier quoted context omitted.

I'm sorry, but being able to perform arithmetic does not equate to higher intelligence or mental capacity. As society begins to perform more calculations via computer, it will allow us to begin address more abstract and higher level mathematics, problems which would be near impossible to address had we been required to do the math with grease pencils. Conrad Wolfram recently gave a wonder TED talk on the subject. htt…

> As society begins to perform more calculations via computer, it will allow us to begin address more abstract and higher level mathematics, problems which would be near impossible to address had we been required to do the math with grease pencils. This is quite likely true, especially for scientists and mathematicians. An interesting question for me though is whether the average citizenry is becoming better or worse…

I think there's a point where further mathematical prowess no longer holds any sort of competitive advantage for the average person. That point is probably grade 6.

The average person will do just fine in their lives without needing to factorize a quadratic equation. They will do swimmingly without knowing the relation between ln and e. The average person will, after high school, never again have to utter the word "pi" in a non desert-related setting. Similarly, "'x' equals" will become nought but a forgotten dream.

Modern life makes no mathematical demands of 98% of humanity. The only mathematical skill beyond basic arithmetic that most people need to know is compound interest, and most people don't know that.

Knowledge is driven by need, and there's simply no need for most people to be anything but marginally proficient in math.

Re: MIT Entrance exam (1869)

#64

Post by zoomzoom »

redthrowaway wrote: post #61
varjag wrote: post #55

Earlier quoted context omitted.

The Greeks got by fine without it.

If by "fine", you mean, "with Bronze Age math", then sure. The Greeks figured some great things out in their time, but your average math undergrad would school their best in most things. We've done more with math in the last 20 years than they did in their entire 600 year history.

Depends what you mean. Some would say that we haven't gotten past pythagoras even with all we have accomplished.

Re: MIT Entrance exam (1869)

#66

Post by varjag »

migiale wrote: post #62
varjag wrote: post #56

Earlier quoted context omitted.

True, but it wasn't typical Russian school level in 1868.

check this out http://upload.wikimedia.org/wikipedia/commons/a/a7/BogdanovB... this is a painting from 1895 pupils were supposed to do calculations like the one on the blackboard in their heads, without any writing

It's not algebra, you wouldn't have gotten to MIT with that even back then.

Re: MIT Entrance exam (1869)

#67

Post by varjag »

redthrowaway wrote: post #61
varjag wrote: post #55

Earlier quoted context omitted.

The Greeks got by fine without it.

If by "fine", you mean, "with Bronze Age math", then sure. The Greeks figured some great things out in their time, but your average math undergrad would school their best in most things. We've done more with math in the last 20 years than they did in their entire 600 year history.

They didn't need to multiply in their heads to lay out the foundations of geometry and discover irrational numbers. Every generation of math grads from then on begins studies from their achievements.

> We've done more with math in the last 20 years than they did in their entire 600 year history.

What Greeks did with advancing the math profoundly affected technology and sciences. What was done in the last 20 years does not even begin to compare in impact.

Re: MIT Entrance exam (1869)

#70

Post by cryptorchidism »

kwantam wrote: post #4
iuytgfrtyuik wrote: post #2

Isn't that kind of high school level algebra? I thought we were all supposed to have been dumbed down compared to our illustrious forefathers?

Depends on how far back you go. For a Roman, mental multiplication was exceedingly difficult. Clearly this implies that there was a period of upward trend. If we believe that we're dumber than some of our forefathers, then there must have been a peak at some point in the past (or perhaps even multiple peaks, but we don't have enough evidence to suspect more than one, so let's assume it's an approximately parabolic tr…

You bring up good points, but mental multiplication is a bad example. That's certainly more related to an inadequate notation for the task than any trend in human intellect.

http://news.ycombinator.com/item?id=1954217

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