I've been postponing a full entrance into the life of a mathematician since the beginning of my excursions into mathematics because it is an extremely difficult road to traverse. The terrain is extremely demanding. The amount of work and concentration required to build the foundation necessary to continue extending the framework is immense. I admire the men and women who have come before me and were able to put in the work necessary to stand in their tower and look upon the landscape they greatly desire to see farther and farther into. That landscape is, of course, the mathematical landscape and it is a beautiful and terrifying scene to gaze upon. It is terrifying, do to its clean, sterile, and powerful nature. I am ready, however, to fully embark on this journey, which I am afraid will consume my life. But it is a necessary sacrifice to make. I am not the most talented mathematician. And because of the extent of the work that is out there and the pace at which mathematics is moving today, to truly make a mark in the mathematical world I must devote more time and energy to this calling than I have to any other task thus far. - David Andrews ( Read his blog if you like his thoughts. )But: is it, really?

Isn't mathematics easier than say particle physics? Look at the thousands of people working with billion dollar equipment at CERN. What about the rules and regulations in biotechnology? All sciences use mathematics to the limit, mathematicians have only math to worry about. - Or what about this one: economy must be the most difficult science because economists fail again and again in their forecasts and there is no consensus among economists which way leads us out of the depression.

What do you think? Is mathematics hard? If so, what in particular makes mathematics hard?

I can only comment from a viewpoint of a former theoretical physicist, who used math as a tool (and a math addict during my teens). I think math is difficult mainly because it gives you the most freedom (in the sense that it is less constrained by the "real world" - I consider an ideal (read - almost unrealistic) situation here, so that you are not under pressure to get grants, research position etc). The hard part IMO is to decide what are the right problems to work on, at any particular time, and this is a very personal thing. You also have to develop independent thinking, to not be trapped in the ways that are currently common or dominant. I think these two things - finding right ways to use your freedom plus being independent without being ignorant - are the hardest.

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ReplyDelete"The hard part IMO is to decide what are the right problems to work on..."

I was just reading "Gamma, exploring Euler's constant" by Julian Havil. He quotes James Glaisher ( 1848-1928 ):

"The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not."

So many societal and psychological barriers exist that prevent people from fully embarrassing and comprehending mathematics. I think this fact is probably evidenced by the book "Mathematics Made Difficult" which you brought to my attention in your last post. John Allen Paulos also provides evidence for this claim in his book "Innumeracy." Comprehending mathematics, I have noticed in my own life, always follows the same pattern. At first, I am perplexed and always face a lot of internal dissonance. Then, the ideas always come together and show me that the they were really simple all along. But getting through the initial dissonance is what seems the most difficult to me. What I see in my future is a very long road before I get to the forefront of mathematics. I have an IQ of 130 and tested in the 98th percentile in the U.S. for visual spatial reasoning when I was about 12. Maybe I'm wrong but I think that's pretty good. But mathematics still seems to be a difficult subject for me. Maybe not as difficult as particle physics or figuring out what's going on with the economy. Certainly, the lack of consensus among economists points out just how confusing the subject can be.

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