The Passion of The Mathematician

I’ve noticed something about the mathematicians we’ve studied in class - D-503, John Nash, Max Cohen and others. They are just like us. They have all have the same hope to make their existence on this earth matter. D-503 writes in his journal for future generations. John Nash attended and taught at some of the most prestigious universities in the world, all while coming up with some of the world’s greatest economic theory and battling schizophrenia. Max discovered the secret number of God (at least in his own mind). There are also others such as Einstein and Pythagoras that we didn’t extensively cover in class but they too are credited with some of the most influential works created thus far. Yes, some of these characters are fictional and yes, many of them were absolutely crazy, but the difference between them and us is that they were fortunate enough to find something in life they were passionate about and dive into it with reckless abandon. I find that to be admirable.

It’s easy to distinguish ourselves from them and say “well, they were all crazy,” but I bet if were to try hard enough we could all find something that we felt so drawn to that it might drive us a little nuts too. Just think about all the crazy things people do for love. This sounds obvious but I believe that mathematicians truly LOVE math and will do almost anything to discover its secrets. What do you love? What are you so passionate enough about that it could drive you crazy? If you don’t know, that’s fine. Neither do I, but summer is coming quickly and it’d be a great time to find out.

Untitled

I have been trying for a while now to come up with some witty, math-related title for this blog post, but to no avail. Maybe it will come to me by the end of the post. But, I didn't want to be left out in including my final thoughts of the class in the blog. So here goes:

This semester, I was originally signed up for M372K, Partial Differential Equations and Applications, TTH 12:30-2. However, after no more than three class periods in the class, I realized the class was more Physics than I cared for and I dropped it. I happened to stumble apon Literature and Mathematics in the Course Schedule in the same time slot, and I needed my second writing component class, so I figured it would be an interesting course to take. To my surprise, after a couple classes, I was possibly more intimidated by this class than I was Partial Differential Equations. The thought that I would write an essay arguing my grade seemed to be a daunting task and gave me even more control over my success or failure in the class, rather than just doing homework assignments the night before they are due. Also, I had not been assigned reading from a novel since my senior year in high school, so I wasn't so sure about that one. I mean, I came to college to study Engineering, and even though I switched to Mathematics last year, I still did not expect to be persuading a teacher to give me an A in any way other than my performance on homeworks and exams.

Regardless, it has been an interesting class, to say the least, and I think I have used portions of my brain that had been dormant for a while, which is always a good feeling. The class has also caused me to think about new things and old things in a different manner. I have long been one to get lost in my head and just think about something endlessly and formulate my own opinions and theories. The class discussions we had were very similar to the conversations I have with myself often and it was fun to be able to vocalize such hypothetical thoughts with someone other than my two cats who care much less about my thoughts about mental illnesses and abortion than they do about when I am going to feed them.

As seems to be a common sentiment with several people in the class who are heading in the Pure Mathematics direction, I have no clue where I will be 5 years from now, but I hope to do Teach for America when I graduate and then would like to have the opportunity to teach in foreign countries. I feel knowing English, Math, and, with some brushing up, Spanish, I have some valuable skills that can take me anywhere I would like to go. Or at least I can hope.

The End

The fact that this is the last blog adds a lot of pressure to make it a good one. I don't really know what to talk about... so lets see where this goes...
I read A Mathematicians Apology yesterday. It was interesting. Hardy was really depressed! I wonder if instead of thinking there's a corollary between being crazy and being a mathematician there's more of one between depression and mathematics. It makes sense. Mathematical truth is harsh, pure and explicit. It is what it is. And math is really difficult and it constantly tests how bright you are in the subject. It's really intimidating and it makes you feel so stupid sometimes. So how do you know if it's worth doing it for yourself? How do you know if you've got what it takes to make a mark in the field? How do you know that you're not just beating your head against the wall forever and for nothing?
Hardy says that mathematics is a young man's game... which is a pretty harsh statement. So those bright enough to accomplish even one great thing in life reach their peak early on and then it's all downhill from there. That's a pretty depressive thought... to know that your life work can only get worse. If that's true, I can see why mathematician's would get depressed. On the other hand, at least they know that at one point they had it... something that I can only imagine most mathematicians will never experience. Hardy was amongst the top five mathematicians in the world at his time. To be the top five in the world of anything is really cool... but to be in the top five best mathematical minds must be the greatest high...
Next year I'm taking my GREs and applying to grad school... and that's it. Then I have to wait and see what the future holds for me. That limbo between schools... I don't even know if I want to go to grad school, but I've been working towards a degree in mathematics for three years with the intent of going to grad school... so that's what I'm doing now. Looking back I don't think I ever made a choice. I was kind of going with the flow at every point. My dad's a mathematician, my mom did her bachelor's in mathematics... I'm good at it and I like it so it seemed like the reasonable thing to do. But now it's serious business... because I'm kind of committed to doing this thing for the rest of my life... and a pure math degree by itself... I don't know what that's good for... so I must get something else... and what can I do? I don't want to work at a bank, or for a company... so I guess I'll teach. I don't want to teach middle school or high school really, so I guess I'll get a PhD and teach college... but that's math for life!
How do these mathematicians know that they're passionate enough about math to do it for little pay for the rest of their lives and doing it purely for the improvement of math. It's so pure and so... pointless it feels.
"I shall ask, then, why is it really worth while to make a serious study of mathematics? What is the proper justification of a mathematician's life?" - Hardy

What Do Trees and Math Have in Common?

After watching "A Beautiful Mind," I got to thinking about how weird it would be to not be able to discern between reality and delusion. I started thinking about certainty. This got me to thinking about trees.

You have heard the old question:
"If a tree falls in the forest, but no one is there to hear it, then does the tree make a sound?"

I'm sure you've thought about this question at some point or another. It gets at the idea that we can't have complete certainty of something's existence (in this case, sound) without perceiving it ourselves.

In one of the discussion-based philosophy courses that I took, we talked about knowledge and certainty, and this same question came up. However, the professor changed it up a bit. He and a student in the class had the following discussion in class (a paraphrase):
Professor: "If tomorrow, at noon, humanity ceased to exist, then would mathematics also cease to exist?"
Student: "Yes, because mathematics is a creation of humanity."
P: "So are you arguing that all creations cease to exist when their creators cease to exist?"
S: "Uh, yah, I guess so."
P: "Ok. Tell me something. Is your great grandmother still alive?"
S: "No."
P: "When she passed away or ceased to exist here on earth, did your grandmother (her daughter) also cease to exist?"
S: "Ok, I see your point. But humans are different from things."
P: "Alright then, lets look at the creator of this building. Do you suspect that when he or she ceases to exist, that this building will consequently cease to exist?"
S: "No, I guess not. What I was trying to say is that math only exists in peoples' thoughts. When people cease to exist, so do their thoughts. Therefore so does math."
P: "What do you mean when you say mathematics exists only in thoughts?"
S: "Well, take the number 3 for example. The word 'three' and the symbol '3' are just constructions, created by humans for the purpose of explaining certain occurences in nature. So in essence '3' means nothing without a human to give the symbol significance."
P: "Oh I see. So you are not saying that the occurence, for which the symbol '3' was created, would cease to exist as a result of humanity ceasing to exist. Just the significance of the symbol '3' would cease to exist."
S: "Thats right."
P: "Lets look at a particular mathematical truth: 1+1 = 2 . So when humans cease to exist tomorrow at noon, the symbols '1', '+', '=', '2' would lose their meaning. But would the principal that underlies the sybols cease to exist. Lets look at another example: the standard gravity constant, 'g', which is used to explain the acceleration due to gravity on earth. Once again, when humans cease to exist, so does the significance of the symbol 'g'. But does that mean that gravity itself ceases to exist? Would the old rule of 'what goes up must come down' cease to exist?"

Would love to continue discussion on these questions.

Happily Ever After? Part II

The ending of Pi shows Max ridding his mind of the evils of mathematics with a drill to his temple. Although this can't be taken literally, it makes me wonder if he was truly happy after everything was said and done. His whole life, or the span of time we could witness in the film, revolved around mathematics. Could someone really be at ease if they lose the one thing they're truly passionate about?

One part of the ending that we didn't talk about in class that I feel is relevant is the scene where the bratty little neighbor asks Max to solve some equations and he fails to come up with answers. Did Max not know the solutions or did he just choose not to answer?

Overall, I believe that Max is still a deeply troubled person. The erratic behavior that he displays could easily be triggered by other events, possibly those that contain the intricate patterns that math contains. I'm still rather confused as to what scenes in the film actually occurred and what were nothing more than dreams. For instance, the battle between money and religion could be interpreted as literal, or as simply a nightmare or inner conflict. However, the appeal of this movie, to me, is that it is up for so many different interpretations.

What is your interpretation?

VAS-related readings

One of the great things about VAS is the way it encourages associative thinking. So, in honor of Tomasula and Farrell’s associative method, here are some texts that our last reading brought to mind:

• Malcolm Gladwell on the fallacies of IQ testing: “If what I.Q. tests measure is immutable and innate, what explains the Flynn effect—the steady rise in scores across generations?”

• A review of Stephen Wolfram’s attempt to displace mathematics as the foundation of all sciences

Enjoy.