Thursday, January 16, 2014

What is Math?

As a preassessment for my capstone course in mathematics, I asked these soon to graduate math majors what is math, and what are the big developments in math. This goes along with both my belief in preassessment, and wanting to ask questions about what I really want to know. Here are some of their responses. (See all their blogs in a urlist.)
Roz Chast

What is math?
  • Lots of "math is more than numbers" or "it is not about computation"
  • Relationships
    • Sara: "math is patterns."
    • Jennifer: "Math is more of a way of thinking.  It is logical reasoning.  It is looking at patterns and relationships.  It is problem solving and explaining phenomena that seem unexplainable."
    • Kate: "I think math is thinking logically, understanding facts and finding relationships between different mathematical concepts."
    • Alex: "Math is the study of relationships that many people take for granted."
    • Annette: "math is an explanation or an attempt to explain relationships we find in nature or ones that we create."
    • Kristine: "math is how we can apply numerical values to how the world works."
  • Basis of science
    • Becky: "Math can be used to problem solve, find patterns, make predictions, provide reasoning, and much more which is all in the tool box of math – the resource for information."
    • Bryce: "Math is the science of solving problems."
    • Josh: "Math is the one science that every other subject has in common."
    • Kenton: "The reason that I call math a "science" is because without math, no scientific studies would be able to be quantified, all studies would have to be qualitative and therefore much less precise."
  • Logical system
    • Kerry: "Mathematics is a fantastically broad, beautifully intricate, complexly connected concept of numbers and symbols."
    • Emily: "math is thinking critically about different kinds of systems. These systems can range from the number system in algebra and calculus, to a system of shapes, such as geometry, to a system of rings as we saw in modern algebra."
    • Andy: "Mathematics is a method for conveying logical principles. A proven mathematical theorem is a reality about logic; it is some organizing principle inherent in the human mind."
  • Language. 
    • Duncan: "mathematics is the most beautiful language in all of the universe."
  • Final answers:
    • Biz: "For me, math has been a source of intrigue, education, and frustration."
    • Matt: "To ask what is mathematics is like asking what is life. There is no definitive answer."
Top 5
I also asked what are the biggest moments/discoveries in history of math. (Top 5 or milestones, etc.)
  • Famous Stuff
    • Pythagorean theorem 9
    • Fibonacci Sequence 9
    • Pi 4
    • Fundamental Theorem of Calculus 3
    • Natural logarithms and e 2
    • Kepler’s laws of planetary motions
    • Any of the Fundamental Theorems 
    • Law of Sines
    • Quadratic Formula
    • I Ching
    • Fractals
    • ϕ
  • Culture
    • Numbers 9
    • Calculators/Computers 8
    • Abacus 3
    • Discovery of zero 3
    • Understanding of different formulas
    • Development of measuring units
    • Ancient Geometry
    • Math in astronomy.
  • Concepts
    • Unit circle
    • Function
    • Pattern
    • Combinations (in counting)
    • Infinity
    • Axioms
    • Parallel postulate
    • the need for complex numbers
    • prime numbers
  • Fields
    • Calculus 7
    • Algebra 4
    • Calculus 3
    • Non-Euclidean Geometry 3
    • Geometry
    • Differential Equations
  • People
    • Euclid 7
    • Euler
    • Newton
    • Archimedes
    • Gauss
    • Karl Pearson (new to me!)
Not too different than I might expect, although the diversity of responses was pretty interesting here.

One more interesting comment:
  • Danielle: "The founders of mathematics struggled and devoted their whole lives to the theorems we now take for granted when studying in our classes. I can’t imagine devoting my whole life to proving what we consider now a simple concept." 
If you have a moment, I would love to hear your responses to these prompts in the comments!

Image: I saw this at Peter Liljedahl's very worthwhile site. Even Google couldn't help me find the original. Doesn't it look like it's from the New Yorker? EDIT: Tweeps nailed this one: Roz Chast, a frequent New Yorker contributor.

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