In my 5'th grade, the new professor of Mathematics told us a puzzle: there is a jug with water staying in the desert, and a bird wants to drink some water. However, the jug have a tight neck, like the old Greek pottery for olive oil: it is like a sphere at the bottom, becoming tight while going up, only to enlarge a bit at the entry. At least this is how I imagine it. What is clear, the bird cannot reach the water because the head/beak are too big for the jug entry. How can the bird drink some water from the jug?
It turns out that the solution was for the bird to put small pebbles into the jug, so the water level would rise sufficiently, so the bird could drink water from the larger opening in the up part of the jug. Nobody found the right answer. Still, for me this puzzle fueled my passion for Mathematics and science for many years after. I owe to this professor (Alexandru Setelecan) a great respect for his passion and devotion to teach Mathematics.
While I passed the Mathematics and Computer Science faculty, I am not really a mathematician. My intuitive mind preference have a hard time to adjust to making very rigorous proofs. Often, I find it enough to have the mathematical intuition and just play with it. Sometimes I do silly blunders in my proofs, that I discover myself later or others do. But many times, the intuition proves to be valuable, even when the actual proof is wrong.
My answer tentative for the puzzle with the jug and the bird was for the bird to dig at the bottom of the jug, so the jug would lean on that side, so the water would go toward the jug entry. This is not an ideal solution, as a lot of water would be spilled this way, and the water volume that becomes available for the bird is rather low. Still, I think this is my approach to Mathematics: dig at the bottom of it, maybe even spill a lot of it.
Actually, I am more interested in the Philosophy of Mathematics than in the math itself. I try to understand what can Mathematics tell about the world, how that certain mathematical results can be always true, how that we cannot answer some mathematical questions. What is math after all in relation with the human struggle to create model about reality?
I want to understand what mathematical results have support in real-life experience, and what other results might only be artificial constructs from axioms that does not have a lot of sense for modeling the real world - I dig at the bottom of it. I also want to understand the limits of what the human mind can know, including mathematical means. Sometimes, I use mathematical models only as metaphors about what how human mind might represent certain reality patterns. Another inspiration I have for this endeavor is a book from professor Solomon Marcus: "Universal Paradigms".
I'm sure many of my ideas might prove to be silly later, even for me. However, my hope is that some of them could inspire future discoveries of the human mind, from people that are more rigorous than me.
Dear reader, please leave a message if you exist! ;) Also, please share this article if you find it interesting. Thank you.
It turns out that the solution was for the bird to put small pebbles into the jug, so the water level would rise sufficiently, so the bird could drink water from the larger opening in the up part of the jug. Nobody found the right answer. Still, for me this puzzle fueled my passion for Mathematics and science for many years after. I owe to this professor (Alexandru Setelecan) a great respect for his passion and devotion to teach Mathematics.
While I passed the Mathematics and Computer Science faculty, I am not really a mathematician. My intuitive mind preference have a hard time to adjust to making very rigorous proofs. Often, I find it enough to have the mathematical intuition and just play with it. Sometimes I do silly blunders in my proofs, that I discover myself later or others do. But many times, the intuition proves to be valuable, even when the actual proof is wrong.
My answer tentative for the puzzle with the jug and the bird was for the bird to dig at the bottom of the jug, so the jug would lean on that side, so the water would go toward the jug entry. This is not an ideal solution, as a lot of water would be spilled this way, and the water volume that becomes available for the bird is rather low. Still, I think this is my approach to Mathematics: dig at the bottom of it, maybe even spill a lot of it.
Actually, I am more interested in the Philosophy of Mathematics than in the math itself. I try to understand what can Mathematics tell about the world, how that certain mathematical results can be always true, how that we cannot answer some mathematical questions. What is math after all in relation with the human struggle to create model about reality?
I want to understand what mathematical results have support in real-life experience, and what other results might only be artificial constructs from axioms that does not have a lot of sense for modeling the real world - I dig at the bottom of it. I also want to understand the limits of what the human mind can know, including mathematical means. Sometimes, I use mathematical models only as metaphors about what how human mind might represent certain reality patterns. Another inspiration I have for this endeavor is a book from professor Solomon Marcus: "Universal Paradigms".
I'm sure many of my ideas might prove to be silly later, even for me. However, my hope is that some of them could inspire future discoveries of the human mind, from people that are more rigorous than me.
Dear reader, please leave a message if you exist! ;) Also, please share this article if you find it interesting. Thank you.
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