Gauss QQC

Quote: "I mean the word proof not in the sense of lawyers, who set two half proofs equal to a whole one, but int the sense of the mathematician where 1/2 proof=0 and it is demanded for proof that every doubt becomes impossible."

Question: Is it possible to have that much proof for math? Where's the line between 'proof' and 'what just makes sense' in math?

Comment: Because proof, to me, can even be a picture drawn on a white board. It's not necessarily proof, but it certainly makes sense when it's explained. But even if I understand something, there's almost always going to be questions that come up at one point or another. Would that be considered a doubt? Or would that just mean the problem needs to be better explained for me to understand? It's just hard for me to imagine coming up with proof for certain math techniques unless you can physically prove it in the real world (which I know they have done already). All in all, I think this Gauss fellow is pretty witty, and I'm glad he was a critical thinker who thought that proof was just as important as the theory/technique. One thing I've come to realize is that in order for me to truly understand something-- especially in math-- I need to know why we do these steps, how this process applies to what we're solving, and why this makes sense in the first place. It's quite hard for me to find these answers on my own because sadly, I'm not quite creative enough to make sense of many mathematical processes--at least for now.

Euler QQC

I finally found out why none of my articles were loading!

Quote: "From 1727 to 1783 his writings poured out in a seemingly endless flood, constantly adding knowledge to every known branch of pure and applied mathematics"

Questions: Are people like this still around? Are people continuously writing new findings about math, or are most math articles just for explaining what was already proven in Euler's time?

Comment: I mean, I don't know much about the mathematical world around me, or rather, I have never been all that interested in reading articles about math, but this line just made me wonder if we're still making a lot of mathematical discoveries, or at least making new theories about them and publishing them. Honestly, I love learning new things, especially when I have a lot of sources I can refer to. That way I can take the pieces of information from each source that makes sense to me, and piece together my understanding of the subject. So I wonder if more people were interested in learning math back then because there were constantly so many new theories and discoveries and wonders.

Leibniz QQC

Quote: "Leibniz lived at a time when the passion for metaphysics was deep and strong, when it was still believed possible to understand the world purely by thought."

Question: Do we not still hold that belief to an extent?

Comment: It sounds like this point of time was a very beautiful and creative one. But I think that to this day we still believe that we can understand the world--at least a large chunk of it--purely by thought. For example, we have many mathematical hypothesis that were derived purely by thought, and sometimes certain steps in these hypothesis aren't easily explained. Also, whenever I learn about Biology, most of the information I take in seems to be hypothesis, or in otherwords, derived purely by thought, because we don't necessarily have proof that a cell moves exactly in the way it does, but it makes sense. Another example might be dinosaurs. Yes, we have the proof that they existed, but we can be sure what they looked like. For now, all we have is how we think the bones connect, and that they had scales, but there are still many arguments over it. Some scientists believe that many dinosaurs actually had feathers, rather than scales--there was once an exhibit on it in the Natural History Museum.

All in all, I think a lot of our world is still purely derived by thought, and each thought, analysis, hypothesis, and discovery brings us more power and potential.