Mathematical KnowledgeA pure math blogZola2023-04-08T00:00:00+00:00https://mathematical-knowledge.neocities.org/atom.xmlQuantity vs Quality - and how to get both2023-04-08T00:00:00+00:002023-04-08T00:00:00+00:00Unknownhttps://mathematical-knowledge.neocities.org/doubt/<hr />
<p>A few days ago, a friend told me about the dangers of reading many books in the same topic and also
the memorization trap, i stayed up the whole night trying to figure out what exactly was that, and which assumptions led him to think that one can fall into those traps. So that's what we're going to discuss.</p>
<blockquote>
<p>Why i read too many books on the same topic?
<br> How bad can it be?</p>
</blockquote>
<p>Every process can become dangerous when you just blindly apply procedures, without taking a moment to think about what exactly you're doing and why you're doing, it just might sound obvious for most of the readers.
If a read one book on geometry, and then another 2 or 3, will i become better at geometry?
<br>short answer: no
<br>long answer: it's more likely that you're just repeating procedures, and this is not what math is about.</p>
<p>Let's make an analogy, a book is not only a collection of papers glued together, rather, it's a mirror in which what you see depends on either the mirror itself, but most importantly: what is in the front of it, You. <br></p>
<p><img src="/images/mirror.webp"
style="max-width: 50%;" />
Everytime you read a book, there's a different version of yourself being reflected in it, which means that your thoughts might have changed, and the more knowledge you acquire, more the book makes sense, and the more you can relate.
Now, that was way too obvious to me... at least until his explanation (thanks to him).</p>
<br>
Your internal dialogue matters a lot when it comes to how you read books, and what kind of insight your subconscious is seeking, as pointed by Poincare:
<br> "[...] The subconscious wokr in other hand, is capable of making connections and associations between simingly unrelated topics, in a way that the concious cannot."
<p><br> At that point, you would say: "but if those books have the same topic, why would it be somehow possible to make relations?"
<br> That's a valid question, and the answer is quite simple: each author has its own point of view and way of explaining things.
Hence, the exposure to different perspectives can lead you to gain a better comprehension of the topic, but i fully understand why he warned about that.
<br> Simply reading math books won't make you better or give you more insight, but this is only true if you're not a critical thinker.
Such assumption is kind of a offense to a mathematician, since critical thinking is a requirement for mathematics, otherwise we cannot produce new work.
<br> A example from physics: Eistein only did progress because of his doubt at classical physics.
<br> To put it simply, you won't beneficiate from reading any real math book if you're not engaged with it, and also not able to criticize it.
<br> We learned from Socrates that no knowledge can be built without critical thinking, a exploration and examination of different perspectives is necessary to achieve a point where you can develop your won original point of view in the target topic.
<br> This is only suited for those who pursue a more accurate perception in their field of study, and that's why it's inneficient/innefective for the majority of the people.
<br> We are here to pursue real knowledge and the fast way to do so is from self-examination, "do i really understand that?". <br>
The greatest scientific breakthroughts have come as a result of doubt and skepticism.
<br>
<br> In part 2, i'll discuss more about memorization and why it's a double-edged sword
<br> Thanks for reading! cheers.</p>
Heidegger Theory and qualitative research2023-03-12T00:00:00+00:002023-03-12T00:00:00+00:00Unknownhttps://mathematical-knowledge.neocities.org/heidegger/Analysis is a exciting topic2023-03-08T00:00:00+00:002023-03-08T00:00:00+00:00Unknownhttps://mathematical-knowledge.neocities.org/fourth/<hr />
<p><img src="/images/girl_holding_a_analysis_book.webp"
style="max-width: 80%;" /></p>
<p>Post coming soon... </p>
A list of papers related to Habit Forming2023-02-19T00:00:00+00:002023-02-19T00:00:00+00:00Unknownhttps://mathematical-knowledge.neocities.org/third/<p>“Most of the time what we do is what we do most of the time”
<br></br>
(Townsend and Bever, 2001: 2).</p>
About me2023-02-18T00:00:00+00:002023-02-18T00:00:00+00:00Unknownhttps://mathematical-knowledge.neocities.org/about/about/<p><img src="/images/me_and_surreal_numbers.webp"
style="max-width: 70%;" /></p>
<p>I love <a href="/documents/meet-the-surreal.pdf">surreal numbers</a>.</p>
Beautiful, yet useful2023-02-18T00:00:00+00:002023-02-18T00:00:00+00:00Unknownhttps://mathematical-knowledge.neocities.org/first/<hr />
<div class="content">
<blockquote>
<p>Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music. </p>
</blockquote>
<ul>
<li>Bertrand Russel</li>
</ul>
<p><img src="/images/wolfram-mathematica.webp"
style="max-width: 90%;" /></p>
<p><img src="/images/tritanopicMedical.webp"
style="max-width: 70%;" /></p>
<p><img src="/images/tritanopic.png"
style="max-width: 50%;" /></p>
</div>
Mathematician roadmap for newbies2023-02-18T00:00:00+00:002023-02-18T00:00:00+00:00Unknownhttps://mathematical-knowledge.neocities.org/second/<p>Despite the little jokes that are made here, the roadmap above is very relatable.
Coping with ambiguity and failure are the biggest problems that beginners will face while their slowly realize that mathematics is not what they learned in school.</p>
<p>In Fact, mathematics is not about being able to simply do arithmetics, if so, why we don't replace all mathematicians and put calculators instead?
Enjoy the roadmap, but i advice not taking it back to back, after learning half of that, you can choose whatever field you like more.</p>
<p><img src="/images/mathematician-roadmap.webp"
style="max-width: 100%;" /></p>
This website is not ready! still in development.2019-11-28T00:00:00+00:002019-11-28T00:00:00+00:00Unknownhttps://mathematical-knowledge.neocities.org/test/<p>sadThis is my secondadas blog post.</p>