500天数学
500 days of math

原始链接: https://gmays.com/500-days-of-math/

## Math Academy 500天每日数学练习总结 作者出于理解人工智能背后的数学原理,开始使用Math Academy进行每日数学练习,尽管此前学业有成,但起步阶段却出乎意料地基础。经过500天,他们从基础知识学习到微积分和线性代数,尽管遇到挑战,但进步显著。 关键在于持续性至关重要,但练习的*数量*更为重要。早期进步迅速,但随着概念变得更难,且无重点的学习效果不佳,进度放缓。为了应对这个问题,作者创建了一个习惯追踪应用“HabitGraph”,以鼓励专注练习并通过社交媒体进行公开问责。 在繁忙的生活(创业公司、家庭)中,优先安排并合理安排数学学习至关重要。专门的、专注的时间——比如每日午餐时间——比在干扰中挤时间学习更有效。这段旅程不仅仅是掌握数学,更是培养成长型思维,并从持续挑战困难材料中获得意想不到的个人收益。作者仍然决心继续前进,设定未来的里程碑,并更深入地理解数学世界。

## 数学学院:体验各异 最近的 Hacker News 讨论围绕着数学学院展开,这是一个订阅制的在线数学学习平台(每月 49 美元)。用户分享了不同的体验,突出了它的优点和缺点。 许多人赞赏其结构化的课程和间隔重复系统,认为它有效地帮助回顾概念并建立坚实的基础,尤其适合那些长期脱离数学的人。有些人认为它比自学更有效率,因为它减轻了课程规划的负担。然而,也有人批评其缺乏深入的解释以及潜在的高成本,建议使用开放大学教科书或 Khan Academy 等免费资源。 一个共同的主题是在生活需求的同时保持持续学习的困难。多位用户强调,无论选择哪种方法,都需要投入专门的时间和精力。数学学院并非万能药,但对于寻求结构化路径的积极学习者来说,它可以是一个有价值的工具,特别是与 ChatGPT 等补充资源结合使用,以获得更深入的理解。最终,该平台似乎最适合那些受益于指导式、问题导向的学习方法,并且愿意投入持续练习的人。
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原文

I recently crossed 500 days of practicing math daily with Math Academy. I wrote about my experience after 100 days here.

TL;DR: I am still very impressed by the Math Academy system and highly recommend it, but you get out of it what you put in. My consistency has been exceptional, but my volume has been frequently low, which has had a cascading impact on my progress.

To help, I spent January and February building a habit app to help improve my volume along with some other changes in how I handle my habits.

All that said, despite my best efforts to sabotage myself, I’m amazed at how much I’ve improved and at my fledgling superpowers. I didn’t even know what derivatives or integrals were, let alone what the symbols meant. I still have a long way to go, but I’m more determined than ever.


Why I started

From the initial 100 day post:

“I’ve worked on various AI products over the last year and like understanding the technical aspects of the products I build. 

But as I dug in to learn more about how large language models (LLMs) and transformers worked…I was lost.

It was humbling.”

A friend had been building a math education app called Math Academy for most of the last decade, so this finally gave me an excuse to try it and support him as I do with most of my friends’ products.

But before we get into how it’s going, I’d like to confess talk about where I was starting from, which was even worse than I thought.

The gap

When I wrote the first post, I knew I’d have a long way to go, but I somehow still underestimated how far behind I was.

Growing up, a lot of things came easy to me, so I rarely studied. I could just absorb it in class and mostly get A’s. But when things started getting harder, I just avoided it. “Oh, this honors math class means I need to work harder and study? No thanks, I’d rather play EverQuest/StarCraft/World of Warcraft.” I started skipping the hard stuff since past a certain point it was all optional.

I did the same thing in college. I majored in Psychology (I know, I know) because it came easy to me (and I really enjoyed it) and finished my 4 year degree in ~2 years. Then I joined the Marine Corps for 8 years (spent 2 years between Iraq and Afghanistan operating on small teams), then left to start a startup.

I taught myself to code well enough to launch a half-decent product and later ended up as a product manager (and eventually Director) at a public tech company in 2015. I loved building products and always earned the respect of my team by being the most technical PM, understanding deeply how the product worked and even committing code from time to time.

But then came AI. And just like every other technology, I would understand it by digging in and learning about it. How hard could it be?

How am I so dumb?

And that’s where my past caught up with me. It turns out, I suck at math compared to how I ‘felt’ I was. I have decent number sense (or so I thought), but beyond the basic high school stuff it doesn’t come easy to me and it’s not intuitive (a feeling I’m not used to). And just like that, everything I’ve secretly been self-conscious of and had been able to fake my way through (including two graduate degrees, an MS and an MBA) hit me in the face like a ton of bricks.

This became glaringly obvious when I took the Math Academy diagnostic placement exam and it put me in Math Foundations 1, the lowest level of the adult courses.

“Hey dummy, there’s nowhere to hide, come here and do this remedial shit!”

It was at the same time depressing (I’m dumb), liberating (I don’t have to pretend I’m not dumb anymore) and exciting (I have a chance to be not dumb anymore).

(insert math joke about it being half depressing, half liberating and half exciting just to make Jason, Justin and Alex shake their heads…)

It was easy…

The nice part about the diagnostic is a lot of the stuff was familiar, I just hadn’t done it in decades. So I was able to fly through course material early on and make quick progress. Life was good. I’d be through all the courses in no time!

…until it wasn’t

Then it got harder as I encountered new stuff. I actually had to focus and concentrate. And this is when I slowed down and my volume fell off a cliff.

See, I developed the habit of squeezing my math lessons in whenever I had time. Often in the evening when the kids were watching Bluey before bed, or at the beach while the kids were playing in the sand, or between sets working out (yeah, I know), or anywhere else I was partially distracted, but had a few “free” minutes.

Why did I do that? Well, because life is busy with two young kids. I also try to workout almost every day. I have a startup. I invest. I also <insert some other random excuses>.

But those are just excuses. Learning is hard work, and if you don’t respect the process, it won’t happen.

You get out what you put in

This was the crux of my problem. Where bits and pieces of unfocused time was enough to make solid progress early on, it wasn’t anymore as I encountered new material.

My progress often slowed to just one review or a partial lesson a day. The slower progress drove worse performance on quizzes because I wasn’t getting the reps fast enough to solidify a foundation. This meant more reviews, which meant slower progress towards course completion.

To maintain the momentum I’d have to aim for at least 100XP a week, which should be sustainable long-term.

Priorities & motivation

Priorities

I plan to write more on this later, but what made me consistent was my focus on habits. However, over time my various habits (math was one of them) piled up and I was spread too thin. I had to prune them to make room for the most important ones.

I also had to be honest about my personal priorities. For example, in the summer I took my kids (3 and 5 at the time) to the beach (we live on Cape Cod) or played in the pool with them almost every day, and I wasn’t going to compromise that time just to get an extra math lesson done.

One major change that helped is going out to lunch to the same place every day and spending ~45 min of focused time knocking out math lessons. I work from home, so this change of scenery and focus time became my daily ritual.

Any time I spent later (even if it was unfocused) was a bonus. For example, I still have ‘unfocused’ math time, e.g. while my kids are at gymnastics or while they are watching TV before bed.

Motivation

One thing I loved seeing on X/Twitter are people posting their progress in the Math Academy group on X. I eventually started doing the same and wow, it was magical. It was like a passive accountability system that made me show up every day and share with others on the same journey. It’s also a great way to meet new people and make friends with common interests along the way.

Another hack that helped is visually tracking my progress in a GitHub-style graph. Math Academy shows weekly progress, but I wanted to see it long-term over months and years. It’s pretty awesome to be able to look back and see my daily progress updates from any day in the past, something that’s becoming an increasingly valuable asset the longer I go.

Scratching my own itch

To automate it, a friend and I made a little X app called HabitGraph that lets me track habits with a tweet. It uses AI to automatically recognize and track my math tweets as habit check-ins.

This was exceptionally effective because it’s passive (it tracks it automatically), so I also started doing it for other habits. It became a motivating way to learn in public. Most of my tweets these days are daily progress updates.

A few asked if they could use it too, so with a little extra work, I made it public. It feels good to see that dozens of other Math Academy users are now using it for accountability and to track their progress!

It’s a work in progress, but it has made the journey so much more fulfilling.

So, where am I now?

Since the first update, I’ve completed Mathematical Foundations I and II. I’m now in the middle of Mathematical Foundations III, which covers calculus, linear algebra, advanced trigonometry, probability/statistics and other topics that prepare me for higher-level university courses, like Mathematics for Machine Learning and Methods of Proof, which I’m particularly excited about.

An ongoing journey

I feel like I’m still in the middle of finding my stride, a balance that works, and a sustainable process. One forcing function is my kids, who are constantly growing and changing, so my process and priorities change with them as I experiment with new ways to maintain momentum.

As part of this process, my ‘why’ seems to also be changing. It’s not just the end goal of learning the math behind AI, but I’ve noticed personal benefits through this journey that have their own unexpected rewards and have opened up new interests that I’m exploring.

Interestingly, doing something hard every day that makes me feel dumb by stretching my brain is also changing me, but it’s hard to explain how. It’s also bleeding into other areas of my life in a positive way. Assuming I keep it up, I hope to have more to share in a future update, maybe at 700 or 800 days.

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