“mathematics gives you power” — the power to understand chemistry, physics and other aspects of the world.
“Do not give up,” she likes to tell them when they’re struggling. “A problem proves its worth by fighting back.”
These Ramsey numbers are not very big. With all the computing power today, shouldn’t someone just crank out an improved lower bound by computer? The thing that drives many people crazy is that even in this case, it’s beyond the boundary of our knowledge.
Mathematics is big. No one knows everything. So collaboration helps give you a broader point of view — a wider scope.
Also, a problem usually will not die as easily if you’re collaborating on it. If you’re frustrated or discouraged, then your collaborator might share some light and pull you out. Usually, one piece of work will lead to another, so it’s just continued year after year. That’s the best situation.
Math is a great career. It’s fun. It’s interesting. It keeps the mind curious. It’s good for making friends. It’s very good for your health.
Here's how the AI pricing bait-and-switch works: 1. Launch with generous/unlimited limits 2. Build user dependency 3. Add caps targeting “less than 5%” of users 4. Frame as “sustainability” or “fairness”
Sound familiar? That's because we've seen this movie before. Cursor did it. Windsurf followed. GitHub Copilot tightened screws. Now Claude Code.
The real damage: You're not frustrating 5% of users—you're breaking trust with the exact people who drive growth and adoption.
What we want: Transparent costs upfront so we can make informed decisions.