Without equations, most of our technology would never have been invented. Of course, important inventions such as fire and the wheel came about without any mathematical knowledge. Yet without equations we would be stuck in a medieval world.

Equations reach far beyond technology too. Without them, we would have no understanding of the physics that governs the tides, waves breaking on the beach, the ever-changing weather, the movements of the planets, the nuclear furnaces of the stars, the spirals of galaxies - the vastness of the universe and our place within it.

There are thousands of important equations. The seven I focus on here - the wave equation, Maxwell's four equations, the Fourier transform and Schrödinger's equation - illustrate how empirical observations have led to equations that we use both in science and in everyday life.

We cannot escape the troubling conclusion that some—perhaps many—cherished generalities are at best exaggerated in their biological significance and at worst a collective illusion nurtured by strong a-priori beliefs often repeated.

As the 2012 Russian presidential election approaches, Putin has put himself forward as a critical protagonist in Russia's historical narrative. We propose here to offer a portrait of the man from official biographical accounts, his numerous interviews and speeches, our personal interactions with individuals who have known and worked with him, and our participation in the annual Valdai sessions. These offer an image of Putin as a student of Russian history who is moving increasingly into the dangerous territory of writer, manufacturer and manipulator of history.

Twilight, by Dr. Seuss

Jake likes a girl. Her name is Bella.
Bella likes a different fella.

See this vamp? This is Ed.
Ed is pale. Ed is dead.

Ed saved Bella from a van.
Ed must be a special man.

Ed won't kill boys. He won't kill girls.
Ed gets fed on deer and squirrels.

This is James. He's a tracker.
He's a sort of vamp attacker.

James hunts Bella for a thrill.
Will Ed kill him? Yes, he will.

But James gave her a little bite.
Will she be a vamp? She might!

Edward fixes Bella's cut.
She won't be a vampire.
But...

She becomes one. Read some more.
She's a vampire in book 4.

We’ve juiced up the entirely artificial copyright laws of the world to the point that if libraries weren’t already a centuries-old cultural institution, there’s no chance they’d ever be able to come into existence today.

But there may be hope for the humble globe. Bound atlases have stood up to digital encroachment much better than encyclopedias, because no screen can yet duplicate the tactile, immersive experience of exploring the Earth via paper maps. Globes have the same advantage, only in three dimensions.

I’ve been typing these last few paragraphs amid constant interruptions from my 4-year-old daughter, who can’t keep her hands off the globe at my side. “Are these mountains?” she wants to know, rubbing her fingers over the relief of the Andes. “Why does this red line stay in the same place when I spin the world?” she asks about the equator.

Consensus is growing that young adults aren’t being taught the basic skills that lead to critical thinking.

Most universities don’t require the courses considered core educational subjects — math, science, foreign languages at the intermediate level, U.S government or history, composition, literature, and economics.

The nonprofit American Council of Trustees and Alumni (ACTA) has rated schools according to how many of the core subjects are required. A review of more than 1,000 colleges and universities found that 29 percent of schools require two or fewer subjects. Only 5 percent require economics. Less than 20 percent require U.S. government or history.