Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth.

Sometimes attaining the deepest familiarity with a question is our best substitute for actually having the answer.

Physicists are more like avant-garde composers, willing to bend traditional rules... Mathematicians are more like classical composers.

When I give this talk to a physics audience, I remove the quotes from my 'Theorem'.

We might be the holographic image of a two-dimensional structure.

In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture.

Over the centuries, monumental upheavals in science have emerged time and again from following the leads set out by mathematics.

All mathematics is is a language that is well tuned, finely honed, to describe patterns; be it patterns in a star, which has five points that are regularly arranged, be it patterns in numbers like 2, 4, 6, 8, 10 that follow very regular progression.

We do not know whether there are extra dimensions or multiverse. Let's go forward with the possible ideas that come out of the mathematics. It's hard for us to imagine a universe that would have no time at all.

That is, you can have nothingness, absolute nothingness for maybe a tiny fraction of a second, if a second can be defined in that arena, but then it falls apart into a something and an anti-something. And that something is then what we call the universe. But can we really understand that or put rigorous mathematics or testable experiments against that? Not yet. So one of the big holy grail of physics is to understand why there is something rather than nothing.

For most people, the major hurdle in grasping modern insights into the nature of the universe is that these developments are usually phrased using mathematics.

I think math is a hugely creative field, because there are some very well-defined operations that you have to work within. You are, in a sense, straightjacketed by the rules of the mathematics. But within that constrained environment, it's up to you what you do with the symbols.

Evidence in support of general relativity came quickly. Astronomers had long known that Mercury’s orbital motion around the sun deviated slightly from what Newton’s mathematics predicted. In 1915, Einstein used his new equations to recalculate Mercury’s trajectory and was able to explain the discrepancy, a realization he later described to his colleague Adrian Fokker as so thrilling that for some hours it gave him heart palpitations.

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