<p>Consider HYPSMC+Berkeley only.
<a href="http://www.nasonline.org/site/Dir?sid=1011&view=basic&pg=srch%5B/url%5D">http://www.nasonline.org/site/Dir?sid=1011&view=basic&pg=srch</a></p>
<p>NAS=national academy of science. NAS membership is one of the best, if not the best, measure of faculty reputation of a university in academia.</p>
<h2>MATH (pure)</h2>
<p>Princeton (14 members)
Harvard (10)</p>
<p>Berkeley (7)
MIT (7)
Stanford (6)
Yale (4)
Caltech (2)</p>
<h2>Applied MATH</h2>
<p>Stanford (9 members)
Berkeley (7)</p>
<p>Harvard(2)
Yale (2)
MIT (2)
Caltech (2)
Princeton (1)</p>
<h2>Physics</h2>
<p>Berkeley (18)
MIT (14)
Stanford (12)
Princeton (12)</p>
<p>Harvard (9)
Caltech (7)
Yale (3)</p>
<h2>Chemistry</h2>
<p>Berkeley (18)
Stanford (13)
Caltech (13)
Harvard (12)</p>
<p>MIT (7)
Yale (5)
Princeton (3)</p>
<p>By looking at the numbers, I conclude that B/S/H/M are strongest in these areas. Yale is the weakest. Princeton is strong in Math and physics only (#1 in pure math). Caltech is strong in physics and chemsitry. </p>
<p>In US NEWS and NRC ranking, Stanford and Harvard are #1 and #2 in biology.</p>
<p>In NRC and US NEWS ranking, Stanford, only Stanford, has been #1 in Computer science for decades. No other university in the world can really match against Stanford in CS faculty reputation. When counting Turing Award winners, Stanford has 18 ties to Turing awards, while MIT has about 10 only.</p>