I’ll be back with some thoughts, but just going to post some research I did. I used College Navigator (feds’ website with IPEDS data) and this site that looked at the undergraduate origins of people who arned a doctorate in the U.S.: https://public.tableau.com/app/profile/jonboeckenstedt/viz/DoctoralRecipients1958-2023/AllData. I looked at the areas of Chemistry and Mathematics & Statistics to see the number of alumni who went on to earn a doctorate in the field (viewing that as solid preparation in those fields) as well as how many Bachelors degrees were earned in SY22-23 (the latest year available in the IPEDS data).
In addition to gathering those two data points, I created a ratio of the number of doctorates earned in a field between 2010-2023 by the number of bachelors received in SY22-23 to get a sense of how many students were going on for their doctorates from a given program.
You may find the ratio helpful, or you may not. Or your son may prefer to look at the size of an undergraduate math or chemistry department as a more helpful gauge. As a frame of reference, IIRC off the top of my head, the ratio for state flagship students majoring in anything going on to earn a doctorate in anything is around 0.81 (WRONG), meaning that all of these have strong doctoral outcomes for these fields.
EDIT 2: I should not have given a number off the top of my head as I was off by a whole place value. Going back to my notes in this post, the average ratio among the 50 flagships is 0.0928 and the median is 0.0849 (for doctorates earned 2000-2018).
This chart is sorted from highest to lowest ratio for Chemistry:
| School | # of Chem PhDs earned by alumni between 2010-2023 | # of Chem Bachelors Awarded SY22-23 | Chem Ratio of Doctorates to Bachelors | Highest Chem Degree Offered |
|---|---|---|---|---|
| Cal Tech | 82 | 7 | 11.7143 | Doctorate |
| Harvey Mudd | 50 | 8 | 6.2500 | Bachelors |
| Clarkson | 31 | 5 | 6.2000 | Doctorate |
| Worcester Polytechnic | 38 | 7 | 5.4286 | Doctorate |
| Washington U. | 66 | 13 | 5.0769 | Doctorate |
| Case Western | 63 | 15 | 4.2000 | Doctorate |
| Stanford | 46 | 11 | 4.1818 | Doctorate |
| U. of Arizona | 79 | 19 | 4.1579 | Doctorate |
| Cornell | 140 | 34 | 4.1176 | Doctorate |
| U. at Buffalo | 91 | 27 | 3.3704 | Doctorate |
| U. of Rochester | 75 | 23 | 3.2609 | Doctorate |
| Boston U. | 91 | 28 | 3.2500 | Doctorate |
| MIT | 86 | 27 | 3.1852 | Doctorate |
| Carnegie Mellon | 63 | 20 | 3.1500 | Doctorate |
| Northwestern | 68 | 22 | 3.0909 | Doctorate |
| U. of Chicago | 104 | 34 | 3.0588 | Doctorate |
| U. of Michigan | 129 | 43 | 3.0000 | Doctorate |
| Rensselaer Polytechnic | 59 | 22 | 2.6818 | Doctorate |
| Brandeis | 40 | 15 | 2.6667 | Doctorate |
| U. of Wisconsin | 152 | 60 | 2.5333 | Doctorate |
| Rice | 40 | 16 | 2.5000 | Doctorate |
| U. of Maryland | 70 | 28 | 2.5000 | Doctorate |
| Colorado State | 56 | 23 | 2.4348 | Doctorate |
| Harvard | 86 | 38 | 2.2632 | Doctorate |
| U. of Pittsburgh | 122 | 57 | 2.1404 | Doctorate |
| New Mexico M&T | 14 | 7 | 2.0000 | Doctorate |
| Purdue | 126 | 65 | 1.9385 | Doctorate |
| Missouri Science & Technology | 22 | 12 | 1.8333 | Doctorate |
| U. of Minnesota | 124 | 68 | 1.8235 | Doctorate |
| Arizona State | 46 | 31 | 1.4839 | Doctorate |
| Ohio State | 96 | 66 | 1.4545 | Doctorate |
| Binghamton | 76 | 55 | 1.3818 | Doctorate |
| U. of Utah | 66 | 48 | 1.3750 | Doctorate |
| Michigan State | 80 | 60 | 1.3333 | Doctorate |
| U. of Illinois | 130 | 116 | 1.1207 | Doctorate |
| U. of Texas - Dallas | 30 | 30 | 1.0000 | Doctorate |
This chart is sorted from highest to lowest ratio for Math:
| School | # of Math Phds earned by alumni between 2010-2013 | # of Math Bachelors Awarded SY22-23 | Math Ratio of Doctorates to Bachelors | Highest Math Degree Offered |
|---|---|---|---|---|
| Harvey Mudd | 88 | 14 | 6.2857 | Bachelors |
| Cal Tech | 117 | 25 | 4.6800 | Doctorate |
| Clarkson | 18 | 9 | 2.0000 | Doctorate |
| MIT | 184 | 99 | 1.8586 | Doctorate |
| U. of Texas - Dallas | 99 | 63 | 1.5714 | Doctorate |
| U. of Chicago | 201 | 156 | 1.2885 | Doctorate |
| Cornell | 96 | 82 | 1.1707 | Doctorate |
| Case Western | 44 | 39 | 1.1282 | Doctorate |
| Stanford | 96 | 88 | 1.0909 | Doctorate |
| Washington U. | 53 | 53 | 1.0000 | Doctorate |
| New Mexico M&T | 9 | 9 | 1.0000 | Doctorate |
| Harvard | 161 | 198 | 0.8131 | Doctorate |
| Rice | 64 | 80 | 0.8000 | Doctorate |
| U. of Utah | 63 | 79 | 0.7975 | Doctorate |
| Colorado State | 41 | 52 | 0.7885 | Doctorate |
| Rensselaer Polytechnic | 59 | 75 | 0.7867 | Doctorate |
| U. of Rochester | 66 | 84 | 0.7857 | Doctorate |
| Worcester Polytechnic | 19 | 32 | 0.5938 | Doctorate |
| Northwestern | 47 | 82 | 0.5732 | Doctorate |
| U. of Arizona | 66 | 116 | 0.5690 | Doctorate |
| Carnegie Mellon | 94 | 188 | 0.5000 | Doctorate |
| Missouri Science & Technology | 14 | 28 | 0.5000 | Doctorate |
| U. of Michigan | 115 | 235 | 0.4894 | Doctorate |
| U. of Pittsburgh | 43 | 92 | 0.4674 | Doctorate |
| U. of Maryland | 71 | 155 | 0.4581 | Doctorate |
| Arizona State | 77 | 183 | 0.4208 | Doctorate |
| Michigan State | 54 | 132 | 0.4091 | Doctorate |
| Brandeis | 21 | 55 | 0.3818 | Doctorate |
| U. of Minnesota | 77 | 202 | 0.3812 | Doctorate |
| U. of Wisconsin | 77 | 221 | 0.3484 | Doctorate |
| Ohio State | 74 | 265 | 0.2792 | Doctorate |
| Binghamton | 23 | 88 | 0.2614 | Doctorate |
| Boston U. | 34 | 136 | 0.2500 | Doctorate |
| U. of Illinois | 87 | 415 | 0.2096 | Doctorate |
| U. at Buffalo | 22 | 105 | 0.2095 | Doctorate |
| Purdue | 47 | 288 | 0.1632 | Doctorate |
(Edited to make charts that were only for math or chemistry, to improve readability.)