1 00:00:01,370 --> 00:00:06,089 I'm David Farmer from the 2 00:00:03,959 --> 00:00:07,500 American Institute of Mathematics. Today 3 00:00:06,089 --> 00:00:08,820 we're here to talk about the research statement, 4 00:00:07,500 --> 00:00:10,800 which is one of the key components 5 00:00:08,820 --> 00:00:13,380 of an application for a 6 00:00:10,800 --> 00:00:15,210 tenure-track position in mathematics. 7 00:00:13,380 --> 00:00:17,220 The research statement is one of the items 8 00:00:15,210 --> 00:00:18,660 the search committee will use in 9 00:00:17,220 --> 00:00:20,550 determining its short list of people 10 00:00:18,660 --> 00:00:22,800 who are invited to campus for an interview. 11 00:00:20,550 --> 00:00:24,689 Judgments made from the 12 00:00:22,800 --> 00:00:27,390 research statement include the quality 13 00:00:24,689 --> 00:00:30,330 of past research, the likelihood of 14 00:00:27,390 --> 00:00:32,600 future research success, the prospects 15 00:00:30,330 --> 00:00:34,950 for receiving funding for your research, 16 00:00:32,600 --> 00:00:36,899 overlap with research interests of 17 00:00:34,950 --> 00:00:39,540 current department members, and whether 18 00:00:36,899 --> 00:00:42,090 or not students can be involved in your 19 00:00:39,540 --> 00:00:43,530 research program. Different institutions 20 00:00:42,090 --> 00:00:54,210 will give different weighting to these factors. 21 00:00:43,530 --> 00:00:57,120 Basor: Here are some things that I think 22 00:00:54,210 --> 00:01:00,690 are important for a research statement. 23 00:00:57,120 --> 00:01:03,539 I think that first of all the 24 00:01:00,690 --> 00:01:08,090 very beginning is a really crucial part. 25 00:01:03,539 --> 00:01:12,900 The first part of your research statement 26 00:01:08,090 --> 00:01:16,830 should be written in rather broad terms. 28 00:01:16,830 --> 00:01:24,060 Something that I would not do is 29 00:01:19,380 --> 00:01:26,880 jump into one of your very particular 30 00:01:24,060 --> 00:01:30,990 problems that you worked on. What you 31 00:01:26,880 --> 00:01:33,840 want to do is indicate the area and your 32 00:01:30,990 --> 00:01:36,479 particular area of research. 33 00:01:33,840 --> 00:01:38,280 You want to give a good overall picture. 34 00:01:36,479 --> 00:01:41,430 What is the big picture there? 36 00:01:41,430 --> 00:01:49,079 What are the important things that are 37 00:01:44,189 --> 00:01:50,640 happening in this field? 38 00:01:49,079 --> 00:01:52,649 This is really good practice, and this 39 00:01:50,640 --> 00:01:55,229 is maybe the hardest part to do, 40 00:01:52,649 --> 00:01:57,570 because it's often easy to write about 41 00:01:55,229 --> 00:02:00,689 your own research on a very particular problem. 42 00:01:57,570 --> 00:02:04,649 But you have to remember first of all, 43 00:02:00,689 --> 00:02:07,369 that on committees there can be 44 00:02:04,649 --> 00:02:12,840 people who are not in your area reading this. 45 00:02:07,369 --> 00:02:13,680 They may be far from your area. 47 00:02:13,680 --> 00:02:17,340 You really have to put it in context. 48 00:02:15,659 --> 00:02:19,890 You have to give the big picture, 49 00:02:17,340 --> 00:02:22,560 then it's okay to launch into the things 51 00:02:22,560 --> 00:02:26,750 that you've been thinking about and 52 00:02:25,230 --> 00:02:30,090 the things that you've been doing. 53 00:02:26,750 --> 00:02:31,980 For postdocs maybe the description of your 54 00:02:30,090 --> 00:02:36,239 thesis problem and the work you've done 55 00:02:31,980 --> 00:02:38,519 since you've been a postdoc - 56 00:02:36,239 --> 00:02:40,620 that is going to, of course, take up a 57 00:02:38,519 --> 00:02:44,389 good portion of this research statement. 58 00:02:40,620 --> 00:02:48,930 Then after that, or interwoven 59 00:02:44,389 --> 00:02:54,480 with that, is the fact that 60 00:02:48,930 --> 00:02:58,560 you need to present a plan for 61 00:02:54,480 --> 00:03:03,030 future work that is robust enough. 62 00:02:58,560 --> 00:03:04,560 I think this is important no 63 00:03:03,030 --> 00:03:07,500 matter what kind of institution you're 64 00:03:04,560 --> 00:03:09,989 going to, because if you're going to 65 00:03:07,500 --> 00:03:12,599 something like an R1 research place, 66 00:03:09,989 --> 00:03:14,129 or you're writing it for that particular place 67 00:03:12,599 --> 00:03:19,109 (although you might want to have two versions) 69 00:03:19,109 --> 00:03:25,560 you need to convince people 70 00:03:23,099 --> 00:03:28,260 on that hiring committee 71 00:03:25,560 --> 00:03:32,549 that you understand the big problems 72 00:03:28,260 --> 00:03:34,470 in the area; that you have enough ideas 73 00:03:32,549 --> 00:03:37,290 for work that are going to carry you 74 00:03:34,470 --> 00:03:39,930 into the future; that you might be 75 00:03:37,290 --> 00:03:41,489 able to support graduate students 76 00:03:39,930 --> 00:03:43,590 - your own graduate students - with your work; 77 00:03:41,489 --> 00:03:46,259 that you might be able to apply for grants. 78 00:03:43,590 --> 00:03:49,949 You're not going to say all that 79 00:03:46,259 --> 00:03:51,930 explicitly, but if you have 80 00:03:49,949 --> 00:03:54,540 an ambitious enough program, 81 00:03:51,930 --> 00:03:57,569 with "meat" there, 82 00:03:54,540 --> 00:04:00,000 then I think that will be clear. 83 00:03:57,569 --> 00:04:04,290 That's your future plans, future work. 84 00:04:00,000 --> 00:04:06,629 Even if you are going to 85 00:04:04,290 --> 00:04:09,019 more of a liberal arts college, or a 86 00:04:06,629 --> 00:04:15,259 place where it's teaching research 87 00:04:09,019 --> 00:04:17,250 emphasis more, you still need enough, 88 00:04:15,259 --> 00:04:18,900 and you still need to convince them that 89 00:04:17,250 --> 00:04:20,579 you've done enough research, and that you 90 00:04:18,900 --> 00:04:23,099 have enough research ideas to carry you further, 91 00:04:20,579 --> 00:04:24,090 because in those places you're 92 00:04:23,099 --> 00:04:26,440 going to tend to be a little more isolated. 94 00:04:26,440 --> 00:04:33,480 You're going to have less time, so people 95 00:04:29,890 --> 00:04:35,740 will want to see that you have 97 00:04:35,740 --> 00:04:40,840 enough ideas to continue your research, 98 00:04:38,170 --> 00:04:44,260 and that you're able to move forward. 99 00:04:40,840 --> 00:04:46,960 Farmer: A lot of what I say applies 100 00:04:44,260 --> 00:04:49,300 equally to the job research summary 101 00:04:46,960 --> 00:04:52,780 and a research proposal you 102 00:04:49,300 --> 00:04:56,140 submit for funding. Both of them are 103 00:04:52,780 --> 00:04:58,240 persuasive documents. The fact that 104 00:04:56,140 --> 00:05:00,880 you've logically explained things and 105 00:04:58,240 --> 00:05:04,570 certain material is there, is irrelevant 106 00:05:00,880 --> 00:05:07,240 if a quick reading of the document does 107 00:05:04,570 --> 00:05:09,010 not convey what you're trying to do. 108 00:05:07,240 --> 00:05:10,780 It's not like a proof where you could say 109 00:05:09,010 --> 00:05:13,810 "my proof is correct". It's: are you being 110 00:05:10,780 --> 00:05:15,400 persuasive or not? A lot of what 111 00:05:13,810 --> 00:05:18,670 helps the persuasiveness is the 112 00:05:15,400 --> 00:05:21,610 structure of the document. 113 00:05:18,670 --> 00:05:23,980 Here I'm showing you part of someone's research 114 00:05:21,610 --> 00:05:24,280 statement, which I can tell you right away 116 00:05:24,280 --> 00:05:29,950 it is not effective. I'm not saying it's bad. 117 00:05:27,340 --> 00:05:31,780 I'm saying it's not effective. 118 00:05:29,950 --> 00:05:34,180 What, even from your seats, you can see 119 00:05:31,780 --> 00:05:38,290 is missing, is there are no section or 120 00:05:34,180 --> 00:05:40,270 subsection headings on these pages. 121 00:05:38,290 --> 00:05:42,700 The people on the committee don't want to 122 00:05:40,270 --> 00:05:45,010 read page after page, especially if it's 123 00:05:42,700 --> 00:05:46,660 technical detail. If it's not 124 00:05:45,010 --> 00:05:48,310 technical detail and you're actually 125 00:05:46,660 --> 00:05:50,290 changing topics in the middle of the page, 126 00:05:48,310 --> 00:05:53,850 then they're not going to notice 127 00:05:50,290 --> 00:05:57,460 that without a section heading. 128 00:05:53,850 --> 00:05:58,990 In many cases just by adding section and 129 00:05:57,460 --> 00:06:01,150 subsection headings you can vastly 130 00:05:58,990 --> 00:06:05,170 improve your statement. Let me put this 131 00:06:01,150 --> 00:06:08,650 in the broader context of how panels work. 132 00:06:05,170 --> 00:06:11,680 Both research proposals and job materials 133 00:06:08,650 --> 00:06:14,320 are evaluated by panels. 134 00:06:11,680 --> 00:06:16,330 The panel's first and most important goal 135 00:06:14,320 --> 00:06:19,060 is to come up with a short shortlist. 136 00:06:16,330 --> 00:06:21,420 Before we talked about that there's 137 00:06:19,060 --> 00:06:24,030 a longer shortlist along the way, and 138 00:06:21,420 --> 00:06:27,130 often you can formally get to that point. 139 00:06:24,030 --> 00:06:30,250 You don't get on the short shortlist in 140 00:06:27,130 --> 00:06:31,930 either case without an advocate: somebody 141 00:06:30,250 --> 00:06:35,800 on the panel who becomes your champion. 142 00:06:31,930 --> 00:06:38,710 You need to give ammunition to your champion. 143 00:06:35,800 --> 00:06:39,850 If this is the kind of thing you've written, 145 00:06:39,850 --> 00:06:45,280 a large block of text, the best your champion's 146 00:06:42,610 --> 00:06:48,100 going to be able to say is, "take my word 147 00:06:45,280 --> 00:06:52,180 for it, this is great work". 148 00:06:48,100 --> 00:06:54,960 For some advocates, that's all they need 149 00:06:52,180 --> 00:06:58,750 to say, but often that's not the case. 150 00:06:54,960 --> 00:07:02,680 It would be better if they could say: 151 00:06:58,750 --> 00:07:04,240 "this is work essential to lots of 152 00:07:02,680 --> 00:07:06,970 the other work going on in this area; 153 00:07:04,240 --> 00:07:09,250 look they've described the connections 154 00:07:06,970 --> 00:07:11,560 with other areas". Then they can point to a 155 00:07:09,250 --> 00:07:17,349 section called 'connection with other work'. 156 00:07:11,560 --> 00:07:22,470 Or, especially at a liberal arts college 157 00:07:17,349 --> 00:07:26,169 and other smaller places, it's nice if more 158 00:07:22,470 --> 00:07:27,610 than just a few people in the department 159 00:07:26,169 --> 00:07:33,900 are interested in your research. 160 00:07:27,610 --> 00:07:37,960 If you have a section called 161 00:07:33,900 --> 00:07:39,639 'historical context' or a 'X as a tool', 162 00:07:37,960 --> 00:07:41,620 where X is the particular thing, 163 00:07:39,639 --> 00:07:43,479 then people can read an accessible 164 00:07:41,620 --> 00:07:45,970 introduction and say, "Oh, I can 165 00:07:43,479 --> 00:07:48,310 imagine talking to them." If you give 166 00:07:45,970 --> 00:07:50,830 your advocate ammunition to explain why 167 00:07:48,310 --> 00:07:52,720 other people will be interested in your work, 168 00:07:50,830 --> 00:07:55,030 and why you will be able to talk to them, 169 00:07:52,720 --> 00:07:57,909 that's great. Or maybe you're at a place 170 00:07:55,030 --> 00:08:00,070 or you're applying to a place that has 171 00:07:57,909 --> 00:08:02,770 lots of honors theses for their students. 172 00:08:00,070 --> 00:08:04,630 A clear explanation in your 173 00:08:02,770 --> 00:08:06,729 research statement that non-experts can 174 00:08:04,630 --> 00:08:09,159 understand, will go a long way to making 175 00:08:06,729 --> 00:08:12,610 the case that you may be able to advise 176 00:08:09,159 --> 00:08:14,409 students and projects. You could even have a 177 00:08:12,610 --> 00:08:16,449 section called 'possible student projects'. 178 00:08:14,409 --> 00:08:19,330 But if that's at the end of 179 00:08:16,449 --> 00:08:21,099 an incomprehensible 15 pages, 180 00:08:19,330 --> 00:08:24,490 no one's going to get to that point anyway, 181 00:08:21,099 --> 00:08:26,740 except the hardcore person in that area, 182 00:08:24,490 --> 00:08:28,150 who will not be able 183 00:08:26,740 --> 00:08:30,039 to make a good case that you could 184 00:08:28,150 --> 00:08:34,050 advise undergraduate students. 185 00:08:30,039 --> 00:08:37,390 So that structure really helps a lot. 186 00:08:34,050 --> 00:08:40,209 Think in terms of how would someone 187 00:08:37,390 --> 00:08:42,640 quickly find the information in here 188 00:08:40,209 --> 00:08:43,440 that says how you're work relates to other 189 00:08:42,640 --> 00:08:45,780 recent work, or how it relates to other areas, 191 00:08:45,780 --> 00:08:50,460 or possible applications. If you have actual 192 00:08:48,000 --> 00:08:52,680 possible applications, you should 193 00:08:50,460 --> 00:08:54,560 have a heading somewhere that explains that, 194 00:08:52,680 --> 00:08:58,110 and in that section you have 195 00:08:54,560 --> 00:09:00,980 comprehensible words about it. 196 00:08:58,110 --> 00:09:04,980 It's thinking in terms of the structure and 197 00:09:00,980 --> 00:09:06,240 imagining someone who looks at it 198 00:09:04,980 --> 00:09:08,520 and sees these headings: 199 00:09:06,240 --> 00:09:11,160 'there's historical context', 200 00:09:08,520 --> 00:09:13,560 'this section explains why this tool has broad use', 201 00:09:11,160 --> 00:09:16,050 and 'this tells how their work relates to 202 00:09:13,560 --> 00:09:17,790 prior work'. Just by reading the section 203 00:09:16,050 --> 00:09:19,830 headings they might get a good 204 00:09:17,790 --> 00:09:21,510 impression about you. "Oh, this person is 205 00:09:19,830 --> 00:09:23,460 doing interesting work, they can explain 206 00:09:21,510 --> 00:09:26,070 stuff pretty well." And they only read the 207 00:09:23,460 --> 00:09:28,620 section headings! That could happen, 208 00:09:26,070 --> 00:09:31,020 and that would be a good thing. 209 00:09:28,620 --> 00:09:32,850 You may need to add more material. 210 00:09:31,020 --> 00:09:34,830 If you don't actually define 211 00:09:32,850 --> 00:09:39,510 your fundamental object, you should. 212 00:09:34,830 --> 00:09:41,130 Some of you may have 213 00:09:39,510 --> 00:09:43,200 received mistaken advice from someone 214 00:09:41,130 --> 00:09:46,020 like your advisor, who says "just write it 215 00:09:43,200 --> 00:09:48,180 for the experts." That's bad advice, 216 00:09:46,020 --> 00:09:50,520 but there's a grain of truth. 217 00:09:48,180 --> 00:09:52,830 The grain of truth is: the advisor and other 218 00:09:50,520 --> 00:09:55,590 big shots in that area don't want to read 219 00:09:52,830 --> 00:09:56,190 historical background, or context, and 220 00:09:55,590 --> 00:09:58,560 stuff like that. 221 00:09:56,190 --> 00:10:00,870 Well, what will they do when they get to 222 00:09:58,560 --> 00:10:04,410 the section called 'historical context'? 223 00:10:00,870 --> 00:10:05,760 They'll skip it. If that's not my area, 224 00:10:04,410 --> 00:10:07,560 I'll read that and I'll find it 225 00:10:05,760 --> 00:10:09,770 interesting. But when I get to a thing 226 00:10:07,560 --> 00:10:13,080 called technical details, I'll skip it. 227 00:10:09,770 --> 00:10:15,360 A good research statement is not read in 228 00:10:13,080 --> 00:10:17,520 entirety by anyone, because there's no 229 00:10:15,360 --> 00:10:19,200 person on earth who actually wants to 230 00:10:17,520 --> 00:10:21,000 read the whole thing. On the other hand, 231 00:10:19,200 --> 00:10:23,190 you can make everybody happy when they 232 00:10:21,000 --> 00:10:25,200 read it, because everybody can easily 233 00:10:23,190 --> 00:10:28,770 navigate to exactly what they want to 234 00:10:25,200 --> 00:10:30,990 get out of it. That's how I would 235 00:10:28,770 --> 00:10:33,030 propose you to think about restructuring 236 00:10:30,990 --> 00:10:35,820 your statement. You will need to add some 237 00:10:33,030 --> 00:10:37,350 background and context. If you work in 238 00:10:35,820 --> 00:10:39,000 multiple areas you may need to 239 00:10:37,350 --> 00:10:41,490 separately introduce things several times. 240 00:10:39,000 --> 00:10:43,500 If you have a paragraph 241 00:10:41,490 --> 00:10:45,570 which starts about your result 242 00:10:43,500 --> 00:10:47,520 and then starts talking about other work, 243 00:10:45,570 --> 00:10:49,470 well that should be a section break, 244 00:10:47,520 --> 00:10:51,300 not just stuck in the middle of a paragraph. 245 00:10:49,470 --> 00:10:54,510 Basor: Just to add to what David said, 246 00:10:51,300 --> 00:10:56,850 people that are perhaps 247 00:10:54,510 --> 00:10:59,430 not in your area that are reading it, 248 00:10:56,850 --> 00:11:01,529 may only read that very beginning, 249 00:10:59,430 --> 00:11:05,100 the introduction, because after that they 250 00:11:01,529 --> 00:11:08,300 won't understand things. So as David said, 251 00:11:05,100 --> 00:11:11,790 if you can section that out, 252 00:11:08,300 --> 00:11:13,380 it's helpful to them. I also don't 253 00:11:11,790 --> 00:11:15,899 think these things should be overly long. 254 00:11:13,380 --> 00:11:17,430 You're not writing a grant proposal. 255 00:11:15,899 --> 00:11:22,130 You're just writing a research proposal, 256 00:11:17,430 --> 00:11:24,959 I mean a research statement. 257 00:11:22,130 --> 00:11:28,440 Again, just think about the 258 00:11:24,959 --> 00:11:30,300 people reading this. They're going to have a 259 00:11:28,440 --> 00:11:33,029 lot of these to read. They don't 260 00:11:30,300 --> 00:11:34,949 want to read overly long technical ones. 261 00:11:33,029 --> 00:11:37,139 I'm not saying there shouldn't be 262 00:11:34,949 --> 00:11:42,060 anything technical in it. I'm just saying 263 00:11:37,139 --> 00:11:47,790 it should not be too too long. 264 00:11:42,060 --> 00:11:50,850 If you are in double digits, that's too long. 265 00:11:47,790 --> 00:11:53,940 If you can keep it to 5 or 6 pages, it's better. 266 00:11:50,850 --> 00:11:55,680 Farmer: Some of you are 267 00:11:53,940 --> 00:11:57,899 getting to the point where you're going to 268 00:11:55,680 --> 00:11:59,910 have to jettison your first results. 269 00:11:57,899 --> 00:12:02,550 You've done more recent things and a few 270 00:11:59,910 --> 00:12:04,230 years have gone by. It's not "my whole 271 00:12:02,550 --> 00:12:07,079 history of research". It's what you're up 272 00:12:04,230 --> 00:12:10,290 to now, so some of you can cut out 273 00:12:07,079 --> 00:12:11,430 or relegate them to something small. 274 00:12:10,290 --> 00:12:13,259 Let me make a comment about the 275 00:12:11,430 --> 00:12:17,750 similarities between proposals and 276 00:12:13,259 --> 00:12:20,819 research summaries. Don't go looking for 277 00:12:17,750 --> 00:12:23,910 successful research proposals as a model 278 00:12:20,819 --> 00:12:26,550 for your own research proposals. 279 00:12:23,910 --> 00:12:30,120 They are a persuasive document. If you're a 280 00:12:26,550 --> 00:12:32,610 big shot, a poorly written proposal, with 281 00:12:30,120 --> 00:12:34,170 no context and no explanation, that merely lists 282 00:12:32,610 --> 00:12:37,620 what you're planning to work on, 283 00:12:34,170 --> 00:12:41,399 is completely persuasive to the panel. 284 00:12:37,620 --> 00:12:44,220 But that's not a model you should use. 285 00:12:41,399 --> 00:12:45,480 I don't know if the 286 00:12:44,220 --> 00:12:47,579 same advice applies to research summaries. 287 00:12:45,480 --> 00:12:49,110 People don't usually 288 00:12:47,579 --> 00:12:50,819 ask to view other people's 289 00:12:49,110 --> 00:12:53,310 research summaries. You often ask to see 290 00:12:50,819 --> 00:12:55,019 other people's proposals. If it's a big 291 00:12:53,310 --> 00:12:56,790 shot who received funding for years, 292 00:12:55,019 --> 00:12:59,699 that's an indication that they maybe 293 00:12:56,790 --> 00:13:01,439 don't write good proposals, because they 294 00:12:59,699 --> 00:13:04,589 don't need to, because they're so good at 295 00:13:01,439 --> 00:13:06,190 research. So don't go looking for 296 00:13:04,589 --> 00:13:07,660 models like that. 297 00:13:06,190 --> 00:13:11,160 But the advice we're giving you here 298 00:13:07,660 --> 00:13:13,870 definitely applies to your NSF proposal. 299 00:13:11,160 --> 00:13:17,200 There's a big difference between 300 00:13:13,870 --> 00:13:20,110 someone who's given a problem by their 301 00:13:17,200 --> 00:13:22,180 adviser and solves it, versus someone who 302 00:13:20,110 --> 00:13:24,550 actually understood why is that a good problem, 303 00:13:22,180 --> 00:13:26,380 what does it lead to, 304 00:13:24,550 --> 00:13:28,330 what are other people doing. You want to be 305 00:13:26,380 --> 00:13:31,110 the person who actually understands why 306 00:13:28,330 --> 00:13:34,750 you did it. Especially at a 307 00:13:31,110 --> 00:13:38,530 liberal arts college, a place with a big 308 00:13:34,750 --> 00:13:40,360 variety of faculty, being able to share 309 00:13:38,530 --> 00:13:41,830 perspectives and explain why your work 310 00:13:40,360 --> 00:13:43,810 is interesting. It's good it's 311 00:13:41,830 --> 00:13:46,270 interesting to you, but it does require 312 00:13:43,810 --> 00:13:50,230 explanation to other people for why they 313 00:13:46,270 --> 00:13:52,000 should find it interesting. 314 00:13:50,230 --> 00:13:55,840 You will reference other things. If you are 315 00:13:52,000 --> 00:13:58,810 talking about context and prior results, you can 316 00:13:55,840 --> 00:13:59,760 have the references to those, and we 317 00:13:58,810 --> 00:14:04,450 weren't including the references 318 00:13:59,760 --> 00:14:07,390 necessarily in the page count. 319 00:14:04,450 --> 00:14:09,100 You need a technical part, but that can 320 00:14:07,390 --> 00:14:11,860 be done in a way that the people in that 321 00:14:09,100 --> 00:14:13,150 area see that that's what they want to 322 00:14:11,860 --> 00:14:17,230 pay attention to, and the people outside 323 00:14:13,150 --> 00:14:19,210 that area see they can skip it. 324 00:14:17,230 --> 00:14:22,180 Basor: In my mind I was thinking 325 00:14:19,210 --> 00:14:25,720 about a half page. 326 00:14:22,180 --> 00:14:27,610 Farmer: If you work in multiple areas, 327 00:14:25,720 --> 00:14:29,980 such that the people in that area think of it 328 00:14:27,610 --> 00:14:33,310 as multiple different things, you might 329 00:14:29,980 --> 00:14:35,950 have a short introduction and then you 330 00:14:33,310 --> 00:14:38,530 might have short things later. 331 00:14:35,950 --> 00:14:40,720 So the one page the non-experts read 332 00:14:38,530 --> 00:14:43,420 might not be literally the first 333 00:14:40,720 --> 00:14:45,610 physical page. They might skip around, 334 00:14:43,420 --> 00:14:47,890 and good section headings, appropriate use of 335 00:14:45,610 --> 00:14:51,490 bold and small caps, can help that happen. 336 00:14:47,890 --> 00:14:54,370 Basor: I think it's really good to have 337 00:14:51,490 --> 00:14:55,660 different areas. I mean, if you 338 00:14:54,370 --> 00:14:57,340 have interests in those areas and you've 339 00:14:55,660 --> 00:14:59,440 done work in them. I think you can 340 00:14:57,340 --> 00:15:03,220 section those, as David says. 341 00:14:59,440 --> 00:15:06,130 You can section on the different areas and maybe 342 00:15:03,220 --> 00:15:08,050 the more technical part and, as David 343 00:15:06,130 --> 00:15:10,840 just said, you could also have a little 344 00:15:08,050 --> 00:15:13,810 bit of context in front of each of those areas, 345 00:15:10,840 --> 00:15:16,740 to put those in some sort of bigger picture. 346 00:15:13,810 --> 00:15:19,340 And then at the beginning 347 00:15:16,740 --> 00:15:21,920 you can have a broader statement 348 00:15:19,340 --> 00:15:23,810 that talks about your interests, 349 00:15:21,920 --> 00:15:28,040 as long as there's some sort of 350 00:15:23,810 --> 00:15:30,440 overlap or however they fit together. 351 00:15:28,040 --> 00:15:32,330 You can say you are interested 352 00:15:30,440 --> 00:15:36,920 in the broader field of something, 353 00:15:32,330 --> 00:15:38,930 and with applications to 354 00:15:36,920 --> 00:15:41,570 something something something, 355 00:15:38,930 --> 00:15:45,860 and I've worked in all of these areas. 356 00:15:41,570 --> 00:15:48,290 But at some point you want to 357 00:15:45,860 --> 00:15:50,380 make sure that, by the time someone is 358 00:15:48,290 --> 00:15:54,710 done reading whatever part of this they 359 00:15:50,380 --> 00:15:59,540 they've read, they understand that 360 00:15:54,710 --> 00:16:01,760 you understand how your mathematics fits 361 00:15:59,540 --> 00:16:06,950 into the bigger picture of mathematics, 362 00:16:01,760 --> 00:16:09,410 to historical problems of mathematics, 363 00:16:06,950 --> 00:16:11,450 to important problems of mathematics, 364 00:16:09,410 --> 00:16:14,770 to the timeliness of those problems. 365 00:16:11,450 --> 00:16:17,900 If you can get that across, that's really good. 367 00:16:17,900 --> 00:16:24,710 You definitely want to talk 368 00:16:22,370 --> 00:16:27,110 about both things, so you need to 369 00:16:24,710 --> 00:16:31,520 establish that you've done interesting work. 370 00:16:27,110 --> 00:16:33,070 That word 'interesting' is interesting! 372 00:16:33,070 --> 00:16:39,110 Don't say "my work is interesting", 373 00:16:35,540 --> 00:16:42,380 because it's not. It's interesting to you. 374 00:16:39,110 --> 00:16:44,840 It is okay, but on the edge, to say 375 00:16:42,380 --> 00:16:46,430 "this is interesting because...". 376 00:16:44,840 --> 00:16:48,950 But to announce that your work is interesting, 377 00:16:46,430 --> 00:16:50,660 it automatically invites the reader to 378 00:16:48,950 --> 00:16:52,130 say that by comparison, 379 00:16:50,660 --> 00:16:53,780 you must think your work is more 380 00:16:52,130 --> 00:16:55,640 interesting than others. So at best 381 00:16:53,780 --> 00:16:59,090 you're work is interesting to you, 382 00:16:55,640 --> 00:17:01,340 and my work is interesting to me. 383 00:16:59,090 --> 00:17:03,440 Interesting work is work that other 384 00:17:01,340 --> 00:17:05,270 people find interesting, so you need to 385 00:17:03,440 --> 00:17:07,640 establish credibility that you've done 386 00:17:05,270 --> 00:17:10,130 good work. But if you don't have a 387 00:17:07,640 --> 00:17:15,670 trajectory with clear plans that are 388 00:17:10,130 --> 00:17:18,770 likely to result in new theorems 389 00:17:15,670 --> 00:17:23,209 or get funding, you have to have both. 390 00:17:18,770 --> 00:17:25,310 What I alluded to before is you 391 00:17:23,209 --> 00:17:27,470 may want to not mention your oldest 392 00:17:25,310 --> 00:17:28,970 results, but definitely you want to 393 00:17:27,470 --> 00:17:30,169 mention your most interesting results, 394 00:17:28,970 --> 00:17:33,200 which hopefully are your more recent ones. 395 00:17:30,169 --> 00:17:36,590 It's not a pick and choose: 396 00:17:33,200 --> 00:17:38,419 you need both. 397 00:17:36,590 --> 00:17:40,070 If you study L-functions, 398 00:17:38,419 --> 00:17:42,289 L-functions are studied for many things. 399 00:17:40,070 --> 00:17:44,029 Someone who's research is in p-adic 400 00:17:42,289 --> 00:17:46,340 L-functions would have a very different 401 00:17:44,029 --> 00:17:48,639 introduction to someone who studies the 402 00:17:46,340 --> 00:17:51,109 L-functions of Siegel modular forms. 403 00:17:48,639 --> 00:17:53,149 They are still both introductions 404 00:17:51,109 --> 00:17:55,070 about L-functions, but because 405 00:17:53,149 --> 00:17:57,169 there is a particular target they're 406 00:17:55,070 --> 00:18:01,190 heading toward, they would have 407 00:17:57,169 --> 00:18:03,950 vastly different introductions. 408 00:18:01,190 --> 00:18:05,749 In one case, it might be about 409 00:18:03,950 --> 00:18:07,190 sum 1/n^2 equals pi^2/6 410 00:18:05,749 --> 00:18:09,139 as an example of a special value, 411 00:18:07,190 --> 00:18:12,139 which leads to p-adic L-functions. 412 00:18:09,139 --> 00:18:14,179 Another might be about Dirichlet L-functions 413 00:18:12,139 --> 00:18:16,489 and primes in arithmetic progressions. 414 00:18:14,179 --> 00:18:18,859 There could be almost no overlap in the 415 00:18:16,489 --> 00:18:21,590 introduction to L-functions in those 416 00:18:18,859 --> 00:18:25,899 two research statements. 417 00:18:21,590 --> 00:18:29,869 Basor: It doesn't have to be overly long 418 00:18:25,899 --> 00:18:33,470 or over overly simplified. 419 00:18:29,869 --> 00:18:37,269 It could start off with: several years ago 420 00:18:33,470 --> 00:18:41,029 so-and-so investigated the question of 421 00:18:37,269 --> 00:18:45,019 some invariant in topology. 422 00:18:41,029 --> 00:18:47,359 (I'm just making this up.) 423 00:18:45,019 --> 00:18:49,909 The research I'm doing is a part of that, 424 00:18:47,359 --> 00:18:52,970 and it fits in in this particular way. 425 00:18:49,909 --> 00:18:56,210 Something along those lines. 426 00:18:52,970 --> 00:18:58,999 If you can somehow say why that is important, 427 00:18:56,210 --> 00:19:01,429 I mean, why you think it's important. 428 00:18:58,999 --> 00:19:03,080 Something where someone can get a picture 429 00:19:01,429 --> 00:19:09,649 in the beginning of what you're trying to do. 430 00:19:03,080 --> 00:19:14,509 We've been on lots of proposal panels, 431 00:19:09,649 --> 00:19:18,230 and if I have a first page where I can understand, 433 00:19:18,230 --> 00:19:23,149 I'm very grateful for that when I'm reading these things. 434 00:19:23,149 --> 00:19:27,470 These are proposals that are supposed 436 00:19:24,889 --> 00:19:29,509 to be in my area, but still, they can be so 437 00:19:27,470 --> 00:19:31,700 muddled that you don't know where people 438 00:19:29,509 --> 00:19:33,429 are heading in the beginning. 439 00:19:31,700 --> 00:19:37,609 So if it can be clear in the beginning and you 440 00:19:33,429 --> 00:19:39,590 can say things pretty simply, it's very 441 00:19:37,609 --> 00:19:42,139 very helpful to the person reading it. 442 00:19:39,590 --> 00:19:44,080 It just it sort of grounds them so that 443 00:19:42,139 --> 00:19:47,090 they can read the rest of it. 445 00:19:47,090 --> 00:19:53,180 I'm contradicting myself right now, 446 00:19:49,700 --> 00:19:57,020 but don't worry about it being too easy. 448 00:19:57,020 --> 00:20:03,140 People usually make these things too hard, too technical. 449 00:19:59,210 --> 00:20:05,650 Farmer: You're going to need help from 450 00:20:03,140 --> 00:20:09,080 other people. You are going to need 451 00:20:05,650 --> 00:20:11,570 experts in the field, and non-experts, 452 00:20:09,080 --> 00:20:14,450 to read and offer you feedback. 453 00:20:11,570 --> 00:20:16,340 You want to not use everybody at once: 454 00:20:14,450 --> 00:20:21,110 get an expert or non expert to read it. Revise. 455 00:20:16,340 --> 00:20:24,080 Then get fresh eyes to look at it. 456 00:20:21,110 --> 00:20:25,970 It couldn't hurt to tell them the context 457 00:20:24,080 --> 00:20:29,900 in which this will be read. Like: 458 00:20:25,970 --> 00:20:32,330 "I'm using this as application material 459 00:20:29,900 --> 00:20:34,010 at an R1 school, what do you think?" 460 00:20:32,330 --> 00:20:35,630 Or, "I'm applying to a liberal arts college 461 00:20:34,010 --> 00:20:38,510 and they asked for research statement, 462 00:20:35,630 --> 00:20:39,770 what do you think?" 463 00:20:38,510 --> 00:20:43,040 You may need two versions, 464 00:20:39,770 --> 00:20:44,780 maybe two versions of everything: a cover letter for a research place or a primarily teaching place. A research statement in two versions.