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One answer is that it is certainly not always a waste of time to apply for a job even if you don't think that you fit the ad. It's easy to just keep copying your application, even trivial in MathJobs. Moreover, you should take the details of ads with a grain of salt. The semantics of research areas are often based on internal department politics. Who knows what they really mean if they say that they want to hire in "mathematical physics" or "geometry", etc. Even the advertised level of seniority is sometimes negotiable.

Another answer is that, for the sake of your sanity, you should have a "Plan B" if you want a tenure-track research job in mathematics. It is not so difficult to major in mathematics, but after that the available positions from graduate school, to postdocs, to tenure-track research positions are a severe pyramid at every stage. Then, two-body problems can make things even more difficult. The two basic choices for a Plan B are industry and teaching, and you have to decide which one is more livable for you.

In my case, it would have been industry. It is true that it takes new skills to have a career in industry, almost always involving computer programming, and sometimes also statistics and applied math. But it is not necessarily all that formidable. If you can get past the personnel office, many managers realize that mathematicians are fairly adaptable to new skills.

Likewise, teaching is not necessarily all that limiting; many people with teaching positions find ways to have good access to the research community. A few even get good research positions at a later stage. But if "Dr. H" is not at peace with this type of "Plan B", then maybe he should consider the other type.

For both answers, my experience is in the United States. That said, an important answer for all countries is to expand your geographical range as much as possible. Going by the obvious statistical calculation, it can make a huge difference. When my wife and I were on the job market, we applied all over the US. Although we're happy where we are, we could have given more consideration to the rest of the English-speaking world, certainly Canada but also even places like Singapore.

Also, since the question seemed to steer away from it, I didn't say anything above about the mechanics of "obvious" methods. However, here is one thought that may not be so obvious. There are more effective and less effective methods for getting visibility as a research mathematician, and for that purpose the Web is a new world. It makes a big difference if someone on the search committee knows your name before they see your application. Of course, it's obvious to just try to "be visible" by writing papers, giving talks, and meeting people. What's not so obvious is that it can help a lot if you make effective but judicious use of new tools: A good home page, the arXiv, and now MathOverflow. Of course you shouldn't semi-spam the arXiv or MathOverflow --- that will lead to bad consequences. But if you use them properly, they can be more effective, and differently effective, than giving talks at this or that meeting. By contrast, e-mail during job season is one of the more obvious steps, and I have to say that that tactic is overused.

One answer is that it is certainly not always a waste of time to apply for a job even if you don't think that you fit the ad. It's easy to just keep copying your application, even trivial in MathJobs. Moreover, you should take the details of ads with a grain of salt. The semantics of research areas are often based on internal department politics. Who knows what they really mean if they say that they want to hire in "mathematical physics" or "geometry", etc. Even the advertised level of seniority is sometimes negotiable not an obstruction, because the department can consider workarounds such as early promotion. (Corrected at fedja's suggestion; I didn't mean that it was "negotiable" in the direct sense.)

Another answer is that, for the sake of your sanity, you should have a "Plan B" if you want a tenure-track research job in mathematics. It is not so difficult to major in mathematics, but after that the available positions from graduate school, to postdocs, to tenure-track research positions are a severe pyramid at every stage. Then, two-body problems can make things even more difficult. The two basic choices for a Plan B are industry and teaching, and you have to decide which one is more livable for you.

In my case, it would have been industry. It is true that it takes new skills to have a career in industry, almost always involving computer programming, and sometimes also statistics and applied math. But it is not necessarily all that formidable. If you can get past the personnel office, many managers realize that mathematicians are fairly adaptable to new skills.

Likewise, teaching is not necessarily all that limiting; many people with teaching positions find ways to have good access to the research community. A few even get good research positions at a later stage. But if "Dr. H" is not at peace with this type of "Plan B", then maybe he should consider the other type.

For both answers, my experience is in the United States. That said, an important answer for all countries is to expand your geographical range as much as possible. Going by the obvious statistical calculation, it can make a huge difference. When my wife and I were on the job market, we applied all over the US. Although we're happy where we are, we could have given more consideration to the rest of the English-speaking world, certainly Canada but also even places like Singapore.

Also, since the question seemed to steer away from it, I didn't say anything above about the mechanics of "obvious" methods. However, here is one thought that may not be so obvious. There are more effective and less effective methods for getting visibility as a research mathematician, and for that purpose the Web is a new world. It makes a big difference if someone on the search committee knows your name before they see your application. Of course, it's obvious to just try to "be visible" by writing papers, giving talks, and meeting people. What's not so obvious is that it can help a lot if you make effective but judicious use of new tools: A good home page, the arXiv, and now MathOverflow. Of course you shouldn't semi-spam the arXiv or MathOverflow --- that will lead to bad consequences. But if you use them properly, they can be more effective, and differently effective, than giving talks at this or that meeting. By contrast, e-mail during job season is one of the more obvious steps, and I have to say that that tactic is overused.

One answer is that it is certainly not always a waste of time to apply for a job even if you don't think that you fit the ad. It's easy to just keep copying your application, even trivial in MathJobs. Moreover, you should take the details of ads with a grain of salt. The semantics of research areas are often based on internal department politics. Who knows what they really mean if they say that they want to hire in "mathematical physics" or "geometry", etc. Even the advertised level of seniority is sometimes negotiable.

Another answer is that, for the sake of your sanity, you should have a "Plan B" if you want a tenure-track research job in mathematics. It is not so difficult to major in mathematics, but after that the available positions from graduate school, to postdocs, to tenure-track research positions are a severe pyramid at every stage. Then, two-body problems can make things even more difficult. The two basic choices for a Plan B are industry and teaching, and you have to decide which one is more livable for you.

In my case, it would have been industry. It is true that it takes new skills to have a career in industry, almost always involving computer programming, and sometimes also statistics and applied math. But it is not necessarily all that formidable. If you can get past the personnel office, many managers realize that mathematicians are fairly adaptable to new skills.

Likewise, teaching is not necessarily all that limiting; many people with teaching positions find ways to have good access to the research community. A few even get good research positions at a later stage. But if "Dr. H" is not at peace with this type of "Plan B", then maybe he should consider the other type.

For both answers, my experience is in the United States. That said, an important answer for all countries is to expand your geographical range as much as possible. Going by the obvious statistical calculation, it can make a huge difference. When my wife and I were on the job market, we applied all over the US. Although we're happy where we are, we could have given more consideration to the rest of the English-speaking world, certainly Canada but also even places like Singapore.

One answer is that it is certainly not always a waste of time to apply for a job even if you don't think that you fit the ad. It's easy to just keep copying your application, even trivial in MathJobs. Moreover, you should take the details of ads with a grain of salt. The semantics of research areas are often based on internal department politics. Who knows what they really mean if they say that they want to hire in "mathematical physics" or "geometry", etc. Even the advertised level of seniority is sometimes negotiable.

Another answer is that, for the sake of your sanity, you should have a "Plan B" if you want a tenure-track research job in mathematics. It is not so difficult to major in mathematics, but after that the available positions from graduate school, to postdocs, to tenure-track research positions are a severe pyramid at every stage. Then, two-body problems can make things even more difficult. The two basic choices for a Plan B are industry and teaching, and you have to decide which one is more livable for you.

In my case, it would have been industry. It is true that it takes new skills to have a career in industry, almost always involving computer programming, and sometimes also statistics and applied math. But it is not necessarily all that formidable. If you can get past the personnel office, many managers realize that mathematicians are fairly adaptable to new skills.

Likewise, teaching is not necessarily all that limiting; many people with teaching positions find ways to have good access to the research community. A few even get good research positions at a later stage. But if "Dr. H" is not at peace with this type of "Plan B", then maybe he should consider the other type.

For both answers, my experience is in the United States. That said, an important answer for all countries is to expand your geographical range as much as possible. Going by the obvious statistical calculation, it can make a huge difference. When my wife and I were on the job market, we applied all over the US. Although we're happy where we are, we could have given more consideration to the rest of the English-speaking world, certainly Canada but also even places like Singapore.

Also, since the question seemed to steer away from it, I didn't say anything above about the mechanics of "obvious" methods. However, here is one thought that may not be so obvious. There are more effective and less effective methods for getting visibility as a research mathematician, and for that purpose the Web is a new world. It makes a big difference if someone on the search committee knows your name before they see your application. Of course, it's obvious to just try to "be visible" by writing papers, giving talks, and meeting people. What's not so obvious is that it can help a lot if you make effective but judicious use of new tools: A good home page, the arXiv, and now MathOverflow. Of course you shouldn't semi-spam the arXiv or MathOverflow --- that will lead to bad consequences. But if you use them properly, they can be more effective, and differently effective, than giving talks at this or that meeting. By contrast, e-mail during job season is one of the more obvious steps, and I have to say that that tactic is overused.

One answer is that it is certainly not always a waste of time to apply for a job even if you don't think that you fit the ad. It's easy to just keep copying your application, even trivial in MathJobs. Moreover, you should take the details of ads with a grain of salt. The semantics of research areas are often based on internal department politics. Who knows what they really mean if they say that they want to hire in "mathematical physics" or "geometry", etc. Even the advertised level of seniority is sometimes negotiable.

Another answer is that, for the sake of your sanity, you should have a "Plan B" if you want a tenure-track research job in mathematics. The set of available positions from math majors, to graduate school, to postdocs, to tenure-track research positions is a severe pyramid at every stage. Then, two-body problems can make things even more difficult. The two basic choices for a Plan B are industry and teaching, and you have to decide which one is more livable for you.

In my case, it would have been industry. It is true that it takes new skills to have a career in industry, some combination of training especially in computer programming, and sometimes also statistics and applied math. But it is not necessarily all that formidable. If you can get past the personnel office, many managers realize that mathematicians are fairly adaptable to new skills.

Likewise, teaching is not necessarily all that limiting; many people with teaching positions find ways to have good access to the research community. Some go on to get good research positions at a later stage. But if "Dr. H" is not at peace with this type of "Plan B", then maybe he should consider the other type.

For both answers, my experience is in the United States. That said, an important answer for all countries is to expand your geographical range as much as possible. Just as a matter of basic statistics, it can make a huge difference. When my wife and I were on the job market, we applied all over the US. Although we're happy where we are, we could have given more consideration to the rest of the English-speaking world, certainly Canada but also even places like Singapore.

One answer is that it is certainly not always a waste of time to apply for a job even if you don't think that you fit the ad. It's easy to just keep copying your application, even trivial in MathJobs. Moreover, you should take the details of ads with a grain of salt. The semantics of research areas are often based on internal department politics. Who knows what they really mean if they say that they want to hire in "mathematical physics" or "geometry", etc. Even the advertised level of seniority is sometimes negotiable.

Another answer is that, for the sake of your sanity, you should have a "Plan B" if you want a tenure-track research job in mathematics. It is not so difficult to major in mathematics, but after that the available positions from graduate school, to postdocs, to tenure-track research positions are a severe pyramid at every stage. Then, two-body problems can make things even more difficult. The two basic choices for a Plan B are industry and teaching, and you have to decide which one is more livable for you.

In my case, it would have been industry. It is true that it takes new skills to have a career in industry, almost always involving computer programming, and sometimes also statistics and applied math. But it is not necessarily all that formidable. If you can get past the personnel office, many managers realize that mathematicians are fairly adaptable to new skills.

Likewise, teaching is not necessarily all that limiting; many people with teaching positions find ways to have good access to the research community. A few even get good research positions at a later stage. But if "Dr. H" is not at peace with this type of "Plan B", then maybe he should consider the other type.

For both answers, my experience is in the United States. That said, an important answer for all countries is to expand your geographical range as much as possible. Going by the obvious statistical calculation, it can make a huge difference. When my wife and I were on the job market, we applied all over the US. Although we're happy where we are, we could have given more consideration to the rest of the English-speaking world, certainly Canada but also even places like Singapore.